{"task_id": "HumanEval/0", "entry_point": "has_close_elements", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 291, "latency_s": 89.68, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem efficiently, we can sort the list of numbers first. Once sorted, the two closest numbers must be adjacent to each other in the sorted sequence. This reduces the time complexity from $O(n^2)$ (checking every pair) to $O(n \\log n)$ (due to sorting).\n\n```python\nfrom typing import List\n\ndef has_close_elements(numbers: List[float], threshold: float) -> bool:\n    \"\"\" Check if in given list of numbers, are any two numbers closer to each other than\n    given threshold.\n    >>> has_close_elements([1.0, 2.0, 3.0], 0.5)\n    False\n    >>> has_close_elements([1.0, 2.8, 3.0, 4.0, 5.0, 2.0], 0.3)\n    True\n    \"\"\"\n    # Sort the numbers to ensure that the closest elements are adjacent\n    sorted_numbers = sorted(numbers)\n    \n    # Iterate through the sorted list and check the difference between adjacent elements\n    for i in range(len(sorted_numbers) - 1):\n        if sorted_numbers[i+1] - sorted_numbers[i] < threshold:\n            return True\n            \n    return False\n```"}
{"task_id": "HumanEval/1", "entry_point": "separate_paren_groups", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 460, "latency_s": 94.9, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through the string while keeping track of the \"nesting level\" (the balance of open and closed parentheses). \n\n1.  **Preprocessing**: First, remove all spaces from the input string.\n2.  **Tracking Balance**: Maintain a counter `balance`. Increment it for every `(` and decrement it for every `)`.\n3.  **Identifying Groups**: A complete group is finished when the `balance` returns to zero after being greater than zero.\n4.  **Extraction**: Every time the balance hits zero (and we have processed at least one character), the substring accumulated since the last zero-point is a complete group.\n\nComplexity:\n- Time: $O(n)$ where $n$ is the length of the string, as we traverse the string once.\n- Space: $O(n)$ to store the resulting list of strings.\n\n```python\nfrom typing import List\n\ndef separate_paren_groups(paren_string: str) -> List[str]:\n    \"\"\" Input to this function is a string containing multiple groups of nested parentheses. Your goal is to\n    separate those group into separate strings and return the list of those.\n    Separate groups are balanced (each open brace is properly closed) and not nested within each other\n    Ignore any spaces in the input string.\n    >>> separate_paren_groups('( ) (( )) (( )( ))')\n    ['()', '(())', '(()())']\n    \"\"\"\n    # Remove all spaces from the input string\n    s = paren_string.replace(\" \", \"\")\n    \n    result = []\n    current_group = []\n    balance = 0\n    \n    for char in s:\n        current_group.append(char)\n        if char == '(':\n            balance += 1\n        elif char == ')':\n            balance -= 1\n        \n        # When balance reaches 0, it means a top-level group has closed\n        if balance == 0 and current_group:\n            result.append(\"\".join(current_group))\n            current_group = []\n            \n    return result\n```"}
{"task_id": "HumanEval/2", "entry_point": "truncate_number", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 160, "latency_s": 82.81, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To extract the decimal part of a floating-point number, we subtract the integer part (the floor of the number) from the original number. Using `math.floor` ensures that the integer part is correctly identified as the largest integer smaller than or equal to the given number.\n\n```python\nimport math\n\ndef truncate_number(number: float) -> float:\n    \"\"\" Given a positive floating point number, it can be decomposed into\n    an integer part (largest integer smaller than given number) and decimals\n    (leftover part always smaller than 1).\n\n    Return the decimal part of the number.\n    >>> truncate_number(3.5)\n    0.5\n    \"\"\"\n    return number - math.floor(number)\n```"}
{"task_id": "HumanEval/3", "entry_point": "below_zero", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 310, "latency_s": 86.36, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through the list of operations while maintaining a running total of the balance. Since the account starts at zero, we initialize a variable `balance` to 0. For each operation in the list, we add its value to the `balance`. If at any step the `balance` becomes negative (less than 0), we immediately return `True`. If we finish iterating through all operations without the balance ever dropping below zero, we return `False`.\n\nComplexity:\n- Time Complexity: O(n), where n is the number of operations, as we iterate through the list once.\n- Space Complexity: O(1), as we only store a single integer for the balance.\n\n```python\nfrom typing import List\n\ndef below_zero(operations: List[int]) -> bool:\n    \"\"\" You're given a list of deposit and withdrawal operations on a bank account that starts with\n    zero balance. Your task is to detect if at any point the balance of account fallls below zero, and\n    at that point function should return True. Otherwise it should return False.\n    >>> below_zero([1, 2, 3])\n    False\n    >>> below_zero([1, 2, -4, 5])\n    True\n    \"\"\"\n    balance = 0\n    for op in operations:\n        balance += op\n        if balance < 0:\n            return True\n    return False\n```"}
{"task_id": "HumanEval/4", "entry_point": "mean_absolute_deviation", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 368, "latency_s": 16.21, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To calculate the Mean Absolute Deviation (MAD), we first need to find the arithmetic mean of the dataset. Then, we calculate the absolute difference between each number and that mean. Finally, we return the average of those absolute differences.\n\nEdge cases to consider:\n1. An empty list: The mean is undefined, so we should handle this (though the prompt implies a valid dataset, standard behavior is to return 0.0 or raise an error; I will assume a non-empty list based on the docstring).\n2. A list with one element: The MAD will be 0.0.\n\nComplexity:\n- Time: O(n) where n is the number of elements (one pass for mean, one pass for deviations).\n- Space: O(1) if we calculate the sum of deviations in a generator/loop.\n\n```python\nfrom typing import List\n\ndef mean_absolute_deviation(numbers: List[float]) -> float:\n    \"\"\" For a given list of input numbers, calculate Mean Absolute Deviation\n    around the mean of this dataset.\n    Mean Absolute Deviation is the average absolute difference between each\n    element and a centerpoint (mean in this case):\n    MAD = average | x - x_mean |\n    >>> mean_absolute_deviation([1.0, 2.0, 3.0, 4.0])\n    1.0\n    \"\"\"\n    if not numbers:\n        return 0.0\n    \n    mean = sum(numbers) / len(numbers)\n    absolute_deviations = [abs(x - mean) for x in numbers]\n    mad = sum(absolute_deviations) / len(numbers)\n    \n    return mad\n```"}
{"task_id": "HumanEval/5", "entry_point": "intersperse", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 293, "latency_s": 15.99, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through the input list and insert the delimiter between every pair of adjacent elements. If the list is empty or has only one element, no delimiters should be added. A common approach is to build a new list, appending the current element and then appending the delimiter if the current element is not the last one in the input list.\n\nComplexity:\n- Time: O(n), where n is the length of the input list.\n- Space: O(n), to store the resulting list.\n\n```python\nfrom typing import List\n\ndef intersperse(numbers: List[int], delimeter: int) -> List[int]:\n    \"\"\" Insert a number 'delimeter' between every two consecutive elements of input list `numbers'\n    >>> intersperse([], 4)\n    []\n    >>> intersperse([1, 2, 3], 4)\n    [1, 4, 2, 4, 3]\n    \"\"\"\n    if not numbers:\n        return []\n    \n    result = []\n    for i in range(len(numbers)):\n        result.append(numbers[i])\n        # Append the delimiter if this is not the last element\n        if i < len(numbers) - 1:\n            result.append(delimeter)\n            \n    return result\n```"}
{"task_id": "HumanEval/6", "entry_point": "parse_nested_parens", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 399, "latency_s": 17.21, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to split the input string into individual groups based on spaces. For each group, we iterate through the characters to track the current depth of nesting. We increment a counter when we encounter an opening parenthesis `(` and decrement it when we encounter a closing parenthesis `)`. The maximum value reached by this counter during the traversal of a group represents the deepest level of nesting for that group.\n\nComplexity:\n- Time: O(N), where N is the total number of characters in the input string, as we visit each character once.\n- Space: O(M), where M is the number of groups, to store the result list.\n\n```python\nfrom typing import List\n\ndef parse_nested_parens(paren_string: str) -> List[int]:\n    \"\"\" Input to this function is a string represented multiple groups for nested parentheses separated by spaces.\n    For each of the group, output the deepest level of nesting of parentheses.\n    E.g. (()()) has maximum two levels of nesting while ((())) has three.\n\n    >>> parse_nested_parens('(()()) ((())) () ((())()())')\n    [2, 3, 1, 3]\n    \"\"\"\n    results = []\n    # Split the string into individual groups based on whitespace\n    groups = paren_string.split()\n    \n    for group in groups:\n        max_depth = 0\n        current_depth = 0\n        for char in group:\n            if char == '(':\n                current_depth += 1\n                # Update max_depth if current_depth exceeds it\n                if current_depth > max_depth:\n                    max_depth = current_depth\n            elif char == ')':\n                current_depth -= 1\n        results.append(max_depth)\n        \n    return results\n```"}
{"task_id": "HumanEval/7", "entry_point": "filter_by_substring", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 213, "latency_s": 14.43, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I will iterate through each string in the input list and use the `in` operator to check if the specified substring exists within that string. If it does, the string is included in the resulting list. This approach has a time complexity of O(n * m), where n is the number of strings and m is the average length of the strings, and a space complexity of O(k) where k is the number of matching strings.\n\n```python\nfrom typing import List\n\ndef filter_by_substring(strings: List[str], substring: str) -> List[str]:\n    \"\"\" Filter an input list of strings only for ones that contain given substring\n    >>> filter_by_substring([], 'a')\n    []\n    >>> filter_by_substring(['abc', 'bacd', 'cde', 'array'], 'a')\n    ['abc', 'bacd', 'array']\n    \"\"\"\n    return [s for s in strings if substring in s]\n```"}
{"task_id": "HumanEval/8", "entry_point": "sum_product", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 257, "latency_s": 13.19, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through the list of integers once. We initialize the sum to 0 and the product to 1, as specified for empty lists. During the iteration, we accumulate the sum by adding each number and the product by multiplying it by each number. This approach has a time complexity of O(n) and a space complexity of O(1).\n\n```python\nfrom typing import List, Tuple\n\ndef sum_product(numbers: List[int]) -> Tuple[int, int]:\n    \"\"\" For a given list of integers, return a tuple consisting of a sum and a product of all the integers in a list.\n    Empty sum should be equal to 0 and empty product should be equal to 1.\n    >>> sum_product([])\n    (0, 1)\n    >>> sum_product([1, 2, 3, 4])\n    (10, 24)\n    \"\"\"\n    total_sum = 0\n    total_product = 1\n    \n    for num in numbers:\n        total_sum += num\n        total_product *= num\n        \n    return (total_sum, total_product)\n```"}
{"task_id": "HumanEval/9", "entry_point": "rolling_max", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 281, "latency_s": 13.06, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through the input list while maintaining a variable that tracks the maximum value encountered so far. For each element in the list, we update the current maximum if the current element is larger, and then append that maximum to our result list.\n\nComplexity:\n- Time Complexity: O(n), where n is the length of the input list, as we iterate through the list once.\n- Space Complexity: O(n) to store the resulting list of maximums.\n\n```python\nfrom typing import List\n\ndef rolling_max(numbers: List[int]) -> List[int]:\n    \"\"\" From a given list of integers, generate a list of rolling maximum element found until given moment\n    in the sequence.\n    >>> rolling_max([1, 2, 3, 2, 3, 4, 2])\n    [1, 2, 3, 3, 3, 4, 4]\n    \"\"\"\n    if not numbers:\n        return []\n    \n    result = []\n    current_max = float('-inf')\n    \n    for num in numbers:\n        if num > current_max:\n            current_max = num\n        result.append(int(current_max))\n        \n    return result\n```"}
{"task_id": "HumanEval/10", "entry_point": "make_palindrome", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 423, "latency_s": 13.31, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to find the longest suffix of the input string that is already a palindrome. Once identified, the characters preceding this suffix must be reversed and appended to the end of the original string to form the shortest possible palindrome.\n\nFor example, in \"cata\", the longest palindromic suffix is \"ata\". The prefix before \"ata\" is \"c\". Reversing \"c\" gives \"c\", so we append it to get \"catac\".\n\nComplexity:\n- Time: $O(n^2)$ where $n$ is the length of the string (due to checking suffixes).\n- Space: $O(n)$ to store the resulting string.\n\n```python\ndef is_palindrome(string: str) -> bool:\n    \"\"\" Test if given string is a palindrome \"\"\"\n    return string == string[::-1]\n\n\ndef make_palindrome(string: str) -> str:\n    \"\"\" Find the shortest palindrome that begins with a supplied string.\n    Algorithm idea is simple:\n    - Find the longest postfix of supplied string that is a palindrome.\n    - Append to the end of the string reverse of a string prefix that comes before the palindromic suffix.\n    >>> make_palindrome('')\n    ''\n    >>> make_palindrome('cat')\n    'catac'\n    >>> make_palindrome('cata')\n    'catac'\n    \"\"\"\n    if not string:\n        return \"\"\n\n    # Iterate through the string to find the longest palindromic suffix\n    # We start from the beginning and check if the substring from i to the end is a palindrome\n    for i in range(len(string)):\n        suffix = string[i:]\n        if is_palindrome(suffix):\n            # The part before this suffix needs to be reversed and appended\n            prefix_to_reverse = string[:i]\n            return string + prefix_to_reverse[::-1]\n    \n    return string + string[:-1][::-1]\n```"}
{"task_id": "HumanEval/11", "entry_point": "string_xor", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 245, "latency_s": 13.68, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we iterate through the characters of both strings simultaneously. Since the strings are guaranteed to consist of '1's and '0's, we can compare the characters at each index. If the characters are different, the XOR result is '1'; if they are the same, the result is '0'. This is equivalent to the logical XOR operation.\n\n```python\nfrom typing import List\n\ndef string_xor(a: str, b: str) -> str:\n    \"\"\" Input are two strings a and b consisting only of 1s and 0s.\n    Perform binary XOR on these inputs and return result also as a string.\n    >>> string_xor('010', '110')\n    '100'\n    \"\"\"\n    result = []\n    # Assuming a and b are of the same length as per standard XOR operations\n    for char_a, char_b in zip(a, b):\n        if char_a != char_b:\n            result.append('1')\n        else:\n            result.append('0')\n    return \"\".join(result)\n```"}
{"task_id": "HumanEval/12", "entry_point": "longest", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 255, "latency_s": 13.64, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I will iterate through the list of strings and keep track of the longest string encountered so far. By using a strict \"greater than\" comparison (`len(current) > len(longest_so_far)`), I ensure that if two strings have the same length, the first one encountered is preserved. I will handle the empty list case by returning `None` immediately.\n\n```python\nfrom typing import List, Optional\n\ndef longest(strings: List[str]) -> Optional[str]:\n    \"\"\" Out of list of strings, return the longest one. Return the first one in case of multiple\n    strings of the same length. Return None in case the input list is empty.\n    >>> longest([])\n    None\n    >>> longest(['a', 'b', 'c'])\n    'a'\n    >>> longest(['a', 'bb', 'ccc'])\n    'ccc'\n    \"\"\"\n    if not strings:\n        return None\n    \n    longest_str = strings[0]\n    for s in strings[1:]:\n        if len(s) > len(longest_str):\n            longest_str = s\n            \n    return longest_str\n```"}
{"task_id": "HumanEval/13", "entry_point": "greatest_common_divisor", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 202, "latency_s": 12.76, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To find the greatest common divisor (GCD) of two integers, the most efficient and standard approach is the Euclidean Algorithm. This algorithm works by repeatedly replacing the larger number with the remainder of the division of the two numbers until one of them becomes zero. The non-zero number remaining is the GCD.\n\nComplexity:\n- Time: O(log(min(a, b)))\n- Space: O(1) (iterative approach)\n\n```python\ndef greatest_common_divisor(a: int, b: int) -> int:\n    \"\"\" Return a greatest common divisor of two integers a and b\n    >>> greatest_common_divisor(3, 5)\n    1\n    >>> greatest_common_divisor(25, 15)\n    5\n    \"\"\"\n    a, b = abs(a), abs(b)\n    while b:\n        a, b = b, a % b\n    return a\n```"}
{"task_id": "HumanEval/14", "entry_point": "all_prefixes", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 146, "latency_s": 9.65, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this, I will iterate through the string using a range from 1 to the length of the string (inclusive). For each index, I will slice the string from the beginning to that index and append it to a list. This ensures the prefixes are ordered from shortest to longest.\n\n```python\nfrom typing import List\n\ndef all_prefixes(string: str) -> List[str]:\n    \"\"\" Return list of all prefixes from shortest to longest of the input string\n    >>> all_prefixes('abc')\n    ['a', 'ab', 'abc']\n    \"\"\"\n    return [string[:i] for i in range(1, len(string) + 1)]\n```"}
{"task_id": "HumanEval/15", "entry_point": "string_sequence", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 171, "latency_s": 8.82, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this, I will iterate through the range from 0 to $n$ (inclusive), convert each integer to a string, and join them using a space as a delimiter.\n\nComplexity:\n- Time: $O(n)$ to iterate through the numbers.\n- Space: $O(n)$ to store the resulting string.\n\n```python\ndef string_sequence(n: int) -> str:\n    \"\"\" Return a string containing space-delimited numbers starting from 0 upto n inclusive.\n    >>> string_sequence(0)\n    '0'\n    >>> string_sequence(5)\n    '0 1 2 3 4 5'\n    \"\"\"\n    return \" \".join(str(i) for i in range(n + 1))\n```"}
{"task_id": "HumanEval/16", "entry_point": "count_distinct_characters", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 213, "latency_s": 8.33, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to count the number of unique characters in a string while ignoring case sensitivity. The most efficient way to do this is to convert the entire string to a single case (either lowercase or uppercase) and then use a `set` to store the characters. Since a set only stores unique elements, its length will represent the count of distinct characters.\n\nComplexity:\n- Time Complexity: O(n), where n is the length of the string, as we must iterate through the string once.\n- Space Complexity: O(k), where k is the number of unique characters stored in the set.\n\n```python\ndef count_distinct_characters(string: str) -> int:\n    \"\"\" Given a string, find out how many distinct characters (regardless of case) does it consist of\n    >>> count_distinct_characters('xyzXYZ')\n    3\n    >>> count_distinct_characters('Jerry')\n    4\n    \"\"\"\n    return len(set(string.lower()))\n```"}
{"task_id": "HumanEval/17", "entry_point": "parse_music", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 504, "latency_s": 11.75, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I need to iterate through the string and identify the specific patterns provided in the legend. Since the patterns vary in length (e.g., 'o' vs 'o|'), I should check for the longer patterns first or use a pointer-based approach to consume the string. \n\nThe patterns are:\n1. `o|` -> 2 beats\n2. `.|` -> 1 beat\n3. `o` -> 4 beats\n\nWait, looking at the example: `parse_music('o o| .| o| o| .| .| .| .| o o')` results in `[4, 2, 1, 2, 2, 1, 1, 1, 1, 4, 4]`.\nThe spaces are separators. I can split the string by whitespace and then check each token.\n\n- If token is `o|`, it's 2.\n- If token is `.|`, it's 1.\n- If token is `o`, it's 4.\n\n```python\nfrom typing import List\n\ndef parse_music(music_string: str) -> List[int]:\n    \"\"\" Input to this function is a string representing musical notes in a special ASCII format.\n    Your task is to parse this string and return list of integers corresponding to how many beats does each\n    not last.\n\n    Here is a legend:\n    'o' - whole note, lasts four beats\n    'o|' - half note, lasts two beats\n    '.|' - quater note, lasts one beat\n\n    >>> parse_music('o o| .| o| o| .| .| .| .| o o')\n    [4, 2, 1, 2, 2, 1, 1, 1, 1, 4, 4]\n    \"\"\"\n    beats = []\n    # Split by whitespace to get individual note tokens\n    tokens = music_string.split()\n    \n    for token in tokens:\n        if token == 'o|':\n            beats.append(2)\n        elif token == '.|':\n            beats.append(1)\n        elif token == 'o':\n            beats.append(4)\n            \n    return beats\n```"}
{"task_id": "HumanEval/18", "entry_point": "how_many_times", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 292, "latency_s": 13.38, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to count occurrences of a substring within a string, including overlapping instances. The standard `str.count()` method in Python does not count overlaps (e.g., `'aaaa'.count('aa')` returns 2, but we need 3). \n\nThe most efficient way to handle overlaps is to iterate through the string and use the `.find()` method starting from the index immediately following the start of the last found occurrence. Alternatively, a simple loop checking every possible starting position is also effective for this task.\n\n```python\ndef how_many_times(string: str, substring: str) -> int:\n    \"\"\" Find how many times a given substring can be found in the original string. Count overlaping cases.\n    >>> how_many_times('', 'a')\n    0\n    >>> how_many_times('aaa', 'a')\n    3\n    >>> how_many_times('aaaa', 'aa')\n    3\n    \"\"\"\n    if not substring:\n        return 0\n    \n    count = 0\n    start = 0\n    while True:\n        start = string.find(substring, start)\n        if start == -1:\n            break\n        count += 1\n        start += 1  # Move forward by 1 to allow for overlapping matches\n    return count\n```"}
{"task_id": "HumanEval/19", "entry_point": "sort_numbers", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 411, "latency_s": 16.09, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I will map each word representation to its corresponding integer value. I will then split the input string into a list of words, convert those words to integers, sort the integers, and finally map them back to their word representations to join them into a space-delimited string.\n\nComplexity:\n- Time: O(N log N) where N is the number of words in the input string (due to sorting).\n- Space: O(N) to store the list of words.\n\n```python\nfrom typing import List\n\ndef sort_numbers(numbers: str) -> str:\n    \"\"\" Input is a space-delimited string of numberals from 'zero' to 'nine'.\n    Valid choices are 'zero', 'one', 'two', 'three', 'four', 'five', 'six', 'seven', 'eight' and 'nine'.\n    Return the string with numbers sorted from smallest to largest\n    >>> sort_numbers('three one five')\n    'one three five'\n    \"\"\"\n    mapping = {\n        'zero': 0, 'one': 1, 'two': 2, 'three': 3, 'four': 4,\n        'five': 5, 'six': 6, 'seven': 7, 'eight': 8, 'nine': 9\n    }\n    \n    # Reverse mapping to get the word back from the integer\n    inv_mapping = {v: k for k, v in mapping.items()}\n    \n    # Split the input string into words\n    words = numbers.split()\n    \n    # Convert words to integers\n    values = [mapping[word] for word in words]\n    \n    # Sort the integers\n    values.sort()\n    \n    # Convert sorted integers back to words and join\n    return \" \".join(inv_mapping[v] for v in values)\n```"}
{"task_id": "HumanEval/20", "entry_point": "find_closest_elements", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 449, "latency_s": 18.76, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To find the two closest elements in a list, the most efficient approach is to first sort the list. Once sorted, the two closest numbers must be adjacent to each other. By iterating through the sorted list once and comparing the difference between every adjacent pair, we can identify the pair with the minimum difference.\n\nComplexity:\n- Time: $O(n \\log n)$ due to the sorting step.\n- Space: $O(n)$ or $O(1)$ depending on the sorting implementation's space complexity.\n\n```python\nfrom typing import List, Tuple\n\ndef find_closest_elements(numbers: List[float]) -> Tuple[float, float]:\n    \"\"\" From a supplied list of numbers (of length at least two) select and return two that are the closest to each\n    other and return them in order (smaller number, larger number).\n    >>> find_closest_elements([1.0, 2.0, 3.0, 4.0, 5.0, 2.2])\n    (2.0, 2.2)\n    >>> find_closest_elements([1.0, 2.0, 3.0, 4.0, 5.0, 2.0])\n    (2.0, 2.0)\n    \"\"\"\n    # Sort the numbers to ensure that the closest elements are adjacent\n    sorted_nums = sorted(numbers)\n    \n    # Initialize with the first pair\n    min_diff = float('inf')\n    closest_pair = (sorted_nums[0], sorted_nums[1])\n    \n    # Iterate through the sorted list and check adjacent pairs\n    for i in range(len(sorted_nums) - 1):\n        current_diff = sorted_nums[i+1] - sorted_nums[i]\n        if current_diff < min_diff:\n            min_diff = current_diff\n            closest_pair = (sorted_nums[i], sorted_nums[i+1])\n            \n    return closest_pair\n```"}
{"task_id": "HumanEval/21", "entry_point": "rescale_to_unit", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 356, "latency_s": 17.09, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To rescale a list of numbers to a unit range $[0, 1]$, we first identify the minimum and maximum values in the list. If all numbers in the list are identical (i.e., $min == max$), the standard formula would result in a division by zero. In such a case, it is standard practice to return a list of zeros (or the original list, but since the goal is a unit range and the range is zero, 0.0 is the logical mapping). Otherwise, we apply the linear transformation: $x' = \\frac{x - \\min}{\\max - \\min}$.\n\n```python\nfrom typing import List\n\ndef rescale_to_unit(numbers: List[float]) -> List[float]:\n    \"\"\" Given list of numbers (of at least two elements), apply a linear transform to that list,\n    such that the smallest number will become 0 and the largest will become 1\n    >>> rescale_to_unit([1.0, 2.0, 3.0, 4.0, 5.0])\n    [0.0, 0.25, 0.5, 0.75, 1.0]\n    \"\"\"\n    min_val = min(numbers)\n    max_val = max(numbers)\n    \n    # Handle the case where all numbers are the same to avoid division by zero\n    if max_val == min_val:\n        return [0.0 for _ in numbers]\n    \n    diff = max_val - min_val\n    return [(x - min_val) / diff for x in numbers]\n```"}
{"task_id": "HumanEval/22", "entry_point": "filter_integers", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 236, "latency_s": 16.45, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this, I will iterate through the input list and use the `type()` check or `isinstance()` to identify integers. Since `bool` is a subclass of `int` in Python, I must explicitly check that the type is exactly `int` to avoid including `True` or `False` in the result, as per standard expectations for \"integers\" in such filtering tasks.\n\n```python\nfrom typing import List, Any\n\ndef filter_integers(values: List[Any]) -> List[int]:\n    \"\"\" Filter given list of any python values only for integers\n    >>> filter_integers(['a', 3.14, 5])\n    [5]\n    >>> filter_integers([1, 2, 3, 'abc', {}, []])\n    [1, 2, 3]\n    \"\"\"\n    # We use type(x) is int instead of isinstance(x, int) \n    # because isinstance(True, int) evaluates to True.\n    return [x for x in values if type(x) is int]\n```"}
{"task_id": "HumanEval/23", "entry_point": "strlen", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 94, "latency_s": 12.87, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To find the length of a string in Python, we use the built-in `len()` function, which operates in $O(1)$ time complexity as Python strings store their length as an attribute.\n\n```python\ndef strlen(string: str) -> int:\n    \"\"\" Return length of given string\n    >>> strlen('')\n    0\n    >>> strlen('abc')\n    3\n    \"\"\"\n    return len(string)\n```"}
{"task_id": "HumanEval/24", "entry_point": "largest_divisor", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 345, "latency_s": 11.68, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To find the largest divisor of a number $n$ that is smaller than $n$, we need to find the smallest prime factor $p$ of $n$. The largest divisor will then be $n / p$. \n\nFor example, if $n = 15$, the smallest prime factor is 2 (no), 3 (yes). $15 / 3 = 5$.\nIf $n = 100$, the smallest prime factor is 2. $100 / 2 = 50$.\n\nThe algorithm iterates from 2 up to the square root of $n$. If a divisor is found, we return $n$ divided by that divisor immediately, as the first (smallest) divisor found will yield the largest quotient. If no divisor is found up to $\\sqrt{n}$, the number is prime, and the largest divisor is 1.\n\n```python\nimport math\n\ndef largest_divisor(n: int) -> int:\n    \"\"\" For a given number n, find the largest number that divides n evenly, smaller than n\n    >>> largest_divisor(15)\n    5\n    \"\"\"\n    if n <= 1:\n        return 0\n    \n    # Find the smallest divisor greater than 1\n    # The largest divisor is n / smallest_divisor\n    for i in range(2, int(math.sqrt(n)) + 1):\n        if n % i == 0:\n            return n // i\n            \n    # If no divisor is found, n is prime, so the largest divisor is 1\n    return 1\n```"}
{"task_id": "HumanEval/25", "entry_point": "factorize", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 435, "latency_s": 12.6, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we use the trial division algorithm. We start by checking the smallest prime number, 2. While the number $n$ is divisible by 2, we append 2 to our list and divide $n$ by 2. We then proceed to check odd numbers starting from 3 up to the square root of the current value of $n$. If $n$ is still greater than 1 after checking all numbers up to $\\sqrt{n}$, the remaining $n$ must be a prime number.\n\nComplexity:\n- Time: $O(\\sqrt{n})$ in the worst case (when $n$ is prime).\n- Space: $O(\\log n)$ to store the factors.\n\n```python\nfrom typing import List\n\ndef factorize(n: int) -> List[int]:\n    \"\"\" Return list of prime factors of given integer in the order from smallest to largest.\n    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.\n    Input number should be equal to the product of all factors\n    >>> factorize(8)\n    [2, 2, 2]\n    >>> factorize(25)\n    [5, 5]\n    >>> factorize(70)\n    [2, 5, 7]\n    \"\"\"\n    factors = []\n    # Handle the factor 2 separately to allow incrementing by 2 in the loop\n    while n % 2 == 0:\n        factors.append(2)\n        n //= 2\n    \n    # Check odd numbers starting from 3\n    d = 3\n    while d * d <= n:\n        while n % d == 0:\n            factors.append(d)\n            n //= d\n        d += 2\n        \n    # If n is still > 1, the remaining n is prime\n    if n > 1:\n        factors.append(n)\n        \n    return factors\n```"}
{"task_id": "HumanEval/26", "entry_point": "remove_duplicates", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 233, "latency_s": 12.57, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to identify and remove any integer that appears more than once in the input list. The requirement is to keep the original order of the elements that appear exactly once.\n\n**Approach:**\n1. Count the occurrences of each number using a dictionary (or `collections.Counter`).\n2. Iterate through the original list and include an element in the result only if its count is exactly 1.\n3. This ensures $O(N)$ time complexity and $O(N)$ space complexity.\n\n```python\nfrom typing import List\nfrom collections import Counter\n\ndef remove_duplicates(numbers: List[int]) -> List[int]:\n    \"\"\" From a list of integers, remove all elements that occur more than once.\n    Keep order of elements left the same as in the input.\n    >>> remove_duplicates([1, 2, 3, 2, 4])\n    [1, 3, 4]\n    \"\"\"\n    counts = Counter(numbers)\n    return [x for x in numbers if counts[x] == 1]\n```"}
{"task_id": "HumanEval/27", "entry_point": "flip_case", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 176, "latency_s": 13.51, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I will iterate through each character in the input string. For each character, I will check if it is uppercase or lowercase. If it is uppercase, I will convert it to lowercase; if it is lowercase, I will convert it to uppercase. Non-alphabetic characters (like numbers or punctuation) will remain unchanged. Python's built-in `.swapcase()` method is the most efficient way to achieve this, but I will implement it using a generator expression for clarity and standard practice.\n\n```python\ndef flip_case(string: str) -> str:\n    \"\"\" For a given string, flip lowercase characters to uppercase and uppercase to lowercase.\n    >>> flip_case('Hello')\n    'hELLO'\n    \"\"\"\n    return \"\".join(char.swapcase() for char in string)\n```"}
{"task_id": "HumanEval/28", "entry_point": "concatenate", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 162, "latency_s": 11.45, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To concatenate a list of strings into a single string, the most efficient and idiomatic way in Python is to use the `str.join()` method. This method handles the concatenation in $O(n)$ time where $n$ is the total number of characters, as it calculates the total length first and allocates memory once, unlike repeated string addition which can lead to $O(n^2)$ complexity due to string immutability.\n\n```python\nfrom typing import List\n\n\ndef concatenate(strings: List[str]) -> str:\n    \"\"\" Concatenate list of strings into a single string\n    >>> concatenate([])\n    ''\n    >>> concatenate(['a', 'b', 'c'])\n    'abc'\n    \"\"\"\n    return \"\".join(strings)\n```"}
{"task_id": "HumanEval/29", "entry_point": "filter_by_prefix", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 207, "latency_s": 8.86, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I will iterate through the list of strings and use the built-in `.startswith()` method to check if each string begins with the specified prefix. This approach is efficient with a time complexity of $O(n \\cdot k)$, where $n$ is the number of strings and $k$ is the maximum length of a string, and a space complexity of $O(n)$ to store the filtered results.\n\n```python\nfrom typing import List\n\ndef filter_by_prefix(strings: List[str], prefix: str) -> List[str]:\n    \"\"\" Filter an input list of strings only for ones that start with a given prefix.\n    >>> filter_by_prefix([], 'a')\n    []\n    >>> filter_by_prefix(['abc', 'bcd', 'cde', 'array'], 'a')\n    ['abc', 'array']\n    \"\"\"\n    return [s for s in strings if s.startswith(prefix)]\n```"}
{"task_id": "HumanEval/30", "entry_point": "get_positive", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 200, "latency_s": 8.48, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this, I will use a list comprehension to iterate through the input list and filter out any numbers that are less than or equal to zero. This approach ensures that only strictly positive integers (greater than 0) are included in the resulting list, maintaining the original order.\n\n```python\ndef get_positive(l: list):\n    \"\"\"Return only positive numbers in the list.\n    >>> get_positive([-1, 2, -4, 5, 6])\n    [2, 5, 6]\n    >>> get_positive([5, 3, -5, 2, -3, 3, 9, 0, 123, 1, -10])\n    [5, 3, 2, 3, 9, 123, 1]\n    \"\"\"\n    return [num for num in l if num > 0]\n```"}
{"task_id": "HumanEval/31", "entry_point": "is_prime", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 392, "latency_s": 10.93, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To determine if a number is prime, we must check if it is greater than 1 and has no divisors other than 1 and itself. An efficient approach is to check for divisibility by 2 and 3 first, and then iterate through potential divisors starting from 5, skipping even numbers and multiples of 3 by using the $6k \\pm 1$ rule. The loop only needs to run up to the square root of $n$, as any factor larger than $\\sqrt{n}$ must have a corresponding factor smaller than $\\sqrt{n}$.\n\n```python\nimport math\n\ndef is_prime(n):\n    \"\"\"Return true if a given number is prime, and false otherwise.\n    >>> is_prime(6)\n    False\n    >>> is_prime(101)\n    True\n    >>> is_prime(11)\n    True\n    >>> is_prime(13441)\n    True\n    >>> is_prime(61)\n    True\n    >>> is_prime(4)\n    False\n    >>> is_prime(1)\n    False\n    \"\"\"\n    if n <= 1:\n        return False\n    if n <= 3:\n        return True\n    if n % 2 == 0 or n % 3 == 0:\n        return False\n    \n    # A prime number (greater than 3) is always of the form 6k \u00b1 1.\n    # We check divisors up to the square root of n.\n    limit = int(math.isqrt(n))\n    for i in range(5, limit + 1, 6):\n        if n % i == 0 or n % (i + 2) == 0:\n            return False\n            \n    return True\n```"}
{"task_id": "HumanEval/32", "entry_point": "find_zero", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 666, "latency_s": 16.64, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve for the zero of a polynomial, we can use the Newton-Raphson method, which is an iterative numerical method to find roots of a real-valued function. Given the constraints (even number of coefficients, largest non-zero coefficient as the leading term), the function is guaranteed to have at least one real root.\n\nThe derivative of the polynomial $P(x) = \\sum_{i=0}^{n} a_i x^i$ is $P'(x) = \\sum_{i=1}^{n} i \\cdot a_i x^{i-1}$.\n\n```python\nimport math\n\ndef poly(xs: list, x: float):\n    \"\"\"\n    Evaluates polynomial with coefficients xs at point x.\n    return xs[0] + xs[1] * x + xs[2] * x^2 + .... xs[n] * x^n\n    \"\"\"\n    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])\n\ndef find_zero(xs: list):\n    \"\"\" xs are coefficients of a polynomial.\n    find_zero find x such that poly(x) = 0.\n    find_zero returns only only zero point, even if there are many.\n    Moreover, find_zero only takes list xs having even number of coefficients\n    and largest non zero coefficient as it guarantees\n    a solution.\n    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x\n    -0.5\n    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3\n    1.0\n    \"\"\"\n    # Derivative coefficients\n    # If xs = [a0, a1, a2, a3], deriv_xs = [a1, 2*a2, 3*a3]\n    deriv_xs = [i * xs[i] for i in range(1, len(xs))]\n    \n    # Initial guess: a simple heuristic or 0.0\n    # For polynomials with even number of coefficients (odd degree), \n    # a root is guaranteed.\n    x = 1.0\n    \n    # Newton-Raphson iteration\n    for _ in range(1000):\n        y = poly(xs, x)\n        dy = poly(deriv_xs, x)\n        \n        if abs(dy) < 1e-12:\n            # If derivative is too small, nudge x to avoid division by zero\n            x += 0.1\n            continue\n            \n        next_x = x - y / dy\n        \n        if abs(next_x - x) < 1e-9:\n            return next_x\n        x = next_x\n        \n    return x\n```"}
{"task_id": "HumanEval/33", "entry_point": "sort_third", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 390, "latency_s": 18.72, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to identify all elements at indices that are divisible by three (0, 3, 6, ...). We extract these values, sort them, and then place them back into their original positions in a new list. The elements at indices not divisible by three remain unchanged.\n\nComplexity:\n- Time: $O(N \\log N)$ where $N$ is the length of the list (due to sorting the extracted elements).\n- Space: $O(N)$ to store the new list and the extracted elements.\n\n```python\ndef sort_third(l: list):\n    \"\"\"This function takes a list l and returns a list l' such that\n    l' is identical to l in the indicies that are not divisible by three, while its values at the indicies that are divisible by three are equal\n    to the values of the corresponding indicies of l, but sorted.\n    >>> sort_third([1, 2, 3])\n    [1, 2, 3]\n    >>> sort_third([5, 6, 3, 4, 8, 9, 2])\n    [2, 6, 3, 4, 8, 9, 5]\n    \"\"\"\n    # Extract elements at indices 0, 3, 6, ...\n    extracted = [l[i] for i in range(0, len(l), 3)]\n    # Sort the extracted elements\n    extracted.sort()\n    \n    # Create a copy of the list to modify\n    result = list(l)\n    \n    # Place sorted elements back into the correct indices\n    for i, val in enumerate(extracted):\n        result[i * 3] = val\n        \n    return result\n```"}
{"task_id": "HumanEval/34", "entry_point": "unique", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 174, "latency_s": 18.42, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this, I will convert the input list into a `set` to automatically remove duplicate elements. Then, I will convert that set back into a list and use the `sorted()` function to ensure the elements are in ascending order. This approach has a time complexity of O(N log N) due to the sorting step and a space complexity of O(N) to store the unique elements.\n\n```python\ndef unique(l: list):\n    \"\"\"Return sorted unique elements in a list\n    >>> unique([5, 3, 5, 2, 3, 3, 9, 0, 123])\n    [0, 2, 3, 5, 9, 123]\n    \"\"\"\n    return sorted(list(set(l)))\n```"}
{"task_id": "HumanEval/35", "entry_point": "max_element", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 208, "latency_s": 16.33, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To find the maximum element in a list, we can use Python's built-in `max()` function. However, to ensure robustness, we should consider the case where the list might be empty (which would normally raise a `ValueError`). Since the docstring implies a standard list of numbers, I will provide the standard implementation.\n\nComplexity:\n- Time: O(n) where n is the number of elements in the list.\n- Space: O(1).\n\n```python\ndef max_element(l: list):\n    \"\"\"Return maximum element in the list.\n    >>> max_element([1, 2, 3])\n    3\n    >>> max_element([5, 3, -5, 2, -3, 3, 9, 0, 123, 1, -10])\n    123\n    \"\"\"\n    if not l:\n        return None\n    return max(l)\n```"}
{"task_id": "HumanEval/36", "entry_point": "fizz_buzz", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 288, "latency_s": 12.04, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through all integers from 1 up to (but not including) $n$. For each integer, we check if it is divisible by 11 or 13. If it is, we convert the integer to a string and count the occurrences of the character '7'. We maintain a running total of these counts and return the final sum.\n\nComplexity:\n- Time: $O(n \\cdot d)$, where $d$ is the number of digits in $n$ (since we iterate up to $n$ and convert each number to a string).\n- Space: $O(d)$ to store the string representation of the current number.\n\n```python\ndef fizz_buzz(n: int) -> int:\n    \"\"\"Return the number of times the digit 7 appears in integers less than n which are divisible by 11 or 13.\n    >>> fizz_buzz(50)\n    0\n    >>> fizz_buzz(78)\n    2\n    >>> fizz_buzz(79)\n    3\n    \"\"\"\n    count = 0\n    for i in range(1, n):\n        if i % 11 == 0 or i % 13 == 0:\n            count += str(i).count('7')\n    return count\n```"}
{"task_id": "HumanEval/37", "entry_point": "sort_even", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 386, "latency_s": 12.0, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to extract the elements at even indices (0, 2, 4, ...), sort them, and then reconstruct the list by placing these sorted values back into the even positions while keeping the odd indices unchanged.\n\n**Approach:**\n1. Identify the elements at even indices using slicing: `l[::2]`.\n2. Sort this sub-list.\n3. Create a new list (or modify a copy) where the even positions are filled with the sorted values and odd positions are filled with the original values.\n4. Complexity: $O(N \\log N)$ due to the sorting step, where $N$ is the length of the list.\n\n```python\ndef sort_even(l: list):\n    \"\"\"This function takes a list l and returns a list l' such that\n    l' is identical to l in the odd indicies, while its values at the even indicies are equal\n    to the values of the even indicies of l, but sorted.\n    >>> sort_even([1, 2, 3])\n    [1, 2, 3]\n    >>> sort_even([5, 6, 3, 4])\n    [3, 6, 5, 4]\n    \"\"\"\n    # Extract elements at even indices\n    even_elements = sorted(l[::2])\n    \n    # Create a result list\n    result = list(l)\n    \n    # Replace even indices with sorted elements\n    # We use an iterator to easily pop elements from the sorted list\n    it = iter(even_elements)\n    for i in range(0, len(result), 2):\n        result[i] = next(it)\n        \n    return result\n```"}
{"task_id": "HumanEval/38", "entry_point": "decode_cyclic", "passed": false, "finish_reason": "stop", "exec_err": "e \"/var/folders/0l/75d7q65918d_j14rb3j30dlm0000gn/T/tmp60whi9ja/cand.py\", line 44, in check\n    encoded_str = encode_cyclic(str)\n                  ^^^^^^^^^^^^^\nNameError: name 'encode_cyclic' is not defined. Did you mean: 'decode_cyclic'?\n", "completion_tokens": 442, "latency_s": 15.03, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To decode the string, we need to reverse the logic applied in `encode_cyclic`. \n\n1.  **Grouping**: The string is split into chunks of 3. We must identify these chunks based on the original length (which is preserved).\n2.  **Reversing the Cycle**: In `encode_cyclic`, a group of exactly 3 characters `[0, 1, 2]` was transformed into `[1, 2, 0]`. To reverse this, we need to shift the characters back. Specifically, the character at index 0 moves to index 2, index 1 moves to index 0, and index 2 moves to index 1. This is equivalent to a right cyclic shift: `group[-1] + group[:-1]`.\n3.  **Edge Cases**: Groups with fewer than 3 characters (at the end of the string) were left unchanged, so they should remain unchanged during decoding.\n\n```python\ndef decode_cyclic(s: str):\n    \"\"\"\n    takes as input string encoded with encode_cyclic function. Returns decoded string.\n    \"\"\"\n    # Split string into groups of 3\n    groups = [s[(3 * i):min((3 * i + 3), len(s))] for i in range((len(s) + 2) // 3)]\n    \n    # Reverse the cycle: if length is 3, shift right to undo the left shift\n    # encode_cyclic: [0, 1, 2] -> [1, 2, 0]\n    # decode_cyclic: [1, 2, 0] -> [0, 1, 2] (which is group[-1] + group[:-1])\n    decoded_groups = []\n    for group in groups:\n        if len(group) == 3:\n            decoded_groups.append(group[-1] + group[:-1])\n        else:\n            decoded_groups.append(group)\n            \n    return \"\".join(decoded_groups)\n```"}
{"task_id": "HumanEval/39", "entry_point": "prime_fib", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 484, "latency_s": 18.14, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to generate Fibonacci numbers sequentially and check each one for primality until we find the $n$-th prime Fibonacci number. \n\n**Approach:**\n1.  **Fibonacci Generation:** We use an iterative approach to generate Fibonacci numbers starting from 1, 1, 2, 3, 5...\n2.  **Primality Testing:** Since Fibonacci numbers grow exponentially, we need an efficient primality test. For small $n$, a simple $O(\\sqrt{x})$ trial division is sufficient.\n3.  **Counting:** We maintain a counter to keep track of how many prime Fibonacci numbers we have encountered.\n4.  **Edge Cases:** The first two Fibonacci numbers are 1 and 1, which are not prime. The first prime Fibonacci number is 2.\n\n```python\nimport math\n\ndef prime_fib(n: int) -> int:\n    \"\"\"\n    prime_fib returns n-th number that is a Fibonacci number and it's also prime.\n    >>> prime_fib(1)\n    2\n    >>> prime_fib(2)\n    3\n    >>> prime_fib(3)\n    5\n    >>> prime_fib(4)\n    13\n    >>> prime_fib(5)\n    89\n    \"\"\"\n    def is_prime(num: int) -> bool:\n        if num < 2:\n            return False\n        if num == 2 or num == 3:\n            return True\n        if num % 2 == 0 or num % 3 == 0:\n            return False\n        i = 5\n        while i * i <= num:\n            if num % i == 0 or num % (i + 2) == 0:\n                return False\n            i += 6\n        return True\n\n    count = 0\n    a, b = 1, 1\n    \n    while count < n:\n        # Generate next Fibonacci number\n        a, b = b, a + b\n        # Check if the current Fibonacci number (b) is prime\n        if is_prime(b):\n            count += 1\n            if count == n:\n                return b\n```"}
{"task_id": "HumanEval/40", "entry_point": "triples_sum_to_zero", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 718, "latency_s": 22.99, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to find if there exist three distinct indices $i, j, k$ such that $l[i] + l[j] + l[k] = 0$. \n\n**Approach:**\n1. **Edge Case:** If the list has fewer than 3 elements, it's impossible to have a triple, so return `False`.\n2. **Algorithm:** We can use a nested loop to pick the first two elements and then check if the required third element (which would be $-(l[i] + l[j])$) exists in the remaining part of the list.\n3. **Optimization:** To ensure we are using \"distinct elements\" (meaning different indices), we can use a frequency map (dictionary) to count occurrences of each number. This handles cases where the same value appears multiple times in the list (e.g., `[1, -1, 0]` or `[1, 1, -2]`).\n4. **Complexity:** The time complexity will be $O(n^2)$ where $n$ is the length of the list, and the space complexity will be $O(n)$ to store the counts.\n\n```python\ndef triples_sum_to_zero(l: list):\n    \"\"\"\n    triples_sum_to_zero takes a list of integers as an input.\n    it returns True if there are three distinct elements in the list that\n    sum to zero, and False otherwise.\n\n    >>> triples_sum_to_zero([1, 3, 5, 0])\n    False\n    >>> triples_sum_to_zero([1, 3, -2, 1])\n    True\n    >>> triples_sum_to_zero([1, 2, 3, 7])\n    False\n    >>> triples_sum_to_zero([2, 4, -5, 3, 9, 7])\n    True\n    >>> triples_sum_to_zero([1])\n    False\n    \"\"\"\n    n = len(l)\n    if n < 3:\n        return False\n    \n    # Use a frequency map to handle duplicate values correctly\n    counts = {}\n    for x in l:\n        counts[x] = counts.get(x, 0) + 1\n        \n    # Iterate through all pairs of indices\n    for i in range(n):\n        for j in range(i + 1, n):\n            val1 = l[i]\n            val2 = l[j]\n            target = -(val1 + val2)\n            \n            # We need to check if 'target' exists in the list \n            # and is not one of the indices we just used.\n            if target in counts:\n                # Calculate how many times 'target' is needed\n                # based on how many times it matches val1 and val2\n                needed = 1\n                if target == val1:\n                    needed += 1\n                if target == val2:\n                    needed += 1\n                \n                # If the count in the original list is enough to satisfy\n                # the requirement of distinct indices, return True\n                if counts[target] >= needed:\n                    return True\n                    \n    return False\n```"}
{"task_id": "HumanEval/41", "entry_point": "car_race_collision", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 488, "latency_s": 24.16, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to analyze the relative motion of the cars. \n\n1.  **The Setup**: We have $n$ cars moving right (let's call them $R_1, R_2, \\dots, R_n$) and $n$ cars moving left (let's call them $L_1, L_2, \\dots, L_n$).\n2.  **The Motion**: Since all cars move at the same constant speed, we can simplify the physics. If we look at the system from the perspective of one of the cars moving right, all cars moving left appear to be moving toward it at twice the speed, while all cars moving right appear stationary.\n3.  **The Collisions**: A collision occurs every time a car moving right \"passes\" a car moving left. Because the cars are \"infinitely sturdy\" and continue their trajectories, every single car moving right will eventually encounter every single car moving left as they pass each other on the infinite line.\n4.  **The Calculation**: Since there are $n$ cars moving right and $n$ cars moving left, and every car in the first set will eventually collide with every car in the second set exactly once, the total number of collisions is the product of the number of cars in each set.\n\nComplexity: $O(1)$ time and space.\n\n```python\ndef car_race_collision(n: int) -> int:\n    \"\"\"\n    Imagine a road that's a perfectly straight infinitely long line.\n    n cars are driving left to right;  simultaneously, a different set of n cars\n    are driving right to left.  The two sets of cars start out being very far from\n    each other.  All cars move in the same speed.  Two cars are said to collide\n    when a car that's moving left to right hits a car that's moving right to left.\n    However, the cars are infinitely sturdy and strong; as a result, they continue moving\n    in their trajectory as if they did not collide.\n\n    This function outputs the number of such collisions.\n    \"\"\"\n    # Each of the n cars moving right will eventually collide with \n    # each of the n cars moving left exactly once.\n    return n * n\n```"}
{"task_id": "HumanEval/42", "entry_point": "incr_list", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 209, "latency_s": 21.52, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I will use a list comprehension to iterate through each element in the input list, add 1 to it, and collect the results into a new list. This approach ensures that the original list remains unmodified (immutability) and provides an $O(n)$ time complexity where $n$ is the length of the list.\n\n```python\ndef incr_list(l: list):\n    \"\"\"Return list with elements incremented by 1.\n    >>> incr_list([1, 2, 3])\n    [2, 3, 4]\n    >>> incr_list([5, 3, 5, 2, 3, 3, 9, 0, 123])\n    [6, 4, 6, 3, 4, 4, 10, 1, 124]\n    \"\"\"\n    return [x + 1 for x in l]\n```"}
{"task_id": "HumanEval/43", "entry_point": "pairs_sum_to_zero", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 459, "latency_s": 21.25, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to determine if there exist two distinct indices $i$ and $j$ such that $l[i] + l[j] = 0$. This is equivalent to checking if there exists an element $x$ in the list such that $-x$ is also in the list (with the caveat that if $x=0$, there must be at least two zeros).\n\nA set-based approach is efficient here. We iterate through the list and for each number $x$, we check if $-x$ has already been seen. If we encounter a $0$, we need to ensure there's another $0$ to form a pair.\n\nComplexity:\n- Time: $O(n)$ where $n$ is the length of the list, as we iterate through the list once.\n- Space: $O(n)$ to store the elements in a set.\n\n```python\ndef pairs_sum_to_zero(l):\n    \"\"\"\n    pairs_sum_to_zero takes a list of integers as an input.\n    it returns True if there are two distinct elements in the list that\n    sum to zero, and False otherwise.\n    >>> pairs_sum_to_zero([1, 3, 5, 0])\n    False\n    >>> pairs_sum_to_zero([1, 3, -2, 1])\n    False\n    >>> pairs_sum_to_zero([1, 2, 3, 7])\n    False\n    >>> pairs_sum_to_zero([2, 4, -5, 3, 5, 7])\n    True\n    >>> pairs_sum_to_zero([1])\n    False\n    \"\"\"\n    seen = set()\n    zero_count = 0\n    \n    for num in l:\n        if num == 0:\n            zero_count += 1\n            if zero_count >= 2:\n                return True\n        elif -num in seen:\n            return True\n        else:\n            seen.add(num)\n            \n    return False\n```"}
{"task_id": "HumanEval/44", "entry_point": "change_base", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 260, "latency_s": 16.08, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To convert a number to a different base, we repeatedly take the remainder of the number when divided by the target base. This remainder represents the digit at the current position (starting from the least significant digit). We then update the number by performing integer division by the base and repeat until the number becomes zero. Since the problem specifies bases less than 10, we only need to deal with digits '0'-'9'.\n\n```python\ndef change_base(x: int, base: int) -> str:\n    \"\"\"Change numerical base of input number x to base.\n    return string representation after the conversion.\n    base numbers are less than 10.\n    >>> change_base(8, 3)\n    '22'\n    >>> change_base(8, 2)\n    '1000'\n    >>> change_base(7, 2)\n    '111'\n    \"\"\"\n    if x == 0:\n        return \"0\"\n    \n    digits = []\n    while x > 0:\n        digits.append(str(x % base))\n        x //= base\n    \n    return \"\".join(reversed(digits))\n```"}
{"task_id": "HumanEval/45", "entry_point": "triangle_area", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 110, "latency_s": 11.79, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To calculate the area of a triangle given the base (side) and the height, the formula is $\\text{Area} = \\frac{1}{2} \\times \\text{base} \\times \\text{height}$.\n\n```python\ndef triangle_area(a, h):\n    \"\"\"Given length of a side and high return area for a triangle.\n    >>> triangle_area(5, 3)\n    7.5\n    \"\"\"\n    return 0.5 * a * h\n```"}
{"task_id": "HumanEval/46", "entry_point": "fib4", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 473, "latency_s": 14.76, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem efficiently without recursion, we can use an iterative approach (dynamic programming with space optimization). Since each term $fib4(n)$ only depends on the four preceding terms, we only need to maintain a list or four variables to store the previous values.\n\nThe base cases are:\n- $fib4(0) = 0$\n- $fib4(1) = 0$\n- $fib4(2) = 2$\n- $fib4(3) = 0$\n\nFor $n \\ge 4$, we compute the value by summing the previous four.\n\n```python\ndef fib4(n: int) -> int:\n    \"\"\"The Fib4 number sequence is a sequence similar to the Fibbonacci sequnece that's defined as follows:\n    fib4(0) -> 0\n    fib4(1) -> 0\n    fib4(2) -> 2\n    fib4(3) -> 0\n    fib4(n) -> fib4(n-1) + fib4(n-2) + fib4(n-3) + fib4(n-4).\n    Please write a function to efficiently compute the n-th element of the fib4 number sequence.  Do not use recursion.\n    >>> fib4(5)\n    4\n    >>> fib4(6)\n    8\n    >>> fib4(7)\n    14\n    \"\"\"\n    if n == 0:\n        return 0\n    if n == 1:\n        return 0\n    if n == 2:\n        return 2\n    if n == 3:\n        return 0\n    \n    # Initial values for n=0, 1, 2, 3\n    a, b, c, d = 0, 0, 2, 0\n    \n    # Iteratively compute up to n\n    for _ in range(4, n + 1):\n        current = a + b + c + d\n        # Shift values forward\n        a, b, c, d = b, c, d, current\n        \n    return d\n```"}
{"task_id": "HumanEval/47", "entry_point": "median", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 312, "latency_s": 13.11, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To find the median of a list of numbers, we first need to sort the list. If the number of elements is odd, the median is the middle element. If the number of elements is even, the median is the average of the two middle elements.\n\nComplexity:\n- Time: $O(n \\log n)$ due to the sorting step.\n- Space: $O(n)$ or $O(1)$ depending on whether the sorting is in-place (the implementation below uses `sorted()` to avoid mutating the input).\n\n```python\ndef median(l: list):\n    \"\"\"Return median of elements in the list l.\n    >>> median([3, 1, 2, 4, 5])\n    3\n    >>> median([-10, 4, 6, 1000, 10, 20])\n    15.0\n    \"\"\"\n    if not l:\n        return None\n    \n    sorted_l = sorted(l)\n    n = len(sorted_l)\n    mid = n // 2\n    \n    if n % 2 == 0:\n        # Even number of elements: average of the two middle elements\n        return (sorted_l[mid - 1] + sorted_l[mid]) / 2.0\n    else:\n        # Odd number of elements: the middle element\n        return sorted_l[mid]\n```"}
{"task_id": "HumanEval/48", "entry_point": "is_palindrome", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 182, "latency_s": 12.24, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To determine if a string is a palindrome, we can compare the string to its reverse. In Python, the most efficient and idiomatic way to reverse a string is using slicing `[::-1]`. This approach handles empty strings and single-character strings correctly (both are palindromes).\n\nComplexity:\n- Time: O(n) where n is the length of the string.\n- Space: O(n) to create the reversed string.\n\n```python\ndef is_palindrome(text: str) -> bool:\n    \"\"\"\n    Checks if given string is a palindrome\n    >>> is_palindrome('')\n    True\n    >>> is_palindrome('aba')\n    True\n    >>> is_palindrome('aaaaa')\n    True\n    >>> is_palindrome('zbcd')\n    False\n    \"\"\"\n    return text == text[::-1]\n```"}
{"task_id": "HumanEval/49", "entry_point": "modp", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 213, "latency_s": 13.41, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To calculate $2^n \\pmod{p}$ efficiently, especially for large values of $n$, we should use the modular exponentiation algorithm (binary exponentiation). Python's built-in `pow(base, exp, mod)` function is specifically optimized for this purpose, handling large integers and modular arithmetic internally to prevent overflow and ensure $O(\\log n)$ time complexity.\n\n```python\ndef modp(n: int, p: int) -> int:\n    \"\"\"Return 2^n modulo p (be aware of numerics).\n    >>> modp(3, 5)\n    3\n    >>> modp(1101, 101)\n    2\n    >>> modp(0, 101)\n    1\n    >>> modp(3, 11)\n    8\n    >>> modp(100, 101)\n    1\n    \"\"\"\n    return pow(2, n, p)\n```"}
{"task_id": "HumanEval/50", "entry_point": "decode_shift", "passed": false, "finish_reason": "stop", "exec_err": " File \"/var/folders/0l/75d7q65918d_j14rb3j30dlm0000gn/T/tmpeooev9gy/cand.py\", line 32, in check\n    encoded_str = encode_shift(str)\n                  ^^^^^^^^^^^^\nNameError: name 'encode_shift' is not defined. Did you mean: 'decode_shift'?\n", "completion_tokens": 162, "latency_s": 9.9, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To decode the string, we need to reverse the shift applied in `encode_shift`. Since the encoding adds 5 to the character's position in the alphabet (modulo 26), the decoding process must subtract 5. \n\nI will ensure the logic handles the modulo operation correctly for negative results (which Python's `%` operator does naturally) and maintains the same logic as the provided `encode_shift` function.\n\n```python\ndef decode_shift(s: str):\n    \"\"\"\n    takes as input string encoded with encode_shift function. Returns decoded string.\n    \"\"\"\n    return \"\".join([chr(((ord(ch) - 5 - ord(\"a\")) % 26) + ord(\"a\")) for ch in s])\n```"}
{"task_id": "HumanEval/51", "entry_point": "remove_vowels", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 245, "latency_s": 9.13, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I will iterate through each character in the input string and check if it belongs to the set of vowels (both lowercase and uppercase). If it is not a vowel, I will append it to a list, which is then joined back into a string. This approach ensures $O(n)$ time complexity where $n$ is the length of the string.\n\n```python\ndef remove_vowels(text):\n    \"\"\"\n    remove_vowels is a function that takes string and returns string without vowels.\n    >>> remove_vowels('')\n    ''\n    >>> remove_vowels(\"abcdef\\nghijklm\")\n    'bcdf\\nghjklm'\n    >>> remove_vowels('abcdef')\n    'bcdf'\n    >>> remove_vowels('aaaaa')\n    ''\n    >>> remove_vowels('aaBAA')\n    'B'\n    >>> remove_vowels('zbcd')\n    'zbcd'\n    \"\"\"\n    vowels = \"aeiouAEIOU\"\n    return \"\".join([char for char in text if char not in vowels])\n```"}
{"task_id": "HumanEval/52", "entry_point": "below_threshold", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 200, "latency_s": 9.34, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I will iterate through each element in the list `l`. If any element is greater than or equal to the threshold `t`, the function should immediately return `False`. If the loop completes without finding such an element (or if the list is empty), the function returns `True`. This approach has a time complexity of O(n) and a space complexity of O(1).\n\n```python\ndef below_threshold(l: list, t: int) -> bool:\n    \"\"\"Return True if all numbers in the list l are below threshold t.\n    >>> below_threshold([1, 2, 4, 10], 100)\n    True\n    >>> below_threshold([1, 20, 4, 10], 5)\n    False\n    \"\"\"\n    for num in l:\n        if num >= t:\n            return False\n    return True\n```"}
{"task_id": "HumanEval/53", "entry_point": "add", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 65, "latency_s": 7.67, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "```python\ndef add(x: int, y: int) -> int:\n    \"\"\"Add two numbers x and y\n    >>> add(2, 3)\n    5\n    >>> add(5, 7)\n    12\n    \"\"\"\n    return x + y\n```"}
{"task_id": "HumanEval/54", "entry_point": "same_chars", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 255, "latency_s": 8.72, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To determine if two words have the same characters, we need to check if the set of unique characters in the first string is identical to the set of unique characters in the second string. Using Python's `set()` data structure is the most efficient way to achieve this, as it automatically handles uniqueness and provides an $O(1)$ average time complexity for lookups and additions.\n\n```python\ndef same_chars(s0: str, s1: str) -> bool:\n    \"\"\"\n    Check if two words have the same characters.\n    >>> same_chars('eabcdzzzz', 'dddzzzzzzzddeddabc')\n    True\n    >>> same_chars('abcd', 'dddddddabc')\n    True\n    >>> same_chars('dddddddabc', 'abcd')\n    True\n    >>> same_chars('eabcd', 'dddddddabc')\n    False\n    >>> same_chars('abcd', 'dddddddabce')\n    False\n    >>> same_chars('eabcdzzzz', 'dddzzzzzzzddddabc')\n    False\n    \"\"\"\n    return set(s0) == set(s1)\n```"}
{"task_id": "HumanEval/55", "entry_point": "fib", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 191, "latency_s": 8.12, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To calculate the $n$-th Fibonacci number efficiently, I will use an iterative approach. This ensures a time complexity of $O(n)$ and a space complexity of $O(1)$, avoiding the exponential overhead of naive recursion and the $O(n)$ space overhead of a full list.\n\n```python\ndef fib(n: int) -> int:\n    \"\"\"Return n-th Fibonacci number.\n    >>> fib(10)\n    55\n    >>> fib(1)\n    1\n    >>> fib(8)\n    21\n    \"\"\"\n    if n <= 0:\n        return 0\n    if n == 1:\n        return 1\n    \n    a, b = 0, 1\n    for _ in range(2, n + 1):\n        a, b = b, a + b\n    return b\n```"}
{"task_id": "HumanEval/56", "entry_point": "correct_bracketing", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 319, "latency_s": 9.45, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to ensure two conditions are met:\n1. At any point while reading the string from left to right, the number of closing brackets `>` must not exceed the number of opening brackets `<`.\n2. By the end of the string, the total number of opening brackets must exactly equal the total number of closing brackets.\n\nWe can track this using a counter (representing the \"balance\"). We increment for `<` and decrement for `>`. If the counter ever drops below zero, it means a closing bracket appeared without a preceding opening bracket. If the counter is zero at the end, all brackets were matched correctly.\n\n```python\ndef correct_bracketing(brackets: str) -> bool:\n    \"\"\" brackets is a string of \"<\" and \">\".\n    return True if every opening bracket has a corresponding closing bracket.\n\n    >>> correct_bracketing(\"<\")\n    False\n    >>> correct_bracketing(\"<>\")\n    True\n    >>> correct_bracketing(\"<<><>>\")\n    True\n    >>> correct_bracketing(\"><<>\")\n    False\n    \"\"\"\n    balance = 0\n    for char in brackets:\n        if char == \"<\":\n            balance += 1\n        elif char == \">\":\n            balance -= 1\n        \n        # If balance is negative, a closing bracket appeared without a match\n        if balance < 0:\n            return False\n            \n    # If balance is zero, all brackets were matched\n    return balance == 0\n```"}
{"task_id": "HumanEval/57", "entry_point": "monotonic", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 298, "latency_s": 12.07, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To determine if a list is monotonic, we need to check if it is either entirely non-increasing or entirely non-decreasing. \n\nA list is non-decreasing if for every index $i$, $l[i] \\le l[i+1]$.\nA list is non-increasing if for every index $i$, $l[i] \\ge l[i+1]$.\n\nIf either condition holds true for the entire list, the function returns `True`. If neither holds, it returns `False`. Empty lists or lists with a single element are considered monotonic by definition.\n\n```python\ndef monotonic(l: list):\n    \"\"\"Return True is list elements are monotonically increasing or decreasing.\n    >>> monotonic([1, 2, 4, 20])\n    True\n    >>> monotonic([1, 20, 4, 10])\n    False\n    >>> monotonic([4, 1, 0, -10])\n    True\n    \"\"\"\n    is_increasing = True\n    is_decreasing = True\n    \n    for i in range(len(l) - 1):\n        if l[i] > l[i+1]:\n            is_increasing = False\n        if l[i] < l[i+1]:\n            is_decreasing = False\n            \n    return is_increasing or is_decreasing\n```"}
{"task_id": "HumanEval/58", "entry_point": "common", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 263, "latency_s": 12.16, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I will convert both lists into sets to efficiently find the intersection. This automatically handles uniqueness. I will then sort the resulting intersection to meet the requirement of returning a sorted list.\n\nComplexity:\n- Time: O(N + M + K log K), where N and M are the lengths of the lists and K is the number of common elements.\n- Space: O(N + M) to store the sets.\n\n```python\ndef common(l1: list, l2: list):\n    \"\"\"Return sorted unique common elements for two lists.\n    >>> common([1, 4, 3, 34, 653, 2, 5], [5, 7, 1, 5, 9, 653, 121])\n    [1, 5, 653]\n    >>> common([5, 3, 2, 8], [3, 2])\n    [2, 3]\n\n    \"\"\"\n    set1 = set(l1)\n    set2 = set(l2)\n    intersection = set1.intersection(set2)\n    return sorted(list(intersection))\n```"}
{"task_id": "HumanEval/59", "entry_point": "largest_prime_factor", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 269, "latency_s": 13.04, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To find the largest prime factor of a number $n$, we can use a variation of trial division. We start by dividing out all factors of 2, then proceed to check odd numbers starting from 3. By dividing $n$ by each factor as many times as possible, the smallest remaining factor at any step is guaranteed to be prime. The process continues until $n$ is reduced to 1. The last factor used to divide $n$ (or the remaining $n$ if it's greater than 1) will be the largest prime factor.\n\nComplexity: $O(\\sqrt{n})$ in the worst case (when $n$ is a product of two large primes).\n\n```python\ndef largest_prime_factor(n: int) -> int:\n    \"\"\"Return the largest prime factor of n. Assume n > 1 and is not a prime.\n    >>> largest_prime_factor(13195)\n    29\n    >>> largest_prime_factor(2048)\n    2\n    \"\"\"\n    d = 2\n    while d * d <= n:\n        if n % d == 0:\n            n //= d\n        else:\n            d += 1\n    return n\n```"}
{"task_id": "HumanEval/60", "entry_point": "sum_to_n", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 188, "latency_s": 11.56, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I will use the arithmetic series formula $S = \\frac{n(n+1)}{2}$. This approach is more efficient than iterating through a loop, as it provides a constant time complexity $O(1)$.\n\n```python\ndef sum_to_n(n: int) -> int:\n    \"\"\"sum_to_n is a function that sums numbers from 1 to n.\n    >>> sum_to_n(30)\n    465\n    >>> sum_to_n(100)\n    5050\n    >>> sum_to_n(5)\n    15\n    >>> sum_to_n(10)\n    55\n    >>> sum_to_n(1)\n    1\n    \"\"\"\n    return n * (n + 1) // 2\n```"}
{"task_id": "HumanEval/61", "entry_point": "correct_bracketing", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 344, "latency_s": 12.09, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we can use a counter to track the balance of the brackets. We iterate through the string character by character:\n1. Increment the counter for every opening bracket `(`.\n2. Decrement the counter for every closing bracket `)`.\n3. If the counter ever drops below zero, it means there is a closing bracket without a preceding opening bracket (e.g., `\")(\"`), so we return `False` immediately.\n4. After the loop, the counter must be exactly zero for the string to be balanced (ensuring every `(` was closed).\n\nComplexity:\n- Time: O(n) where n is the length of the string.\n- Space: O(1) as we only store an integer counter.\n\n```python\ndef correct_bracketing(brackets: str) -> bool:\n    \"\"\" brackets is a string of \"(\" and \")\".\n    return True if every opening bracket has a corresponding closing bracket.\n\n    >>> correct_bracketing(\"(\")\n    False\n    >>> correct_bracketing(\"()\")\n    True\n    >>> correct_bracketing(\"(()())\")\n    True\n    >>> correct_bracketing(\")(()\")\n    False\n    \"\"\"\n    balance = 0\n    for char in brackets:\n        if char == '(':\n            balance += 1\n        elif char == ')':\n            balance -= 1\n        \n        # If balance is negative, a closing bracket appeared without an opening one\n        if balance < 0:\n            return False\n            \n    # The string is correct only if all opened brackets are closed\n    return balance == 0\n```"}
{"task_id": "HumanEval/62", "entry_point": "derivative", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 503, "latency_s": 14.8, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To find the derivative of a polynomial given its coefficients, we apply the power rule: $\\frac{d}{dx}(ax^n) = n \\cdot ax^{n-1}$. \n\nFor a polynomial $P(x) = \\sum_{i=0}^{n} a_i x^i$:\n1. The constant term $a_0$ (at index 0) disappears.\n2. The term $a_1 x^1$ becomes $1 \\cdot a_1 x^0$, which is $a_1$ at index 0 of the new list.\n3. The term $a_i x^i$ becomes $i \\cdot a_i x^{i-1}$, which is $i \\cdot a_i$ at index $i-1$ of the new list.\n\nEdge cases:\n- If the input list has only one element (a constant), the derivative is 0, represented as an empty list or `[0]`. Based on the provided examples, a list of length $N$ results in a list of length $N-1$. If the input is `[c]`, the result should be `[]`.\n\n```python\ndef derivative(xs: list):\n    \"\"\" xs represent coefficients of a polynomial.\n    xs[0] + xs[1] * x + xs[2] * x^2 + ....\n     Return derivative of this polynomial in the same form.\n    >>> derivative([3, 1, 2, 4, 5])\n    [1, 4, 12, 20]\n    >>> derivative([1, 2, 3])\n    [2, 6]\n    \"\"\"\n    if len(xs) <= 1:\n        return []\n    \n    # The derivative of a_0 + a_1*x + a_2*x^2 + ... + a_n*x^n\n    # is a_1 + 2*a_2*x + 3*a_3*x^2 + ... + n*a_n*x^{n-1}\n    # The new coefficient at index i is (i+1) * xs[i+1]\n    return [i * xs[i] for i in range(1, len(xs))]\n```"}
{"task_id": "HumanEval/63", "entry_point": "fibfib", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 435, "latency_s": 16.69, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem efficiently, we need to compute the $n$-th term of a sequence where each term is the sum of the three preceding terms (a Tribonacci-like sequence). Since $n$ can be large, a recursive approach without memoization would result in exponential time complexity. Instead, an iterative approach using dynamic programming (or simply keeping track of the last three values) allows us to compute the result in $O(n)$ time and $O(1)$ space.\n\nEdge cases:\n- $n=0, 1, 2$ are the base cases defined in the prompt.\n- For $n < 0$, the behavior isn't defined, but we assume $n \\ge 0$.\n\n```python\ndef fibfib(n: int):\n    \"\"\"The FibFib number sequence is a sequence similar to the Fibbonacci sequnece that's defined as follows:\n    fibfib(0) == 0\n    fibfib(1) == 0\n    fibfib(2) == 1\n    fibfib(n) == fibfib(n-1) + fibfib(n-2) + fibfib(n-3).\n    Please write a function to efficiently compute the n-th element of the fibfib number sequence.\n    >>> fibfib(1)\n    0\n    >>> fibfib(5)\n    4\n    >>> fibfib(8)\n    24\n    \"\"\"\n    if n == 0:\n        return 0\n    if n == 1:\n        return 0\n    if n == 2:\n        return 1\n    \n    # We use three variables to store the previous three values to achieve O(1) space\n    a, b, c = 0, 0, 1\n    for _ in range(3, n + 1):\n        next_val = a + b + c\n        a, b, c = b, c, next_val\n        \n    return c\n```"}
{"task_id": "HumanEval/64", "entry_point": "vowels_count", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 336, "latency_s": 18.35, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through each character of the input string. We check if the character is one of the standard vowels ('a', 'e', 'i', 'o', 'u') in either lowercase or uppercase. Additionally, we check if the character 'y' (or 'Y') is at the very last position of the string.\n\nComplexity:\n- Time Complexity: O(n), where n is the length of the string, as we iterate through the string once.\n- Space Complexity: O(1), as we only use a constant amount of extra space for the counter and the set of vowels.\n\n```python\ndef vowels_count(s):\n    \"\"\"Write a function vowels_count which takes a string representing\n    a word as input and returns the number of vowels in the string.\n    Vowels in this case are 'a', 'e', 'i', 'o', 'u'. Here, 'y' is also a\n    vowel, but only when it is at the end of the given word.\n\n    Example:\n    >>> vowels_count(\"abcde\")\n    2\n    >>> vowels_count(\"ACEDY\")\n    3\n    \"\"\"\n    count = 0\n    vowels = set(\"aeiouAEIOU\")\n    \n    for i, char in enumerate(s):\n        if char in vowels:\n            count += 1\n        elif char.lower() == 'y' and i == len(s) - 1:\n            count += 1\n            \n    return count\n```"}
{"task_id": "HumanEval/65", "entry_point": "circular_shift", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 1001, "latency_s": 25.78, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to:\n1. Convert the integer `x` to a string to easily manipulate the digits.\n2. Determine the number of digits $n$.\n3. Handle the special condition: if `shift` is greater than $n$, the result should be the digits of $x$ reversed.\n4. Otherwise, perform a circular right shift. A right shift by $k$ means the last $k$ digits move to the front. This can be achieved using string slicing: `s[-shift:] + s[:-shift]`.\n5. Note: If `shift` is 0 or a multiple of $n$ (and not greater than $n$), the string remains unchanged.\n\n```python\ndef circular_shift(x, shift):\n    \"\"\"Circular shift the digits of the integer x, shift the digits right by shift\n    and return the result as a string.\n    If shift > number of digits, return digits reversed.\n    >>> circular_shift(12, 1)\n    \"21\"\n    >>> circular_shift(12, 2)\n    \"12\"\n    \"\"\"\n    s = str(x)\n    n = len(s)\n    \n    if shift > n:\n        return s[::-1]\n    \n    if n == 0:\n        return \"\"\n        \n    # Handle shift = 0 or shift = n (which results in the same string)\n    # The slice logic handles this naturally, but we ensure shift is within bounds\n    shift = shift % n\n    if shift == 0 and shift != 0: # Logic check: if shift was n, it becomes 0\n        pass \n        \n    # Standard circular right shift\n    # If shift is 1, \"12\" -> \"2\" + \"1\" = \"21\"\n    # If shift is 2, \"12\" -> \"12\" (since 2 % 2 == 0)\n    # However, the docstring implies shift 2 on \"12\" returns \"12\".\n    # Let's refine: if shift is a multiple of n, it's the original string.\n    \n    # Re-evaluating based on docstring: \n    # circular_shift(12, 1) -> \"21\" (Right shift 1)\n    # circular_shift(12, 2) -> \"12\" (Right shift 2 is same as 0)\n    \n    # If shift is 0, it's the original string.\n    # If shift is 1, it's s[-1:] + s[:-1]\n    # If shift is 2, it's s[-2:] + s[:-2]\n    \n    # Since we already handled shift > n, we can use modulo for shift == n\n    # but the prompt says \"shift the digits right by shift\".\n    # If shift = 2 and n = 2, s[-2:] + s[:-2] is s + \"\" which is s.\n    \n    # Correct logic for circular shift:\n    # The number of positions to move from the end to the front is shift % n.\n    # But if shift > n, we return reversed.\n    \n    # Let's re-check: if shift = 2, n = 2, shift % n = 0.\n    # s[-0:] + s[:-0] would be s + s (incorrect).\n    # We need to handle the 0 case for slicing.\n    \n    k = shift % n\n    if k == 0:\n        return s\n    return s[-k:] + s[:-k]\n```\n\nWait, the logic above for `k=0` is safer. Let's provide the clean version.\n\n```python\ndef circular_shift(x, shift):\n    \"\"\"Circular shift the digits of the integer x, shift the digits right by shift\n    and return the result as a string.\n    If shift > number of digits, return digits reversed.\n    >>> circular_shift(12, 1)\n    \"21\"\n    >>> circular_shift(12, 2)\n    \"12\"\n    \"\"\"\n    s = str(x)\n    n = len(s)\n    \n    if shift > n:\n        return s[::-1]\n    \n    k = shift % n\n    if k == 0:\n        return s\n    \n    return s[-k:] + s[:-k]\n```"}
{"task_id": "HumanEval/66", "entry_point": "digitSum", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 281, "latency_s": 23.27, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I will iterate through each character in the input string. For each character, I will check if it is an uppercase letter using the `.isupper()` method. If it is, I will retrieve its ASCII value using the `ord()` function and add it to a running total. If the string is empty or contains no uppercase letters, the function will return 0.\n\nComplexity:\n- Time Complexity: O(n), where n is the length of the string.\n- Space Complexity: O(1), as we only store the running sum.\n\n```python\ndef digitSum(s):\n    \"\"\"Task\n    Write a function that takes a string as input and returns the sum of the upper characters only'\n    ASCII codes.\n\n    Examples:\n        digitSum(\"\") => 0\n        digitSum(\"abAB\") => 131\n        digitSum(\"abcCd\") => 67\n        digitSum(\"helloE\") => 69\n        digitSum(\"woArBld\") => 131\n        digitSum(\"aAaaaXa\") => 153\n    \"\"\"\n    total_sum = 0\n    for char in s:\n        if char.isupper():\n            total_sum += ord(char)\n    return total_sum\n```"}
{"task_id": "HumanEval/67", "entry_point": "fruit_distribution", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 385, "latency_s": 22.71, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I need to extract the numerical values associated with \"apples\" and \"oranges\" from the input string. Since the string format is consistent (e.g., \"X apples and Y oranges\"), I can use a regular expression to find all integers in the string. Once I have the counts for apples and oranges, I subtract them from the total number of fruits provided as the second argument to find the number of mangoes.\n\nComplexity:\n- Time Complexity: O(N) where N is the length of the string, as we scan the string once to find numbers.\n- Space Complexity: O(1) as we only store a few integer variables.\n\n```python\nimport re\n\ndef fruit_distribution(s, n):\n    \"\"\"\n    In this task, you will be given a string that represents a number of apples and oranges \n    that are distributed in a basket of fruit this basket contains \n    apples, oranges, and mango fruits. Given the string that represents the total number of \n    the oranges and apples and an integer that represent the total number of the fruits \n    in the basket return the number of the mango fruits in the basket.\n    \"\"\"\n    # Use regular expression to find all numbers in the string\n    numbers = re.findall(r'\\d+', s)\n    \n    # Convert the found strings to integers\n    # Based on the examples, the first number is apples and the second is oranges\n    apples = int(numbers[0]) if len(numbers) > 0 else 0\n    oranges = int(numbers[1]) if len(numbers) > 1 else 0\n    \n    # The number of mangoes is the total minus apples and oranges\n    mangoes = n - apples - oranges\n    return mangoes\n```"}
{"task_id": "HumanEval/68", "entry_point": "pluck", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 345, "latency_s": 22.84, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through the array once to identify all even numbers. We keep track of the minimum even value encountered and its corresponding index. By initializing the minimum value to infinity and updating it only when we find a strictly smaller even number, we naturally preserve the smallest index for duplicate values.\n\nComplexity:\n- Time: O(n), where n is the length of the array, as we traverse the list once.\n- Space: O(1), as we only store a few variables.\n\n```python\ndef pluck(arr):\n    \"\"\"\n    \"Given an array representing a branch of a tree that has non-negative integer nodes\n    your task is to pluck one of the nodes and return it.\n    The plucked node should be the node with the smallest even value.\n    If multiple nodes with the same smallest even value are found return the node that has smallest index.\n\n    The plucked node should be returned in a list, [ smalest_value, its index ],\n    If there are no even values or the given array is empty, return [].\n    \"\"\"\n    if not arr:\n        return []\n\n    min_even_val = float('inf')\n    min_index = -1\n\n    for i, val in enumerate(arr):\n        if val % 2 == 0:\n            if val < min_even_val:\n                min_even_val = val\n                min_index = i\n    \n    if min_index == -1:\n        return []\n    \n    return [min_even_val, min_index]\n```"}
{"task_id": "HumanEval/69", "entry_point": "search", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 364, "latency_s": 15.65, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to count the occurrences of each integer in the provided list. Then, we filter these integers to find those whose frequency is greater than or equal to their value. From that filtered set, we identify the maximum value. If no such value exists, we return -1.\n\nComplexity:\n- Time: O(n), where n is the length of the list, as we iterate through the list once to count frequencies and once through the unique keys.\n- Space: O(k), where k is the number of unique integers in the list, to store the frequency map.\n\n```python\nfrom collections import Counter\n\ndef search(lst):\n    '''\n    You are given a non-empty list of positive integers. Return the greatest integer that is greater than \n    zero, and has a frequency greater than or equal to the value of the integer itself. \n    The frequency of an integer is the number of times it appears in the list.\n    If no such a value exist, return -1.\n    Examples:\n        search([4, 1, 2, 2, 3, 1]) == 2\n        search([1, 2, 2, 3, 3, 3, 4, 4, 4]) == 3\n        search([5, 5, 4, 4, 4]) == -1\n    '''\n    counts = Counter(lst)\n    max_val = -1\n    \n    for num, freq in counts.items():\n        if freq >= num:\n            if num > max_val:\n                max_val = num\n                \n    return max_val\n```"}
{"task_id": "HumanEval/70", "entry_point": "strange_sort_list", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 391, "latency_s": 16.91, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to sort the list first to easily access the smallest and largest elements. We then use a two-pointer approach (or a deque) to pick the minimum from the start and the maximum from the end of the sorted list alternately until all elements are processed.\n\nComplexity:\n- Time: $O(N \\log N)$ due to the initial sort.\n- Space: $O(N)$ to store the result list.\n\n```python\ndef strange_sort_list(lst):\n    '''\n    Given list of integers, return list in strange order.\n    Strange sorting, is when you start with the minimum value,\n    then maximum of the remaining integers, then minimum and so on.\n\n    Examples:\n    strange_sort_list([1, 2, 3, 4]) == [1, 4, 2, 3]\n    strange_sort_list([5, 5, 5, 5]) == [5, 5, 5, 5]\n    strange_sort_list([]) == []\n    '''\n    if not lst:\n        return []\n    \n    # Sort the list to easily pick min and max\n    sorted_lst = sorted(lst)\n    result = []\n    \n    left = 0\n    right = len(sorted_lst) - 1\n    \n    # Alternate between picking from the left (min) and right (max)\n    while left <= right:\n        # Pick minimum\n        result.append(sorted_lst[left])\n        left += 1\n        \n        # Check if there are still elements left for the maximum\n        if left <= right:\n            result.append(sorted_lst[right])\n            right -= 1\n            \n    return result\n```"}
{"task_id": "HumanEval/71", "entry_point": "triangle_area", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 331, "latency_s": 16.3, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To calculate the area of a triangle given three sides, we use Heron's Formula. First, we must validate the triangle inequality: the sum of any two sides must be strictly greater than the third side. If valid, we calculate the semi-perimeter $s = (a + b + c) / 2$ and the area $A = \\sqrt{s(s-a)(s-b)(s-c)}$.\n\n```python\nimport math\n\ndef triangle_area(a, b, c):\n    '''\n    Given the lengths of the three sides of a triangle. Return the area of\n    the triangle rounded to 2 decimal points if the three sides form a valid triangle. \n    Otherwise return -1\n    Three sides make a valid triangle when the sum of any two sides is greater \n    than the third side.\n    Example:\n    triangle_area(3, 4, 5) == 6.00\n    triangle_area(1, 2, 10) == -1\n    '''\n    # Check triangle inequality\n    if (a + b > c) and (a + c > b) and (b + c > a):\n        # Calculate semi-perimeter\n        s = (a + b + c) / 2\n        # Heron's Formula\n        area = math.sqrt(s * (s - a) * (s - b) * (s - c))\n        return round(area, 2)\n    else:\n        return -1\n```"}
{"task_id": "HumanEval/72", "entry_point": "will_it_fly", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 251, "latency_s": 15.21, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to check two conditions:\n1. **Balance**: The list `q` must be a palindrome. A list is a palindrome if it reads the same forwards and backwards (e.g., `q == q[::-1]`).\n2. **Weight**: The sum of all elements in the list `q` must be less than or equal to the maximum weight `w`.\n\nIf both conditions are met, the function returns `True`; otherwise, it returns `False`.\n\n```python\ndef will_it_fly(q, w):\n    '''\n    Write a function that returns True if the object q will fly, and False otherwise.\n    The object q will fly if it's balanced (it is a palindromic list) and the sum of its elements is less than or equal the maximum possible weight w.\n    '''\n    # Check if the list is a palindrome\n    is_balanced = q == q[::-1]\n    \n    # Check if the sum of elements is within the weight limit\n    is_light_enough = sum(q) <= w\n    \n    return is_balanced and is_light_enough\n```"}
{"task_id": "HumanEval/73", "entry_point": "smallest_change", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 408, "latency_s": 15.72, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To find the minimum number of changes required to make an array palindromic, we need to compare elements at symmetric positions from the start and the end of the array. For each pair of indices $(i, n-1-i)$, if the elements are not equal, we must change at least one of them to match the other. Since we want the *minimum* number of changes, we count every pair that is mismatched. If the array has an odd length, the middle element does not need to be changed as it is always symmetric with itself.\n\nComplexity:\n- Time: $O(n)$, where $n$ is the length of the array, as we iterate through half the array.\n- Space: $O(1)$, as we only use a counter variable.\n\n```python\ndef smallest_change(arr):\n    \"\"\"\n    Given an array arr of integers, find the minimum number of elements that\n    need to be changed to make the array palindromic. A palindromic array is an array that\n    is read the same backwards and forwards. In one change, you can change one element to any other element.\n\n    For example:\n    smallest_change([1,2,3,5,4,7,9,6]) == 4\n    smallest_change([1, 2, 3, 4, 3, 2, 2]) == 1\n    smallest_change([1, 2, 3, 2, 1]) == 0\n    \"\"\"\n    changes = 0\n    n = len(arr)\n    # We only need to iterate up to the middle of the array\n    for i in range(n // 2):\n        # Compare element at index i with its symmetric counterpart at the end\n        if arr[i] != arr[n - 1 - i]:\n            changes += 1\n    return changes\n```"}
{"task_id": "HumanEval/74", "entry_point": "total_match", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 226, "latency_s": 13.85, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I will calculate the sum of the lengths of all strings in each list. I will then compare these sums. If the sum of characters in the first list is strictly less than the sum of characters in the second list, I return the first list. If the sum of characters in the second list is strictly less, I return the second list. If the sums are equal, I return the first list as specified.\n\n```python\ndef total_match(lst1, lst2):\n    '''\n    Write a function that accepts two lists of strings and returns the list that has \n    total number of chars in the all strings of the list less than the other list.\n\n    if the two lists have the same number of chars, return the first list.\n    '''\n    sum1 = sum(len(s) for s in lst1)\n    sum2 = sum(len(s) for s in lst2)\n    \n    if sum1 <= sum2:\n        return lst1\n    else:\n        return lst2\n```"}
{"task_id": "HumanEval/75", "entry_point": "is_multiply_prime", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 335, "latency_s": 13.89, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this, we need to determine if a number $a < 100$ can be expressed as the product of exactly three prime numbers. Since the maximum value is small (100), we can use a simple approach:\n1. Identify all prime numbers less than 100.\n2. Iterate through combinations of three primes (allowing duplicates, e.g., $2 \\times 2 \\times 2 = 8$ or $2 \\times 2 \\times 3 = 12$).\n3. Check if their product equals $a$.\n\nAlternatively, we can perform a prime factorization of $a$ and count the number of prime factors (counting multiplicities). If the count is exactly 3, the function returns `True`.\n\n```python\ndef is_multiply_prime(a):\n    \"\"\"Write a function that returns true if the given number is the multiplication of 3 prime numbers\n    and false otherwise.\n    Knowing that (a) is less then 100. \n    Example:\n    is_multiply_prime(30) == True\n    30 = 2 * 3 * 5\n    \"\"\"\n    count = 0\n    temp = a\n    d = 2\n    # Standard prime factorization algorithm\n    while d * d <= temp:\n        while temp % d == 0:\n            count += 1\n            temp //= d\n        d += 1\n    if temp > 1:\n        count += 1\n    \n    return count == 3\n```"}
{"task_id": "HumanEval/76", "entry_point": "is_simple_power", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 504, "latency_s": 16.74, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To determine if $x$ is a simple power of $n$ ($n^k = x$ for some non-negative integer $k$), we need to consider several cases:\n1. If $x = 1$, it is always a power of any $n > 0$ (since $n^0 = 1$). However, if $n=1$, $1^k$ is always 1, so $x=1$ is true.\n2. If $n = 1$, $x$ must be 1 to be a power.\n3. If $n > 1$ and $x > 1$, we can repeatedly divide $x$ by $n$. If $x$ eventually becomes 1 and is divisible by $n$ at every step, it is a simple power.\n4. If $x$ is less than 1 or $n$ is 0/negative, the logic follows standard exponentiation rules, but based on the examples provided, we are dealing with positive integers.\n\nComplexity: $O(\\log_n x)$ time complexity as we divide $x$ by $n$ in each step.\n\n```python\ndef is_simple_power(x, n):\n    \"\"\"Your task is to write a function that returns true if a number x is a simple\n    power of n and false in other cases.\n    x is a simple power of n if n**int=x\n    \"\"\"\n    # Any number to the power of 0 is 1.\n    if x == 1:\n        return True\n    \n    # If n is 1, and x is not 1 (handled above), it's impossible.\n    if n == 1:\n        return x == 1\n    \n    # If n is 0, 0^k is 0 (for k > 0).\n    if n == 0:\n        return x == 0\n\n    # Standard case: check if x is a power of n by repeated division.\n    # We use a loop to ensure x is divisible by n at every step until it reaches 1.\n    temp_x = x\n    while temp_x > 1 and temp_x % n == 0:\n        temp_x //= n\n        \n    return temp_x == 1\n```"}
{"task_id": "HumanEval/77", "entry_point": "iscube", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 426, "latency_s": 16.94, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To determine if an integer $a$ is a perfect cube, we need to find an integer $x$ such that $x^3 = a$. \n\n**Approach:**\n1. Handle the sign: Since the cube of a negative number is negative (e.g., $(-2)^3 = -8$), we can work with the absolute value of $a$ and then check the cube root.\n2. Calculate the cube root: Use the power operator `** (1/3)`.\n3. Rounding: Due to floating-point precision issues (e.g., `64**(1/3)` might result in `3.9999999999999996`), we round the result to the nearest integer.\n4. Verification: Check if the cube of that rounded integer equals the original input $a$.\n\n**Complexity:**\n- Time Complexity: $O(1)$ (constant time for basic arithmetic).\n- Space Complexity: $O(1)$.\n\n```python\ndef iscube(a):\n    '''\n    Write a function that takes an integer a and returns True \n    if this ingeger is a cube of some integer number.\n    Note: you may assume the input is always valid.\n    Examples:\n    iscube(1) ==> True\n    iscube(2) ==> False\n    iscube(-1) ==> True\n    iscube(64) ==> True\n    iscube(0) ==> True\n    iscube(180) ==> False\n    '''\n    # Handle the absolute value to simplify the cube root calculation\n    abs_a = abs(a)\n    \n    # Calculate the cube root and round it to the nearest integer\n    # to account for floating point precision errors.\n    root = round(abs_a ** (1/3))\n    \n    # Check if the cube of the rounded root equals the absolute value\n    return root ** 3 == abs_a\n```"}
{"task_id": "HumanEval/78", "entry_point": "hex_key", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 554, "latency_s": 20.66, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through each character of the input hexadecimal string. We then convert each character to its corresponding decimal value. The hexadecimal digits that are prime numbers are 2, 3, 5, 7, 11 (B), and 13 (D). We count how many times these specific values appear in the input string.\n\nComplexity:\n- Time Complexity: O(n), where n is the length of the input string.\n- Space Complexity: O(1), as we only use a constant amount of extra space for the count.\n\n```python\ndef hex_key(num):\n    \"\"\"You have been tasked to write a function that receives \n    a hexadecimal number as a string and counts the number of hexadecimal \n    digits that are primes (prime number, or a prime, is a natural number \n    greater than 1 that is not a product of two smaller natural numbers).\n    Hexadecimal digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.\n    Prime numbers are 2, 3, 5, 7, 11, 13, 17,...\n    So you have to determine a number of the following digits: 2, 3, 5, 7, \n    B (=decimal 11), D (=decimal 13).\n    Note: you may assume the input is always correct or empty string, \n    and symbols A,B,C,D,E,F are always uppercase.\n    Examples:\n    For num = \"AB\" the output should be 1.\n    For num = \"1077E\" the output should be 2.\n    For num = \"ABED1A33\" the output should be 4.\n    For num = \"123456789ABCDEF0\" the output should be 6.\n    For num = \"2020\" the output should be 2.\n    \"\"\"\n    # The set of hexadecimal digits that are prime numbers\n    # 2, 3, 5, 7, B (11), D (13)\n    primes = {'2', '3', '5', '7', 'B', 'D'}\n    \n    count = 0\n    for char in num:\n        if char in primes:\n            count += 1\n            \n    return count\n```"}
{"task_id": "HumanEval/79", "entry_point": "decimal_to_binary", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 338, "latency_s": 20.69, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To convert a decimal number to a binary string, we can use Python's built-in `bin()` function, which returns a string starting with '0b'. We can slice off the '0b' prefix, convert the remaining bits to a string, and then wrap the result with the required 'db' characters.\n\nComplexity:\n- Time Complexity: O(log n), where n is the decimal number, as the number of bits is proportional to the logarithm of the number.\n- Space Complexity: O(log n) to store the resulting string.\n\n```python\ndef decimal_to_binary(decimal):\n    \"\"\"You will be given a number in decimal form and your task is to convert it to\n    binary format. The function should return a string, with each character representing a binary\n    number. Each character in the string will be '0' or '1'.\n\n    There will be an extra couple of characters 'db' at the beginning and at the end of the string.\n    The extra characters are there to help with the format.\n\n    Examples:\n    decimal_to_binary(15)   # returns \"db1111db\"\n    decimal_to_binary(32)   # returns \"db100000db\"\n    \"\"\"\n    # bin(decimal) returns a string like '0b1111'\n    # We slice from index 2 to remove the '0b'\n    binary_representation = bin(decimal)[2:]\n    return f\"db{binary_representation}db\"\n```"}
{"task_id": "HumanEval/80", "entry_point": "is_happy", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 378, "latency_s": 19.26, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to check two conditions:\n1. The length of the string must be at least 3.\n2. For every sequence of three consecutive characters, all three must be unique.\n\nI will iterate through the string starting from index 0 up to `len(s) - 3`. For each position `i`, I will check if the characters at `i`, `i+1`, and `i+2` are distinct by converting them into a set and checking if the size of that set is 3.\n\nComplexity:\n- Time: O(n), where n is the length of the string, as we traverse the string once.\n- Space: O(1), as the set will contain at most 3 characters.\n\n```python\ndef is_happy(s):\n    \"\"\"You are given a string s.\n    Your task is to check if the string is happy or not.\n    A string is happy if its length is at least 3 and every 3 consecutive letters are distinct\n    For example:\n    is_happy(a) => False\n    is_happy(aa) => False\n    is_happy(abcd) => True\n    is_happy(aabb) => False\n    is_happy(adb) => True\n    is_happy(xyy) => False\n    \"\"\"\n    if len(s) < 3:\n        return False\n    \n    for i in range(len(s) - 2):\n        # Extract three consecutive characters\n        triplet = s[i:i+3]\n        # Check if all three are distinct using a set\n        if len(set(triplet)) != 3:\n            return False\n            \n    return True\n```"}
{"task_id": "HumanEval/81", "entry_point": "numerical_letter_grade", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 677, "latency_s": 22.13, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I will iterate through the list of GPAs and apply a series of conditional checks. Since the table uses \"greater than\" (`>`) for most grades and \"equal to\" for the boundaries (4.0 and 0.0), I will order the checks from highest to lowest. This ensures that a GPA like 3.8 is caught by the `> 3.7` (A) condition before it can be evaluated by lower conditions.\n\nComplexity:\n- Time: O(n) where n is the number of grades.\n- Space: O(n) to store the resulting list of letter grades.\n\n```python\ndef numerical_letter_grade(grades):\n    \"\"\"It is the last week of the semester and the teacher has to give the grades\n    to students. The teacher has been making her own algorithm for grading.\n    The only problem is, she has lost the code she used for grading.\n    She has given you a list of GPAs for some students and you have to write \n    a function that can output a list of letter grades using the following table:\n             GPA       |    Letter grade\n              4.0                A+\n            > 3.7                A \n            > 3.3                A- \n            > 3.0                B+\n            > 2.7                B \n            > 2.3                B-\n            > 2.0                C+\n            > 1.7                C\n            > 1.3                C-\n            > 1.0                D+ \n            > 0.7                D \n            > 0.0                D-\n              0.0                E\n    \"\"\"\n    letter_grades = []\n    for gpa in grades:\n        if gpa == 4.0:\n            letter_grades.append(\"A+\")\n        elif gpa > 3.7:\n            letter_grades.append(\"A\")\n        elif gpa > 3.3:\n            letter_grades.append(\"A-\")\n        elif gpa > 3.0:\n            letter_grades.append(\"B+\")\n        elif gpa > 2.7:\n            letter_grades.append(\"B\")\n        elif gpa > 2.3:\n            letter_grades.append(\"B-\")\n        elif gpa > 2.0:\n            letter_grades.append(\"C+\")\n        elif gpa > 1.7:\n            letter_grades.append(\"C\")\n        elif gpa > 1.3:\n            letter_grades.append(\"C-\")\n        elif gpa > 1.0:\n            letter_grades.append(\"D+\")\n        elif gpa > 0.7:\n            letter_grades.append(\"D\")\n        elif gpa > 0.0:\n            letter_grades.append(\"D-\")\n        else: # This covers gpa == 0.0\n            letter_grades.append(\"E\")\n    return letter_grades\n```"}
{"task_id": "HumanEval/82", "entry_point": "prime_length", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 253, "latency_s": 18.7, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To determine if the length of a string is a prime number, we first calculate the length of the input string. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. We handle the edge cases where the length is less than 2 (not prime) and then check for divisibility up to the square root of the length for efficiency.\n\n```python\nimport math\n\ndef prime_length(string):\n    \"\"\"Write a function that takes a string and returns True if the string\n    length is a prime number or False otherwise\n    Examples\n    prime_length('Hello') == True\n    prime_length('abcdcba') == True\n    prime_length('kittens') == True\n    prime_length('orange') == False\n    \"\"\"\n    n = len(string)\n    \n    if n < 2:\n        return False\n    \n    # Check for factors from 2 up to the square root of n\n    for i in range(2, int(math.sqrt(n)) + 1):\n        if n % i == 0:\n            return False\n            \n    return True\n```"}
{"task_id": "HumanEval/83", "entry_point": "starts_one_ends", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 766, "latency_s": 23.51, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to count the number of $n$-digit positive integers that start with 1, end with 1, or both.\n\n1.  **Total $n$-digit numbers**: The range is from $10^{n-1}$ to $10^n - 1$. The total count is $9 \\times 10^{n-1}$.\n2.  **Numbers starting with 1**: The first digit is fixed as 1. The remaining $n-1$ positions can be any digit from 0-9. There are $10^{n-1}$ such numbers.\n3.  **Numbers ending with 1**: The last digit is fixed as 1. The first digit can be any digit from 1-9 (since it's an $n$-digit number), and the middle $n-2$ digits can be any digit from 0-9. There are $9 \\times 10^{n-2}$ such numbers.\n4.  **Numbers starting and ending with 1 (Intersection)**: The first digit is 1, the last digit is 1. The middle $n-2$ digits can be any digit from 0-9. There are $10^{n-2}$ such numbers.\n    *   *Note*: If $n=1$, the only number is 1, which starts and ends with 1. The formula $10^{n-2}$ doesn't apply directly for $n=1$. For $n=1$, the count is simply 1.\n\n**Inclusion-Exclusion Principle**:\nCount = (Starts with 1) + (Ends with 1) - (Starts and ends with 1)\nFor $n > 1$:\nCount = $10^{n-1} + 9 \\times 10^{n-2} - 10^{n-2}$\nCount = $10^{n-1} + 8 \\times 10^{n-2}$\n\nFor $n = 1$:\nThe only 1-digit number starting or ending with 1 is \"1\". Count = 1.\nUsing the formula for $n=1$: $10^0 + 8 \\times 10^{-1}$ is not applicable. However, the logic \"Starts with 1\" gives 1, \"Ends with 1\" gives 1, and \"Both\" gives 1. $1 + 1 - 1 = 1$.\n\n```python\ndef starts_one_ends(n):\n    \"\"\"\n    Given a positive integer n, return the count of the numbers of n-digit\n    positive integers that start or end with 1.\n    \"\"\"\n    if n == 1:\n        return 1\n    \n    # Numbers starting with 1: 10^(n-1)\n    # Numbers ending with 1: 9 * 10^(n-2)\n    # Numbers starting and ending with 1: 10^(n-2)\n    # Using Inclusion-Exclusion: A + B - (A \\cap B)\n    # Result = 10^(n-1) + 9 * 10^(n-2) - 10^(n-2)\n    # Result = 10^(n-1) + 8 * 10^(n-2)\n    \n    return 10**(n-1) + 8 * (10**(n-2))\n```"}
{"task_id": "HumanEval/84", "entry_point": "solve", "passed": false, "finish_reason": "stop", "exec_err": " <module>\n    check(solve)\n    ~~~~~^^^^^^^\n  File \"/var/folders/0l/75d7q65918d_j14rb3j30dlm0000gn/T/tmpuw062ciy/cand.py\", line 34, in check\n    assert candidate(1000) == \"1\", \"Error\"\n           ^^^^^^^^^^^^^^^^^^^^^^\nAssertionError: Error\n", "completion_tokens": 609, "latency_s": 26.13, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "The problem description contains a slight contradiction between the text and the examples. The text says \"return the total sum of its digits in binary,\" but the examples show that for a given $N$, we calculate the sum of its binary digits (which is the count of set bits, also known as the Hamming weight) and then return the **binary representation of that sum**.\n\nLet's trace the examples:\n1. $N = 1000$: Binary is `1111101000`. Sum of digits = 6. Binary of 6 is `110`. Wait, the example says output is \"1\". Let's re-examine.\n2. $N = 150$: Binary is `10010110`. Sum of digits = 4. Binary of 4 is `100`. Example says \"110\".\n3. $N = 147$: Binary is `10010011`. Sum of digits = 4. Binary of 4 is `100`. Example says \"1100\".\n\nActually, looking at the examples again:\n- $N=1000 \\rightarrow$ Sum of digits is 6. Binary of 6 is `110`.\n- $N=150 \\rightarrow$ Sum of digits is 4. Binary of 4 is `100`.\n- $N=147 \\rightarrow$ Sum of digits is 4. Binary of 4 is `100`.\n\nThere is a pattern mismatch in the prompt's text vs examples. However, the standard interpretation of \"sum of digits in binary\" is the population count (number of 1s). The prompt asks for the output to be a \"string of binary number\". Given the ambiguity, the most logical interpretation of the prompt's logic (Sum of binary digits $\\rightarrow$ convert that sum to binary string) is implemented below.\n\n```python\ndef solve(N):\n    \"\"\"Given a positive integer N, return the total sum of its digits in binary.\n    \n    Variables:\n        @N integer\n             Constraints: 0 \u2264 N \u2264 10000.\n    Output:\n         a string of binary number\n    \"\"\"\n    # Step 1: Calculate the sum of digits in binary (Hamming weight)\n    # bin(N) returns something like '0b1010', so we count '1's.\n    sum_of_digits = bin(N).count('1')\n    \n    # Step 2: Convert that sum into its binary representation as a string\n    # bin(sum_of_digits) returns '0b...', so we strip the '0b' prefix.\n    return bin(sum_of_digits)[2:]\n```"}
{"task_id": "HumanEval/85", "entry_point": "add", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 196, "latency_s": 20.66, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through the list and identify elements that satisfy two conditions:\n1. The index of the element must be odd (1, 3, 5, ...).\n2. The value of the element at that index must be even.\n\nWe can achieve this efficiently using a list comprehension or a generator expression with `enumerate()`, filtering for `i % 2 != 0` and `val % 2 == 0`, and then summing the results.\n\n```python\ndef add(lst):\n    \"\"\"Given a non-empty list of integers lst. add the even elements that are at odd indices.\n\n    Examples:\n        add([4, 2, 6, 7]) ==> 2 \n    \"\"\"\n    return sum(val for i, val in enumerate(lst) if i % 2 != 0 and val % 2 == 0)\n```"}
{"task_id": "HumanEval/86", "entry_point": "anti_shuffle", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 377, "latency_s": 22.07, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through the input string and identify words (sequences of non-space characters) and spaces. For each word, we sort its characters based on their ASCII values while preserving the original position of spaces.\n\n**Approach:**\n1. Split the string into parts while keeping the spaces (or iterate through the string and identify word boundaries).\n2. For every sequence of characters that does not contain a space, sort the characters alphabetically.\n3. Reconstruct the string by joining these sorted words and the original spaces.\n\n**Complexity:**\n- Time: $O(N \\log K)$ where $N$ is the length of the string and $K$ is the length of the longest word (due to sorting).\n- Space: $O(N)$ to store the resulting string.\n\n```python\ndef anti_shuffle(s):\n    \"\"\"\n    Write a function that takes a string and returns an ordered version of it.\n    Ordered version of string, is a string where all words (separated by space)\n    are replaced by a new word where all the characters arranged in\n    ascending order based on ascii value.\n    Note: You should keep the order of words and blank spaces in the sentence.\n    \"\"\"\n    res = []\n    current_word = []\n    \n    for char in s:\n        if char == ' ':\n            if current_word:\n                res.append(\"\".join(sorted(current_word)))\n                current_word = []\n            res.append(' ')\n        else:\n            current_word.append(char)\n            \n    if current_word:\n        res.append(\"\".join(sorted(current_word)))\n        \n    return \"\".join(res)\n```"}
{"task_id": "HumanEval/87", "entry_point": "get_row", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 533, "latency_s": 19.48, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through each row of the nested list and identify the indices where the value matches `x`. For each match, we store the coordinate as a tuple `(row_index, column_index)`. \n\nAfter collecting all coordinates, we need to sort them based on two criteria:\n1. Primary sort: Row index in ascending order.\n2. Secondary sort: Column index in descending order (for the same row).\n\nIn Python, we can achieve this sorting by using a custom key. Since we want ascending for the first element and descending for the second, we can use `(row, -column)` as the sorting key.\n\n```python\ndef get_row(lst, x):\n    \"\"\"\n    You are given a 2 dimensional data, as a nested lists,\n    which is similar to matrix, however, unlike matrices,\n    each row may contain a different number of columns.\n    Given lst, and integer x, find integers x in the list,\n    and return list of tuples, [(x1, y1), (x2, y2) ...] such that\n    each tuple is a coordinate - (row, columns), starting with 0.\n    Sort coordinates initially by rows in ascending order.\n    Also, sort coordinates of the row by columns in descending order.\n    \n    Examples:\n    get_row([\n      [1,2,3,4,5,6],\n      [1,2,3,4,1,6],\n      [1,2,3,4,5,1]\n    ], 1) == [(0, 0), (1, 4), (1, 0), (2, 5), (2, 0)]\n    get_row([], 1) == []\n    get_row([[], [1], [1, 2, 3]], 3) == [(2, 2)]\n    \"\"\"\n    coordinates = []\n    \n    for r_idx, row in enumerate(lst):\n        for c_idx, value in enumerate(row):\n            if value == x:\n                coordinates.append((r_idx, c_idx))\n    \n    # Sort by row ascending, then by column descending\n    # Using -item[1] for the column index handles the descending requirement\n    coordinates.sort(key=lambda pos: (pos[0], -pos[1]))\n    \n    return coordinates\n```"}
{"task_id": "HumanEval/88", "entry_point": "sort_array", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 427, "latency_s": 17.41, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I need to:\n1. Handle edge cases where the array is empty or has only one element (the sum of first and last index values would be the same or non-existent).\n2. Create a copy of the input array to ensure the original remains unchanged.\n3. Calculate the sum of the first and last elements.\n4. Determine the sorting order: ascending if the sum is odd, descending if the sum is even.\n5. Return the sorted copy.\n\nComplexity:\n- Time: O(N log N) due to the sorting algorithm.\n- Space: O(N) to store the copy of the array.\n\n```python\ndef sort_array(array):\n    \"\"\"\n    Given an array of non-negative integers, return a copy of the given array after sorting,\n    you will sort the given array in ascending order if the sum( first index value, last index value) is odd,\n    or sort it in descending order if the sum( first index value, last index value) is even.\n\n    Note:\n    * don't change the given array.\n    \"\"\"\n    if not array:\n        return []\n    \n    # Create a copy to avoid modifying the original array\n    arr_copy = list(array)\n    \n    # If there's only one element, the sum of first and last is just that element\n    # However, the logic remains consistent: sum = arr_copy[0] + arr_copy[-1]\n    first_val = arr_copy[0]\n    last_val = arr_copy[-1]\n    total_sum = first_val + last_val\n    \n    if total_sum % 2 != 0:\n        # Sum is odd: sort ascending\n        arr_copy.sort()\n    else:\n        # Sum is even: sort descending\n        arr_copy.sort(reverse=True)\n        \n    return arr_copy\n```"}
{"task_id": "HumanEval/89", "entry_point": "encrypt", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 583, "latency_s": 21.8, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to determine the shift value. The prompt states the alphabet is rotated such that letters shift \"down by two multiplied to two places.\" This implies a shift of $2 \\times 2 = 4$. \n\nLet's verify with the examples:\n1. `encrypt('hi')` -> `h` (8th letter) + 4 = `l` (12th), `i` (9th) + 4 = `m` (13th). Result: `lm`. Correct.\n2. `encrypt('asdfghjkl')` -> `a`+4=`e`, `s`+4=`w`, `d`+4=`h`, `f`+4=`j`, `g`+4=`k`, `h`+4=`l`, `j`+4=`n`, `k`+4=`o`, `l`+4=`p`. Result: `ewhjklnop`. Correct.\n3. `encrypt('gf')` -> `g`+4=`k`, `f`+4=`j`. Result: `kj`. Correct.\n4. `encrypt('et')` -> `e`+4=`i`, `t`+4=`x`. Result: `ix`. Correct.\n\nThe logic is a Caesar Cipher with a shift of 4. We must handle both lowercase and uppercase letters while keeping non-alphabetic characters unchanged.\n\n```python\ndef encrypt(s):\n    \"\"\"Create a function encrypt that takes a string as an argument and\n    returns a string encrypted with the alphabet being rotated. \n    The alphabet should be rotated in a manner such that the letters \n    shift down by two multiplied to two places.\n    For example:\n    encrypt('hi') returns 'lm'\n    encrypt('asdfghjkl') returns 'ewhjklnop'\n    encrypt('gf') returns 'kj'\n    encrypt('et') returns 'ix'\n    \"\"\"\n    shift = 4\n    result = []\n    for char in s:\n        if char.isalpha():\n            # Determine if the character is uppercase or lowercase to set the base ASCII value\n            start = ord('A') if char.isupper() else ord('a')\n            # Calculate the new character position within the 26-letter alphabet\n            new_char = chr(start + (ord(char) - start + shift) % 26)\n            result.append(new_char)\n        else:\n            # If it's not a letter (space, punctuation, etc.), leave it as is\n            result.append(char)\n    return \"\".join(result)\n```"}
{"task_id": "HumanEval/90", "entry_point": "next_smallest", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 316, "latency_s": 21.11, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To find the second smallest element, we need to identify the unique values in the list and then find the second smallest among them. If the list has fewer than two unique elements, it is impossible to have a \"second smallest\" distinct value, so we return `None`.\n\nComplexity:\n- Time: $O(N)$ to iterate through the list and find unique elements.\n- Space: $O(N)$ in the worst case to store unique elements in a set.\n\n```python\ndef next_smallest(lst):\n    \"\"\"\n    You are given a list of integers.\n    Write a function next_smallest() that returns the 2nd smallest element of the list.\n    Return None if there is no such element.\n    \n    next_smallest([1, 2, 3, 4, 5]) == 2\n    next_smallest([5, 1, 4, 3, 2]) == 2\n    next_smallest([]) == None\n    next_smallest([1, 1]) == None\n    \"\"\"\n    # Use a set to get unique elements\n    unique_elements = list(set(lst))\n    \n    # If there are fewer than 2 unique elements, return None\n    if len(unique_elements) < 2:\n        return None\n    \n    # Sort the unique elements and return the second one\n    unique_elements.sort()\n    return unique_elements[1]\n```"}
{"task_id": "HumanEval/91", "entry_point": "is_bored", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 396, "latency_s": 19.55, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to split the input string into individual sentences based on the delimiters '.', '?', and '!'. After splitting, we should clean each sentence by removing leading/trailing whitespace. A \"boredom\" is defined as a sentence that starts with the word \"I\" (case-sensitive, as per the example). We then count how many such sentences exist.\n\nOne edge case to consider is that splitting by multiple delimiters can result in empty strings (e.g., \"Hello!!\"). We should filter these out before checking the starting word.\n\n```python\nimport re\n\ndef is_bored(S):\n    \"\"\"\n    You'll be given a string of words, and your task is to count the number\n    of boredoms. A boredom is a sentence that starts with the word \"I\".\n    Sentences are delimited by '.', '?' or '!'.\n   \n    For example:\n    >>> is_bored(\"Hello world\")\n    0\n    >>> is_bored(\"The sky is blue. The sun is shining. I love this weather\")\n    1\n    \"\"\"\n    # Use regex to split the string by any of the delimiters: . ? or !\n    # This will create a list of substrings.\n    sentences = re.split(r'[.?!]', S)\n    \n    boredom_count = 0\n    for sentence in sentences:\n        # Strip leading and trailing whitespace\n        trimmed = sentence.strip()\n        \n        # Check if the trimmed sentence is non-empty and starts with \"I\"\n        # We check if the first word is exactly \"I\"\n        if trimmed:\n            words = trimmed.split()\n            if words and words[0] == \"I\":\n                boredom_count += 1\n                \n    return boredom_count\n```"}
{"task_id": "HumanEval/92", "entry_point": "any_int", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 334, "latency_s": 18.5, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to check two conditions:\n1. All three inputs must be of type `int`.\n2. One of the numbers must be equal to the sum of the other two. This can be checked by testing three conditions: $x = y + z$, $y = x + z$, or $z = x + y$.\n\nComplexity:\n- Time Complexity: $O(1)$ as we perform a constant number of arithmetic and type checks.\n- Space Complexity: $O(1)$.\n\n```python\ndef any_int(x, y, z):\n    '''\n    Create a function that takes 3 numbers.\n    Returns true if one of the numbers is equal to the sum of the other two, and all numbers are integers.\n    Returns false in any other cases.\n    \n    Examples\n    any_int(5, 2, 7) \u279e True\n    \n    any_int(3, 2, 2) \u279e False\n\n    any_int(3, -2, 1) \u279e True\n    \n    any_int(3.6, -2.2, 2) \u279e False\n    '''\n    # Check if all inputs are integers\n    if not (isinstance(x, int) and isinstance(y, int) and isinstance(z, int)):\n        return False\n    \n    # Check if any number is the sum of the other two\n    return x == y + z or y == x + z or z == x + y\n```"}
{"task_id": "HumanEval/93", "entry_point": "encode", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 916, "latency_s": 22.27, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through each character of the input string. For each character:\n1. Determine if it is a vowel (a, e, i, o, u).\n2. If it is a vowel, we need to find the character that appears 2 places ahead in the alphabet. Since the problem specifies \"swaps case\" and \"replaces vowels\", we must handle the case logic carefully.\n3. If it is a consonant, we simply swap its case.\n4. If it is a space or non-letter (though the prompt says assume only letters, the example shows spaces), we keep it as is.\n\nWait, looking at the examples:\n`encode('test')` -> `'TGST'`\n- 't' (consonant) -> 'T'\n- 'e' (vowel) -> 'g' (e + 2 = g). But the example shows 'G'. This implies the case swap happens *after* or *during* the vowel transformation.\n- 's' (consonant) -> 'S'\n- 't' (consonant) -> 'T'\n\n`encode('This is a message')` -> `'tHKS KS C MGSSCGG'`\n- 'T' -> 't'\n- 'h' -> 'H'\n- 'i' (vowel) -> 'k' (i + 2 = k). Example shows 'K'.\n- 's' -> 'S'\n- ' ' -> ' '\n- 'i' (vowel) -> 'k' (i + 2 = k). Example shows 'K'.\n- 's' -> 'S'\n- ' ' -> ' '\n- 'a' (vowel) -> 'c' (a + 2 = c). Example shows 'C'.\n- ' ' -> ' '\n- 'm' -> 'M'\n- 'e' (vowel) -> 'g' (e + 2 = g). Example shows 'G'.\n- 's' -> 'S'\n- 's' -> 'S'\n- 'a' (vowel) -> 'c' (a + 2 = c). Example shows 'C'.\n- 'g' -> 'G'\n- 'e' (vowel) -> 'g' (e + 2 = g). Example shows 'G'.\n\nLogic:\n1. If character is a vowel:\n   - Find the letter 2 places ahead.\n   - If the original vowel was lowercase, the result is uppercase.\n   - If the original vowel was uppercase, the result is lowercase.\n2. If character is a consonant:\n   - Swap case.\n3. If character is not a letter:\n   - Keep as is.\n\n```python\ndef encode(message):\n    vowels = \"aeiouAEIOU\"\n    result = []\n    \n    for char in message:\n        if char.isalpha():\n            if char in vowels:\n                # Find the letter 2 places ahead\n                # We use the base (A=65, a=97) to handle wrapping if necessary, \n                # though \"2 places ahead\" usually doesn't wrap for standard vowels.\n                base = ord('A') if char.isupper() else ord('a')\n                # Calculate new position: (current - base + 2) % 26\n                new_pos = (ord(char) - base + 2) % 26\n                new_char = chr(base + new_pos)\n                \n                # Swap case: if original was upper, new is lower; if lower, new is upper\n                if char.isupper():\n                    result.append(new_char.lower())\n                else:\n                    result.append(new_char.upper())\n            else:\n                # Consonant: swap case\n                if char.isupper():\n                    result.append(char.lower())\n                else:\n                    result.append(char.upper())\n        else:\n            # Non-alphabetic characters (like spaces) remain unchanged\n            result.append(char)\n            \n    return \"\".join(result)\n```"}
{"task_id": "HumanEval/94", "entry_point": "skjkasdkd", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 378, "latency_s": 22.99, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I need to:\n1. Identify all prime numbers in the given list. A prime number is an integer greater than 1 that has no positive divisors other than 1 and itself.\n2. Find the maximum prime number among those identified.\n3. Calculate the sum of the digits of that maximum prime number.\n\nEdge cases to consider:\n- The list might contain no prime numbers (the problem implies there will be at least one, but I should handle the case where the max prime is not found).\n- The list might contain negative numbers, 0, or 1, none of which are prime.\n- The numbers can be large, so an efficient primality test (trial division up to the square root) is appropriate.\n\n```python\nimport math\n\ndef skjkasdkd(lst):\n    \"\"\"You are given a list of integers.\n    You need to find the largest prime value and return the sum of its digits.\n    \"\"\"\n    def is_prime(n):\n        if n < 2:\n            return False\n        if n == 2:\n            return True\n        if n % 2 == 0:\n            return False\n        for i in range(3, int(math.sqrt(n)) + 1, 2):\n            if n % i == 0:\n                return False\n        return True\n\n    primes = [x for x in lst if is_prime(x)]\n    \n    if not primes:\n        return 0\n    \n    max_prime = max(primes)\n    \n    # Calculate sum of digits\n    digit_sum = sum(int(digit) for digit in str(max_prime))\n    \n    return digit_sum\n```"}
{"task_id": "HumanEval/95", "entry_point": "check_dict_case", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 710, "latency_s": 26.54, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to:\n1. Check if the dictionary is empty; if so, return `False`.\n2. Verify that every key in the dictionary is a string. If any key is not a string, return `False`.\n3. Check if all keys are lowercase or all keys are uppercase.\n4. A key is considered \"all lowercase\" if `key == key.lower()` and it contains at least one alphabetic character (or simply if it doesn't contain uppercase letters). However, the standard interpretation for \"all lowercase\" in this context is that no key contains uppercase letters, and \"all uppercase\" means no key contains lowercase letters.\n5. We can use the `.islower()` and `.isupper()` methods, but since these return `False` for strings with no alphabetic characters (like \"123\"), we should check if any key contains an uppercase letter for the \"all lower\" check, and if any key contains a lowercase letter for the \"all upper\" check.\n\nActually, a simpler way to satisfy the examples:\n- All keys are lowercase: `all(k.lower() == k for k in dict.keys())`\n- All keys are uppercase: `all(k.upper() == k for k in dict.keys())`\n- We must also ensure all keys are strings first.\n\n```python\ndef check_dict_case(dict):\n    \"\"\"\n    Given a dictionary, return True if all keys are strings in lower \n    case or all keys are strings in upper case, else return False.\n    The function should return False is the given dictionary is empty.\n    \"\"\"\n    if not dict:\n        return False\n    \n    keys = list(dict.keys())\n    \n    # Check if all keys are strings\n    if not all(isinstance(k, str) for k in keys):\n        return False\n    \n    # Check if all keys are lowercase\n    # A key is lowercase if it equals its lower() version\n    all_lower = all(k == k.lower() for k in keys)\n    \n    # Check if all keys are uppercase\n    # A key is uppercase if it equals its upper() version\n    all_upper = all(k == k.upper() for k in keys)\n    \n    # The logic requires that they are either ALL lower or ALL upper.\n    # However, if a key is \"123\", it satisfies both k == k.lower() and k == k.upper().\n    # The examples show that if there is a mix (e.g., \"a\" and \"A\"), it's False.\n    # If all keys are \"a\", \"b\", it's True. If all are \"A\", \"B\", it's True.\n    # If keys are \"123\", \"456\", they satisfy both, so it should return True.\n    \n    # One edge case: if the dict has \"a\" and \"123\", all_lower is True.\n    # If the dict has \"A\" and \"123\", all_upper is True.\n    # If the dict has \"a\" and \"A\", both are False.\n    \n    return all_lower or all_upper\n```"}
{"task_id": "HumanEval/96", "entry_point": "count_up_to", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 377, "latency_s": 27.02, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I will use the Sieve of Eratosthenes algorithm to efficiently find all prime numbers less than $n$. This approach has a time complexity of $O(n \\log \\log n)$, which is optimal for finding primes up to a given limit. I will handle edge cases where $n$ is less than 2 by returning an empty list.\n\n```python\ndef count_up_to(n):\n    \"\"\"Implement a function that takes an non-negative integer and returns an array of the first n\n    integers that are prime numbers and less than n.\n    for example:\n    count_up_to(5) => [2,3]\n    count_up_to(11) => [2,3,5,7]\n    count_up_to(0) => []\n    count_up_to(20) => [2,3,5,7,11,13,17,19]\n    count_up_to(1) => []\n    count_up_to(18) => [2,3,5,7,11,13,17]\n    \"\"\"\n    if n < 2:\n        return []\n    \n    # Sieve of Eratosthenes\n    primes = []\n    is_prime = [True] * n\n    is_prime[0] = is_prime[1] = False\n    \n    for p in range(2, n):\n        if is_prime[p]:\n            primes.append(p)\n            for i in range(p * p, n, p):\n                is_prime[i] = False\n                \n    return primes\n```"}
{"task_id": "HumanEval/97", "entry_point": "multiply", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 273, "latency_s": 19.75, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this, I need to extract the unit digit of each integer. The unit digit of a number can be found using the modulo operator `% 10`. However, since the input can be negative (e.g., -15), I must ensure the result is the absolute value of the unit digit (e.g., the unit digit of -15 is 5). Using `abs(n) % 10` correctly handles both positive and negative integers. Finally, I multiply these two unit digits and return the result.\n\n```python\ndef multiply(a, b):\n    \"\"\"Complete the function that takes two integers and returns \n    the product of their unit digits.\n    Assume the input is always valid.\n    Examples:\n    multiply(148, 412) should return 16.\n    multiply(19, 28) should return 72.\n    multiply(2020, 1851) should return 0.\n    multiply(14,-15) should return 20.\n    \"\"\"\n    unit_a = abs(a) % 10\n    unit_b = abs(b) % 10\n    return unit_a * unit_b\n```"}
{"task_id": "HumanEval/98", "entry_point": "count_upper", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 238, "latency_s": 18.14, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through the string `s` and check two conditions for each character:\n1. Is the index of the character even? (i.e., `i % 2 == 0`)\n2. Is the character an uppercase vowel? (i.e., `char in 'AEIOU'`)\n\nWe can achieve this efficiently using a generator expression inside the `sum()` function, iterating over the string with `enumerate` to keep track of the indices.\n\n```python\ndef count_upper(s):\n    \"\"\"\n    Given a string s, count the number of uppercase vowels in even indices.\n    \n    For example:\n    count_upper('aBCdEf') returns 1\n    count_upper('abcdefg') returns 0\n    count_upper('dBBE') returns 0\n    \"\"\"\n    vowels = \"AEIOU\"\n    count = 0\n    for i, char in enumerate(s):\n        if i % 2 == 0 and char in vowels:\n            count += 1\n    return count\n```"}
{"task_id": "HumanEval/99", "entry_point": "closest_integer", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 434, "latency_s": 15.02, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to convert the input string to a float and then determine the nearest integer. The standard `round()` function in Python uses \"round half to even\" (e.g., `round(0.5)` is 0, `round(1.5)` is 2), which does not match the requirement of \"rounding away from zero\" for equidistant values.\n\nTo implement \"round away from zero\":\n1. Convert the string to a float.\n2. Check the fractional part.\n3. If the fractional part is exactly 0.5, we manually round to the integer with the larger absolute value.\n4. Otherwise, we can use the standard `floor(x + 0.5)` logic for positive numbers and `ceil(x - 0.5)` for negative numbers, or more simply, check if the distance to the floor is greater than the distance to the ceiling.\n\n```python\nimport math\n\ndef closest_integer(value):\n    '''\n    Create a function that takes a value (string) representing a number\n    and returns the closest integer to it. If the number is equidistant\n    from two integers, round it away from zero.\n    '''\n    num = float(value)\n    \n    # Get the floor and ceiling integers\n    lower = math.floor(num)\n    upper = math.ceil(num)\n    \n    # If it's already an integer\n    if lower == upper:\n        return int(lower)\n    \n    # Calculate distances\n    dist_lower = abs(num - lower)\n    dist_upper = abs(num - upper)\n    \n    if dist_lower < dist_upper:\n        return int(lower)\n    elif dist_upper < dist_lower:\n        return int(upper)\n    else:\n        # Equidistant case: round away from zero\n        if num >= 0:\n            return int(upper)\n        else:\n            return int(lower)\n```"}
{"task_id": "HumanEval/100", "entry_point": "make_a_pile", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 372, "latency_s": 14.98, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to generate a sequence of $n$ numbers starting from $n$. The rule for the next number depends on the parity of the current number:\n1. If the current number is odd, the next number is the next odd number (current + 2).\n2. If the current number is even, the next number is the next even number (current + 2).\n\nIn both cases, the rule simplifies to adding 2 to the previous number to maintain the same parity. Since the first level is $n$, the sequence is an arithmetic progression starting at $n$ with a common difference of 2, containing $n$ terms.\n\nComplexity:\n- Time: $O(n)$ to generate $n$ elements.\n- Space: $O(n)$ to store the list of stones.\n\n```python\ndef make_a_pile(n):\n    \"\"\"\n    Given a positive integer n, you have to make a pile of n levels of stones.\n    The first level has n stones.\n    The number of stones in the next level is:\n        - the next odd number if n is odd.\n        - the next even number if n is even.\n    Return the number of stones in each level in a list, where element at index\n    i represents the number of stones in the level (i+1).\n\n    Examples:\n    >>> make_a_pile(3)\n    [3, 5, 7]\n    \"\"\"\n    if n <= 0:\n        return []\n    \n    stones = []\n    current = n\n    for _ in range(n):\n        stones.append(current)\n        current += 2\n    return stones\n```"}
{"task_id": "HumanEval/101", "entry_point": "words_string", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 317, "latency_s": 15.46, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I will use the `re` (regular expression) module. The goal is to split the string by any occurrence of a comma or a space. However, since multiple delimiters might appear consecutively (e.g., \", \" or \"  \"), a simple split might result in empty strings in the resulting list. Using `re.split` with a pattern that matches one or more occurrences of a comma or space, and then filtering out any resulting empty strings, ensures a clean list of words.\n\n```python\nimport re\n\ndef words_string(s):\n    \"\"\"\n    You will be given a string of words separated by commas or spaces. Your task is\n    to split the string into words and return an array of the words.\n    \n    For example:\n    words_string(\"Hi, my name is John\") == [\"Hi\", \"my\", \"name\", \"is\", \"John\"]\n    words_string(\"One, two, three, four, five, six\") == [\"One\", \"two\", \"three\", \"four\", \"five\", \"six\"]\n    \"\"\"\n    # Use regex to split by one or more occurrences of commas or spaces\n    # The [,\\s]+ pattern matches any sequence of commas and whitespace characters\n    words = re.split(r'[,\\s]+', s)\n    \n    # Filter out any empty strings that might occur if the string starts or ends with delimiters\n    return [word for word in words if word]\n```"}
{"task_id": "HumanEval/102", "entry_point": "choose_num", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 359, "latency_s": 16.82, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to check if the range $[x, y]$ is valid (i.e., $x \\le y$). If it is, we look for the largest even integer. The largest integer in the range is $y$. If $y$ is even, it is the answer. If $y$ is odd, the largest even integer would be $y - 1$, provided that $y - 1$ is still greater than or equal to $x$. If $y - 1$ is less than $x$ (which only happens if $y$ is odd and $y = x$), then no even number exists in the range.\n\nComplexity:\n- Time: $O(1)$\n- Space: $O(1)$\n\n```python\ndef choose_num(x, y):\n    \"\"\"This function takes two positive numbers x and y and returns the\n    biggest even integer number that is in the range [x, y] inclusive. If \n    there's no such number, then the function should return -1.\n\n    For example:\n    choose_num(12, 15) = 14\n    choose_num(13, 12) = -1\n    \"\"\"\n    if x > y:\n        return -1\n    \n    # Start from the largest possible integer in the range\n    if y % 2 == 0:\n        return y\n    else:\n        # If y is odd, the largest even number is y - 1\n        candidate = y - 1\n        if candidate >= x:\n            return candidate\n        else:\n            return -1\n```"}
{"task_id": "HumanEval/103", "entry_point": "rounded_avg", "passed": false, "finish_reason": "stop", "exec_err": "ded_avg)\n    ~~~~~^^^^^^^^^^^^^\n  File \"/var/folders/0l/75d7q65918d_j14rb3j30dlm0000gn/T/tmp3z3_2kfh/cand.py\", line 41, in check\n    assert candidate(560,851) == \"0b1011000010\"\n           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\nAssertionError\n", "completion_tokens": 883, "latency_s": 21.91, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to calculate the arithmetic mean of a range of integers from $n$ to $m$. The sum of an arithmetic progression from $n$ to $m$ is given by the formula:\n$\\text{Sum} = \\frac{(n + m) \\times (\\text{number of terms})}{2}$\nwhere the number of terms is $(m - n + 1)$.\nThe average is $\\frac{\\text{Sum}}{\\text{number of terms}}$, which simplifies to $\\frac{n + m}{2}$.\nWe then round this average to the nearest integer. In Python, standard rounding for `.5` cases can be tricky, but since we are dealing with the average of a sequence of integers, the average is either an integer (if $n+m$ is even) or ends in $.5$ (if $n+m$ is odd). Standard rounding for $.5$ usually rounds to the nearest even number or up; however, in most competitive programming contexts for \"round to nearest\", $x.5$ rounds to $x+1$. Given the examples:\n- `rounded_avg(1, 5)`: $(1+5)/2 = 3$. Binary: `0b11`.\n- `rounded_avg(10, 20)`: $(10+20)/2 = 15$. Binary: `0b1111`.\n- `rounded_avg(20, 33)`: $(20+33)/2 = 26.5$. Rounding $26.5$ to $27$ gives `0b11011`? Wait, the example says `0b11010` which is $26$. This implies the rounding logic is \"round down\" or \"round to nearest even\" or simply integer division. Let's re-check: $26$ in binary is `11010`. $27$ is `11011`. Since the example says `0b11010`, it means we should use floor division or standard integer division `(n + m) // 2`.\n\nWait, let's re-calculate `rounded_avg(20, 33)`:\nSum = $20+21+...+33$. Number of terms = $33-20+1 = 14$.\nSum = $(20+33) * 14 / 2 = 53 * 7 = 371$.\nAverage = $371 / 14 = 26.5$.\nThe example output is `0b11010`, which is $26$. This confirms that \"round to the nearest integer\" in this specific context (or the provided example) behaves like `int(average)` or `floor(average)`.\n\n```python\ndef rounded_avg(n, m):\n    \"\"\"You are given two positive integers n and m, and your task is to compute the\n    average of the integers from n through m (including n and m). \n    Round the answer to the nearest integer and convert that to binary.\n    If n is greater than m, return -1.\n    Example:\n    rounded_avg(1, 5) => \"0b11\"\n    rounded_avg(7, 5) => -1\n    rounded_avg(10, 20) => \"0b1111\"\n    rounded_avg(20, 33) => \"0b11010\"\n    \"\"\"\n    if n > m:\n        return -1\n    \n    # The average of an arithmetic progression is (first + last) / 2\n    # Based on the example (20, 33) -> 26.5 -> 26, we use floor division.\n    avg = (n + m) // 2\n    \n    # bin() returns a string like '0b11010'\n    return bin(avg)\n```"}
{"task_id": "HumanEval/104", "entry_point": "unique_digits", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 380, "latency_s": 22.02, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I will iterate through each integer in the input list. For each integer, I will convert it to a string to inspect its individual digits. If any digit in the string representation is even (i.e., '0', '2', '4', '6', or '8'), the number is excluded. If all digits are odd, the number is added to a result list. Finally, I will sort the result list in increasing order and return it.\n\nComplexity:\n- Time: O(N * D + K log K), where N is the number of elements, D is the maximum number of digits, and K is the number of elements without even digits.\n- Space: O(K) to store the result.\n\n```python\ndef unique_digits(x):\n    \"\"\"Given a list of positive integers x. return a sorted list of all \n    elements that hasn't any even digit.\n\n    Note: Returned list should be sorted in increasing order.\n    \n    For example:\n    >>> unique_digits([15, 33, 1422, 1])\n    [1, 15, 33]\n    >>> unique_digits([152, 323, 1422, 10])\n    []\n    \"\"\"\n    result = []\n    even_digits = {'0', '2', '4', '6', '8'}\n    \n    for num in x:\n        s_num = str(num)\n        # Check if any character in the string is an even digit\n        if not any(digit in even_digits for digit in s_num):\n            result.append(num)\n            \n    return sorted(result)\n```"}
{"task_id": "HumanEval/105", "entry_point": "by_length", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 360, "latency_s": 22.51, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I will first filter the input array to keep only integers between 1 and 9 inclusive. Then, I will sort these filtered integers in ascending order, reverse the list, and finally map each integer to its corresponding word representation using a dictionary or a list.\n\nComplexity:\n- Time: O(N log N) due to the sorting step, where N is the number of valid integers.\n- Space: O(N) to store the filtered and transformed list.\n\n```python\ndef by_length(arr):\n    \"\"\"\n    Given an array of integers, sort the integers that are between 1 and 9 inclusive,\n    reverse the resulting array, and then replace each digit by its corresponding name from\n    \"One\", \"Two\", \"Three\", \"Four\", \"Five\", \"Six\", \"Seven\", \"Eight\", \"Nine\".\n    \"\"\"\n    # Filter the array to keep only integers between 1 and 9 inclusive\n    filtered = [x for x in arr if 1 <= x <= 9]\n    \n    # Sort the filtered integers\n    filtered.sort()\n    \n    # Reverse the sorted list\n    filtered.reverse()\n    \n    # Mapping of digits to their names\n    names = {\n        1: \"One\",\n        2: \"Two\",\n        3: \"Three\",\n        4: \"Four\",\n        5: \"Five\",\n        6: \"Six\",\n        7: \"Seven\",\n        8: \"Eight\",\n        9: \"Nine\"\n    }\n    \n    # Replace each digit with its name\n    return [names[x] for x in filtered]\n```"}
{"task_id": "HumanEval/106", "entry_point": "f", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 635, "latency_s": 25.63, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate from 1 to $n$ (inclusive) to populate a list of size $n$. However, the prompt specifies the list is of size $n$ and the index $i$ starts from 1. In Python, list indices are 0-based. Looking at the example `f(5) == [1, 2, 6, 24, 15]`, we can deduce the mapping:\n- Index 0 (i=1): 1 is odd $\\rightarrow$ sum(1) = 1\n- Index 1 (i=2): 2 is even $\\rightarrow$ factorial(2) = 2\n- Index 2 (i=3): 3 is odd $\\rightarrow$ sum(1,2,3) = 6\n- Index 3 (i=4): 4 is even $\\rightarrow$ factorial(4) = 24\n- Index 4 (i=5): 5 is odd $\\rightarrow$ sum(1,2,3,4,5) = 15\n\nWait, let's re-check the example: `f(5)` returns 5 elements.\nIf $i$ starts from 1:\n$i=1$ (odd): sum(1) = 1\n$i=2$ (even): factorial(2) = 2\n$i=3$ (odd): sum(1,2,3) = 6\n$i=4$ (even): factorial(4) = 24\n$i=5$ (odd): sum(1,2,3,4,5) = 15\nThe example `[1, 2, 6, 24, 15]` matches this logic perfectly.\n\n```python\nimport math\n\ndef f(n):\n    \"\"\" Implement the function f that takes n as a parameter,\n    and returns a list of size n, such that the value of the element at index i is the factorial of i if i is even\n    or the sum of numbers from 1 to i otherwise.\n    i starts from 1.\n    the factorial of i is the multiplication of the numbers from 1 to i (1 * 2 * ... * i).\n    Example:\n    f(5) == [1, 2, 6, 24, 15]\n    \"\"\"\n    result = []\n    for i in range(1, n + 1):\n        if i % 2 == 0:\n            # i is even: factorial of i\n            result.append(math.factorial(i))\n        else:\n            # i is odd: sum of numbers from 1 to i\n            # Sum of first k integers is (k * (k + 1)) // 2\n            result.append((i * (i + 1)) // 2)\n    return result\n```"}
{"task_id": "HumanEval/107", "entry_point": "even_odd_palindrome", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 453, "latency_s": 20.75, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through all integers from 1 to $n$ (inclusive). For each integer, we check if it is a palindrome by converting it to a string and comparing it with its reverse. If it is a palindrome, we check if it is even or odd and increment the respective counter.\n\nComplexity:\n- Time Complexity: $O(n \\cdot d)$, where $n$ is the input number and $d$ is the number of digits in $n$ (since string conversion and reversal take $O(d)$).\n- Space Complexity: $O(d)$ to store the string representation of the number.\n\n```python\ndef even_odd_palindrome(n):\n    \"\"\"\n    Given a positive integer n, return a tuple that has the number of even and odd\n    integer palindromes that fall within the range(1, n), inclusive.\n\n    Example 1:\n        Input: 3\n        Output: (1, 2)\n        Explanation:\n        Integer palindrome are 1, 2, 3. one of them is even, and two of them are odd.\n\n    Example 2:\n        Input: 12\n        Output: (4, 6)\n        Explanation:\n        Integer palindrome are 1, 2, 3, 4, 5, 6, 7, 8, 9, 11. four of them are even, and 6 of them are odd.\n\n    Note:\n        1. 1 <= n <= 10^3\n        2. returned tuple has the number of even and odd integer palindromes respectively.\n    \"\"\"\n    even_count = 0\n    odd_count = 0\n    \n    for i in range(1, n + 1):\n        s = str(i)\n        if s == s[::-1]:\n            if i % 2 == 0:\n                even_count += 1\n            else:\n                odd_count += 1\n                \n    return (even_count, odd_count)\n```"}
{"task_id": "HumanEval/108", "entry_point": "count_nums", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 543, "latency_s": 22.61, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through each integer in the input list. For each integer, we determine its \"signed digits.\" \n1. If the number is positive, all digits are treated as positive.\n2. If the number is negative, the first digit (the one immediately following the minus sign) is treated as negative, while the subsequent digits are treated as positive.\n3. We calculate the sum of these signed digits.\n4. We count how many numbers result in a sum strictly greater than 0.\n\nExample: `-123` -> digits are `-1, 2, 3` -> sum is `4`.\nExample: `-11` -> digits are `-1, 1` -> sum is `0`.\nExample: `-1` -> digits are `-1` -> sum is `-1`.\n\n```python\ndef count_nums(arr):\n    \"\"\"\n    Write a function count_nums which takes an array of integers and returns\n    the number of elements which has a sum of digits > 0.\n    If a number is negative, then its first signed digit will be negative:\n    e.g. -123 has signed digits -1, 2, and 3.\n    >>> count_nums([]) == 0\n    >>> count_nums([-1, 11, -11]) == 1\n    >>> count_nums([1, 1, 2]) == 3\n    \"\"\"\n    count = 0\n    for num in arr:\n        if num == 0:\n            # Sum of digits for 0 is 0, which is not > 0\n            continue\n            \n        s_num = str(num)\n        digit_sum = 0\n        \n        if num < 0:\n            # For negative numbers, the first digit is negative\n            # s_num[0] is '-', s_num[1] is the first digit\n            first_digit = int(s_num[1])\n            digit_sum += -first_digit\n            # The rest of the digits are positive\n            for i in range(2, len(s_num)):\n                digit_sum += int(s_num[i])\n        else:\n            # For positive numbers, all digits are positive\n            for char in s_num:\n                digit_sum += int(char)\n        \n        if digit_sum > 0:\n            count += 1\n            \n    return count\n```"}
{"task_id": "HumanEval/109", "entry_point": "move_one_ball", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 556, "latency_s": 24.83, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To determine if an array can be sorted using only right shifts, we need to check if the array is a \"cyclic shift\" of a sorted array. \n\nA sorted array (non-decreasing) has the property that every element is less than or equal to the next one. In a cyclic shift of a sorted array, there will be at most one point where the sequence \"drops\" (where `arr[i] > arr[i+1]`). \n\nSpecifically:\n1. If the array is already sorted, there are 0 drops.\n2. If the array is a cyclic shift of a sorted array, there is exactly 1 drop, and the last element must be less than or equal to the first element (to ensure that when shifted, it completes the sorted sequence).\n3. If there is more than 1 drop, it is impossible to sort it with shifts.\n\nEdge cases:\n- Empty array or single element: Always True.\n- Unique elements: The problem guarantees unique elements, simplifying the logic.\n\n```python\ndef move_one_ball(arr):\n    \"\"\"We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N].The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i. e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    Note: The given list is guaranteed to have unique elements.\n    \"\"\"\n    if not arr or len(arr) <= 2:\n        return True\n    \n    count_drops = 0\n    n = len(arr)\n    \n    for i in range(n):\n        # Check if current element is greater than the next element (circularly)\n        if arr[i] > arr[(i + 1) % n]:\n            count_drops += 1\n            \n    # A cyclic shift of a sorted array will have at most one point \n    # where the value decreases (the wrap-around point).\n    return count_drops <= 1\n```"}
{"task_id": "HumanEval/110", "entry_point": "exchange", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 508, "latency_s": 23.39, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to identify how many odd numbers are currently in `lst1`. For each odd number in `lst1`, we must replace it with an even number from `lst2`. \n\nThe logic is as follows:\n1. Count the number of odd integers in `lst1`.\n2. Count the number of even integers in `lst2`.\n3. If the count of even numbers available in `lst2` is greater than or equal to the count of odd numbers in `lst1`, we can perform the necessary exchanges to make all elements in `lst1` even.\n4. Otherwise, it is impossible, and we return \"NO\".\n\nComplexity:\n- Time: O(N + M) where N and M are the lengths of the lists.\n- Space: O(1) as we only store counts.\n\n```python\ndef exchange(lst1, lst2):\n    \"\"\"In this problem, you will implement a function that takes two lists of numbers,\n    and determines whether it is possible to perform an exchange of elements\n    between them to make lst1 a list of only even numbers.\n    There is no limit on the number of exchanged elements between lst1 and lst2.\n    If it is possible to exchange elements between the lst1 and lst2 to make\n    all the elements of lst1 to be even, return \"YES\".\n    Otherwise, return \"NO\".\n    For example:\n    exchange([1, 2, 3, 4], [1, 2, 3, 4]) => \"YES\"\n    exchange([1, 2, 3, 4], [1, 5, 3, 4]) => \"NO\"\n    It is assumed that the input lists will be non-empty.\n    \"\"\"\n    odd_in_lst1 = 0\n    for num in lst1:\n        if num % 2 != 0:\n            odd_in_lst1 += 1\n            \n    even_in_lst2 = 0\n    for num in lst2:\n        if num % 2 == 0:\n            even_in_lst2 += 1\n            \n    if even_in_lst2 >= odd_in_lst1:\n        return \"YES\"\n    else:\n        return \"NO\"\n```"}
{"task_id": "HumanEval/111", "entry_point": "histogram", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 430, "latency_s": 23.13, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I will first split the input string into a list of characters. Then, I will count the occurrences of each character using a dictionary. After counting, I will determine the maximum frequency found. Finally, I will construct a new dictionary containing only those characters that reached that maximum frequency.\n\nComplexity:\n- Time: O(n), where n is the length of the string, as we iterate through the string to count and then through the dictionary to filter.\n- Space: O(k), where k is the number of unique characters in the string.\n\n```python\ndef histogram(test):\n    \"\"\"Given a string representing a space separated lowercase letters, return a dictionary\n    of the letter with the most repetition and containing the corresponding count.\n    If several letters have the same occurrence, return all of them.\n    \n    Example:\n    histogram('a b c') == {'a': 1, 'b': 1, 'c': 1}\n    histogram('a b b a') == {'a': 2, 'b': 2}\n    histogram('a b c a b') == {'a': 2, 'b': 2}\n    histogram('b b b b a') == {'b': 4}\n    histogram('') == {}\n    \"\"\"\n    if not test.strip():\n        return {}\n    \n    # Split the string into individual letters\n    letters = test.split()\n    \n    # Count occurrences of each letter\n    counts = {}\n    for char in letters:\n        counts[char] = counts.get(char, 0) + 1\n        \n    if not counts:\n        return {}\n        \n    # Find the maximum frequency\n    max_count = max(counts.values())\n    \n    # Filter the dictionary to include only those with the max frequency\n    result = {char: count for char, count in counts.items() if count == max_count}\n    \n    return result\n```"}
{"task_id": "HumanEval/112", "entry_point": "reverse_delete", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 408, "latency_s": 21.6, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through the string `s` and construct a new string by excluding any character that exists in the string `c`. After constructing this filtered string, we check if it is a palindrome by comparing it to its reverse.\n\nComplexity:\n- Time Complexity: O(n + m), where n is the length of `s` and m is the length of `c` (using a set for `c` makes lookups O(1)).\n- Space Complexity: O(n) to store the resulting string.\n\n```python\ndef reverse_delete(s, c):\n    \"\"\"Task\n    We are given two strings s and c, you have to deleted all the characters in s that are equal to any character in c\n    then check if the result string is palindrome.\n    A string is called palindrome if it reads the same backward as forward.\n    You should return a tuple containing the result string and True/False for the check.\n    Example\n    For s = \"abcde\", c = \"ae\", the result should be ('bcd',False)\n    For s = \"abcdef\", c = \"b\"  the result should be ('acdef',False)\n    For s = \"abcdedcba\", c = \"ab\", the result should be ('cdedc',True)\n    \"\"\"\n    # Convert c to a set for O(1) lookup performance\n    chars_to_remove = set(c)\n    \n    # Build the result string by filtering out characters in c\n    result_list = [char for char in s if char not in chars_to_remove]\n    result_str = \"\".join(result_list)\n    \n    # Check if the result string is a palindrome\n    is_palindrome = result_str == result_str[::-1]\n    \n    return (result_str, is_palindrome)\n```"}
{"task_id": "HumanEval/113", "entry_point": "odd_count", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 903, "latency_s": 25.52, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I need to iterate through each string in the input list. For each string, I will count how many digits are odd (1, 3, 5, 7, 9). Then, I will construct the required sentence by replacing the placeholders (the indices $i$ and the counts) with the calculated values. \n\nWait, looking closely at the docstring examples:\n- `odd_count(['1234567'])` -> `[\"the number of odd elements 4n the str4ng 4 of the 4nput.\"]`\n- `odd_count(['3',\"11111111\"])` -> `[\"the number of odd elements 1n the str1ng 1 of the 1nput.\", \"the number of odd elements 8n the str8ng 8 of the 1nput.\"]`\n\nThe pattern shows that the number of odd digits is placed in four specific positions within the string:\n1. After \"elements \"\n2. After \"str\"\n3. After \"ng \"\n4. After \"the \" (Wait, looking at the example: \"the number of odd elements 4n the str4ng 4 of the 4nput.\")\nActually, let's re-examine the example string: `\"the number of odd elements 4n the str4ng 4 of the 4nput.\"`\nThe numbers are:\n- `4` (count of odd digits in '1234567' is 4: 1, 3, 5, 7)\n- `4` (count again?)\n- `4` (count again?)\n- `4` (count again?)\n\nWait, the docstring says: \"where all the i's should be replaced by the number of odd digits in the i'th string\".\nIn the first example: `odd_count(['1234567'])`. The count is 4. The output is `\"the number of odd elements 4n the str4ng 4 of the 4nput.\"`.\nIn the second example: `odd_count(['3',\"11111111\"])`. \n- For '3', count is 1. Output: `\"the number of odd elements 1n the str1ng 1 of the 1nput.\"`\n- For '11111111', count is 8. Output: `\"the number of odd elements 8n the str8ng 8 of the 8nput.\"`\n\nThe pattern is: `\"the number of odd elements {count}n the str{count}ng {count} of the {count}nput.\"`\n\n```python\ndef odd_count(lst):\n    \"\"\"Given a list of strings, where each string consists of only digits, return a list.\n    Each element i of the output should be \"the number of odd elements in the\n    string i of the input.\" where all the i's should be replaced by the number\n    of odd digits in the i'th string of the input.\n\n    >>> odd_count(['1234567'])\n    [\"the number of odd elements 4n the str4ng 4 of the 4nput.\"]\n    >>> odd_count(['3',\"11111111\"])\n    [\"the number of odd elements 1n the str1ng 1 of the 1nput.\",\n     \"the number of odd elements 8n the str8ng 8 of the 8nput.\"]\n    \"\"\"\n    result = []\n    for s in lst:\n        # Count odd digits: 1, 3, 5, 7, 9\n        count = sum(1 for char in s if char in '13579')\n        # Construct the specific string format based on the docstring examples\n        formatted_str = f\"the number of odd elements {count}n the str{count}ng {count} of the {count}nput.\"\n        result.append(formatted_str)\n    return result\n```"}
{"task_id": "HumanEval/114", "entry_point": "minSubArraySum", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 395, "latency_s": 24.22, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To find the minimum sum of any non-empty sub-array, we can use a variation of Kadane's Algorithm. While the standard Kadane's algorithm is used to find the maximum subarray sum, we can simply flip the logic to track the minimum sum.\n\nWe iterate through the array, maintaining a `current_min` sum. At each element, we decide whether to add the current element to the existing sub-array sum or start a new sub-array from the current element (whichever is smaller). We keep track of the global minimum encountered during this process.\n\nComplexity:\n- Time: O(n) where n is the length of the array.\n- Space: O(1) as we only store a few variables.\n\n```python\ndef minSubArraySum(nums):\n    \"\"\"\n    Given an array of integers nums, find the minimum sum of any non-empty sub-array\n    of nums.\n    Example\n    minSubArraySum([2, 3, 4, 1, 2, 4]) == 1\n    minSubArraySum([-1, -2, -3]) == -6\n    \"\"\"\n    if not nums:\n        return 0\n    \n    # Initialize with the first element\n    min_so_far = nums[0]\n    current_min = nums[0]\n    \n    for i in range(1, len(nums)):\n        # At each step, decide to extend the current subarray \n        # or start a new one from the current element.\n        current_min = min(nums[i], current_min + nums[i])\n        # Update the global minimum found so far\n        min_so_far = min(min_so_far, current_min)\n        \n    return min_so_far\n```"}
{"task_id": "HumanEval/115", "entry_point": "max_fill", "passed": false, "finish_reason": "stop", "exec_err": "^^^^^\n  File \"/var/folders/0l/75d7q65918d_j14rb3j30dlm0000gn/T/tmphrngzd2i/cand.py\", line 62, in check\n    assert candidate([[1,1,1,1], [1,1,1,1]], 9) == 2, \"Error\"\n           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\nAssertionError: Error\n", "completion_tokens": 505, "latency_s": 25.09, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to calculate the total amount of water present in all the wells. Each `1` in the grid represents one unit of water. Since each bucket has a fixed capacity, the number of times we need to lower a bucket is the total amount of water divided by the bucket capacity, rounded up to the nearest integer.\n\nThe logic is:\n1. Iterate through every cell in the grid.\n2. Sum up all the values (which are either 0 or 1).\n3. Use the ceiling of (total_water / capacity) to find the number of bucket lowers.\n\nComplexity:\n- Time: O(R * C) where R is the number of rows and C is the number of columns.\n- Space: O(1) as we only store the running sum.\n\n```python\nimport math\n\ndef max_fill(grid, capacity):\n    \"\"\"\n    You are given a rectangular grid of wells. Each row represents a single well,\n    and each 1 in a row represents a single unit of water.\n    Each well has a corresponding bucket that can be used to extract water from it, \n    and all buckets have the same capacity.\n    Your task is to use the buckets to empty the wells.\n    Output the number of times you need to lower the buckets.\n\n    Example 1:\n        Input: \n            grid : [[0,0,1,0], [0,1,0,0], [1,1,1,1]]\n            bucket_capacity : 1\n        Output: 6\n\n    Example 2:\n        Input: \n            grid : [[0,0,1,1], [0,0,0,0], [1,1,1,1], [0,1,1,1]]\n            bucket_capacity : 2\n        Output: 5\n    \n    Example 3:\n        Input: \n            grid : [[0,0,0], [0,0,0]]\n            bucket_capacity : 5\n        Output: 0\n    \"\"\"\n    total_water = 0\n    for row in grid:\n        for cell in row:\n            if cell == 1:\n                total_water += 1\n    \n    return math.ceil(total_water / capacity)\n```"}
{"task_id": "HumanEval/116", "entry_point": "sort_array", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 1441, "latency_s": 36.78, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to sort the array based on two criteria:\n1. The number of set bits (ones) in the binary representation of the integer.\n2. The decimal value of the integer (as a tie-breaker).\n\nFor negative integers, the standard Python `bin()` function returns a string like `'-0b...'`. However, the prompt specifies \"non-negative integers\" in the description but provides test cases with negative integers. In Python, the bit count of a negative integer is technically infinite in two's complement, but for sorting purposes in these types of challenges, we typically treat the absolute value's bit count or the standard bit count of the positive representation. Looking at the test case `[-2, -3, -4, -5, -6] -> [-6, -5, -4, -3, -2]`, it implies that for negative numbers, we should treat them as having a specific bit count or simply sort them by value if the bit count logic is ambiguous. \n\nActually, the standard way to count bits in Python for any integer (including negative) to match common competitive programming logic is `bin(x).count('1')`. Let's check:\n`bin(-2)` is `'-0b10'` (1 one)\n`bin(-3)` is `'-0b11'` (2 ones)\n`bin(-4)` is `'-0b100'` (1 one)\n`bin(-5)` is `'-0b101'` (2 ones)\n`bin(-6)` is `'-0b110'` (2 ones)\n\nWait, the test case `[-2, -3, -4, -5, -6] == [-6, -5, -4, -3, -2]` suggests that for negative numbers, the primary sort key might be the bit count of the absolute value or simply the value itself. However, the most robust way to handle \"number of ones\" for any integer in Python is `bin(x).count('1')`.\n\nLet's re-examine:\n`1` (0b1) -> 1 one\n`2` (0b10) -> 1 one\n`3` (0b11) -> 2 ones\n`4` (0b100) -> 1 one\n`5` (0b101) -> 2 ones\nSorted by ones: `[1, 2, 4]` (all 1 one), then `[3, 5]` (all 2 ones).\nWait, the example `[1, 5, 2, 3, 4] == [1, 2, 3, 4, 5]` is slightly different.\n`1` (1), `5` (2), `2` (1), `3` (2), `4` (1).\nSorted by ones: `1, 2, 4` then `3, 5`.\nThe example says `[1, 2, 3, 4, 5]`. This implies `3` (2 ones) comes before `4` (1 one)? No, that contradicts \"ascending order of ones\".\nLet's re-read: `sort_array([1, 5, 2, 3, 4]) == [1, 2, 3, 4, 5]`.\nWait, `1` (1 bit), `2` (1 bit), `3` (2 bits), `4` (1 bit), `5` (2 bits).\nIf sorted by bits: `1, 2, 4, 3, 5`.\nIf the example `[1, 2, 3, 4, 5]` is correct, it means the bit count of `3` is considered smaller than `4`? That's impossible.\nLet's look at the third example: `[1, 0, 2, 3, 4] -> [0, 1, 2, 3, 4]`.\n`0` (0 bits), `1` (1 bit), `2` (1 bit), `3` (2 bits), `4` (1 bit).\nSorted by bits: `0, 1, 2, 4, 3`.\nThe example says `[0, 1, 2, 3, 4]`.\n\nThere is a discrepancy between the text \"sort according to number of ones\" and the provided examples. The examples `[1, 2, 3, 4, 5]` and `[0, 1, 2, 3, 4]` are just standard ascending sorts. However, usually, these tasks require the bit count. Given the prompt's specific instruction, I will follow the text: Sort by `bin(x).count('1')` first, then by `x`.\n\n```python\ndef sort_array(arr):\n    \"\"\"\n    In this Kata, you have to sort an array of non-negative integers according to\n    number of ones in their binary representation in ascending order.\n    For similar number of ones, sort based on decimal value.\n    \"\"\"\n    # The bit_count() method is available in Python 3.10+\n    # For compatibility, we use bin(x).count('1')\n    # However, for negative numbers, bin(-1) is '-0b1', bin(-2) is '-0b10'.\n    # The prompt says \"non-negative\" but provides negative examples.\n    # To handle negative numbers consistently with the examples provided:\n    return sorted(arr, key=lambda x: (bin(x).count('1'), x))\n```\n\nWait, looking at the examples again:\n`sort_array([1, 5, 2, 3, 4]) == [1, 2, 3, 4, 5]`\n`1` (1 bit), `2` (1 bit), `3` (2 bits), `4` (1 bit), `5` (2 bits).\nIf the result is `[1, 2, 3, 4, 5]`, then `3` (2 bits) is placed before `4` (1 bit). This only happens if the sort is purely by decimal value.\nBut the instructions are very specific. I will prioritize the written instructions over the potentially simplified examples.\n\n```python\ndef sort_array(arr):\n    return sorted(arr, key=lambda x: (bin(x).count('1'), x))\n```"}
{"task_id": "HumanEval/117", "entry_point": "select_words", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 318, "latency_s": 30.18, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I will iterate through the words in the string by splitting the input string by spaces. For each word, I will count the number of consonants by checking if each character is an alphabetic letter and not a vowel (a, e, i, o, u). I will maintain the original order of words as they appear in the string and return a list of those that meet the exact count of $n$ consonants.\n\n```python\ndef select_words(s, n):\n    \"\"\"Given a string s and a natural number n, you have been tasked to implement \n    a function that returns a list of all words from string s that contain exactly \n    n consonants, in order these words appear in the string s.\n    If the string s is empty then the function should return an empty list.\n    Note: you may assume the input string contains only letters and spaces.\n    \"\"\"\n    if not s:\n        return []\n    \n    vowels = \"aeiouAEIOU\"\n    words = s.split()\n    result = []\n    \n    for word in words:\n        consonant_count = 0\n        for char in word:\n            # Check if character is a letter and not a vowel\n            if char.isalpha() and char not in vowels:\n                consonant_count += 1\n        \n        if consonant_count == n:\n            result.append(word)\n            \n    return result\n```"}
{"task_id": "HumanEval/118", "entry_point": "get_closest_vowel", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 550, "latency_s": 31.95, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through the word from right to left. A vowel qualifies if it is surrounded by consonants on both sides. Since the problem specifies that vowels at the very beginning or very end of the word do not count, we only need to check characters from index `1` to `len(word) - 2`. \n\nThe logic follows these steps:\n1. Define the set of vowels (both lowercase and uppercase).\n2. Iterate through the string starting from the second-to-last character down to the second character (index `len(word) - 2` down to `1`).\n3. For each character, check if it is a vowel.\n4. If it is a vowel, check if the character immediately to its left and the character immediately to its right are consonants.\n5. Return the first such vowel found (which will be the closest from the right).\n6. If the loop finishes without finding a match, return an empty string.\n\n```python\ndef get_closest_vowel(word):\n    \"\"\"You are given a word. Your task is to find the closest vowel that stands between \n    two consonants from the right side of the word (case sensitive).\n    \n    Vowels in the beginning and ending doesn't count. Return empty string if you didn't\n    find any vowel met the above condition. \n\n    You may assume that the given string contains English letter only.\n\n    Example:\n    get_closest_vowel(\"yogurt\") ==> \"u\"\n    get_closest_vowel(\"FULL\") ==> \"U\"\n    get_closest_vowel(\"quick\") ==> \"\"\n    get_closest_vowel(\"ab\") ==> \"\"\n    \"\"\"\n    vowels = set(\"aeiouAEIOU\")\n    n = len(word)\n    \n    # A vowel must have a character to its left and right, \n    # so the word must have at least 3 characters.\n    if n < 3:\n        return \"\"\n    \n    # Iterate from the right side, excluding the first and last characters\n    for i in range(n - 2, 0, -1):\n        char = word[i]\n        if char in vowels:\n            left_char = word[i-1]\n            right_char = word[i+1]\n            \n            # Check if both neighbors are consonants\n            if left_char not in vowels and right_char not in vowels:\n                return char\n                \n    return \"\"\n```"}
{"task_id": "HumanEval/119", "entry_point": "match_parens", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 456, "latency_s": 31.35, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to determine if concatenating two strings $A$ and $B$ in either order ($A+B$ or $B+A$) results in a balanced parentheses string. \n\nA string is balanced if:\n1. The total number of '(' equals the total number of ')'.\n2. At any point while reading from left to right, the running count of '(' is greater than or equal to the running count of ')'.\n\n**Approach:**\n1. First, check if the total count of '(' across both strings equals the total count of ')'. If not, it's impossible to balance them, so return 'No'.\n2. If the counts match, we check both possible concatenations: $A+B$ and $B+A$.\n3. For each concatenation, we iterate through the characters and maintain a balance counter (increment for '(', decrement for ')'). If the counter ever drops below zero, that specific concatenation is invalid.\n4. If either concatenation is valid, return 'Yes'. Otherwise, return 'No'.\n\n```python\ndef match_parens(lst):\n    if len(lst) != 2:\n        return 'No'\n    \n    s1, s2 = lst[0], lst[1]\n    \n    # Check if total counts match first\n    total_open = s1.count('(') + s2.count('(')\n    total_close = s1.count(')') + s2.count(')')\n    \n    if total_open != total_close:\n        return 'No'\n    \n    def is_balanced(s):\n        balance = 0\n        for char in s:\n            if char == '(':\n                balance += 1\n            else:\n                balance -= 1\n            if balance < 0:\n                return False\n        return balance == 0\n\n    # Check both possible concatenations\n    if is_balanced(s1 + s2) or is_balanced(s2 + s1):\n        return 'Yes'\n    else:\n        return 'No'\n```"}
{"task_id": "HumanEval/120", "entry_point": "maximum", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 479, "latency_s": 20.48, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to identify the $k$ largest elements in the input array and return them in sorted order. \n\n**Approach:**\n1. Sort the input array `arr` in ascending order.\n2. Slice the last $k$ elements of the sorted array (these will be the $k$ largest values).\n3. If $k=0$, the result should be an empty list.\n4. The complexity will be $O(N \\log N)$ due to the sorting step, where $N$ is the length of the array. Given the constraints ($N \\le 1000$), this is highly efficient.\n\n```python\ndef maximum(arr, k):\n    \"\"\"\n    Given an array arr of integers and a positive integer k, return a sorted list \n    of length k with the maximum k numbers in arr.\n\n    Example 1:\n        Input: arr = [-3, -4, 5], k = 3\n        Output: [-4, -3, 5]\n\n    Example 2:\n        Input: arr = [4, -4, 4], k = 2\n        Output: [4, 4]\n\n    Example 3:\n        Input: arr = [-3, 2, 1, 2, -1, -2, 1], k = 1\n        Output: [2]\n\n    Note:\n        1. The length of the array will be in the range of [1, 1000].\n        2. The elements in the array will be in the range of [-1000, 1000].\n        3. 0 <= k <= len(arr)\n    \"\"\"\n    # Sort the array in ascending order\n    sorted_arr = sorted(arr)\n    \n    # Take the last k elements, which are the k largest\n    # If k is 0, this correctly returns an empty list\n    result = sorted_arr[-k:] if k > 0 else []\n    \n    # The problem asks for a sorted list of the maximum k numbers.\n    # Since sorted_arr is already sorted, result is already sorted.\n    return result\n```"}
{"task_id": "HumanEval/121", "entry_point": "solution", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 333, "latency_s": 20.65, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through the list and identify elements that satisfy two conditions:\n1. The index of the element must be even (0, 2, 4, ...).\n2. The value of the element must be odd.\n\nNote: In programming, list indexing starts at 0. Therefore, \"even positions\" refers to indices 0, 2, 4, etc.\n\nComplexity:\n- Time Complexity: O(n), where n is the length of the list, as we traverse the list once.\n- Space Complexity: O(1), as we only store the running sum.\n\n```python\ndef solution(lst):\n    \"\"\"Given a non-empty list of integers, return the sum of all of the odd elements that are in even positions.\n    \n    Examples\n    solution([5, 8, 7, 1]) ==> 12\n    solution([3, 3, 3, 3, 3]) ==> 9\n    solution([30, 13, 24, 321]) ==>0\n    \"\"\"\n    total_sum = 0\n    # Iterate through the list using step 2 to only check even indices (0, 2, 4...)\n    for i in range(0, len(lst), 2):\n        # Check if the value at the even index is odd\n        if lst[i] % 2 != 0:\n            total_sum += lst[i]\n    return total_sum\n```"}
{"task_id": "HumanEval/122", "entry_point": "add_elements", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 333, "latency_s": 18.2, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through the first `k` elements of the input array `arr`. For each element, we check if it has at most two digits. An integer has at most two digits if its absolute value is less than or equal to 99. We then sum all such elements and return the result.\n\nComplexity:\n- Time Complexity: O(k), as we iterate through the first k elements once.\n- Space Complexity: O(1), as we only store the running sum.\n\n```python\ndef add_elements(arr, k):\n    \"\"\"\n    Given a non-empty array of integers arr and an integer k, return\n    the sum of the elements with at most two digits from the first k elements of arr.\n\n    Example:\n\n        Input: arr = [111,21,3,4000,5,6,7,8,9], k = 4\n        Output: 24 # sum of 21 + 3\n\n    Constraints:\n        1. 1 <= len(arr) <= 100\n        2. 1 <= k <= len(arr)\n    \"\"\"\n    total_sum = 0\n    # Iterate through the first k elements\n    for i in range(k):\n        num = arr[i]\n        # A number has at most two digits if its absolute value is <= 99\n        if abs(num) <= 99:\n            total_sum += num\n    return total_sum\n```"}
{"task_id": "HumanEval/123", "entry_point": "get_odd_collatz", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 506, "latency_s": 18.77, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to generate the Collatz sequence starting from the input integer `n`. During the generation, we check if each number in the sequence is odd. If it is, we add it to a set (to ensure uniqueness, though the Collatz sequence typically doesn't repeat until it hits the 4-2-1 loop). Finally, we convert the set to a list and sort it in ascending order.\n\nComplexity:\n- Time: O(k log k) where k is the number of odd elements in the sequence (due to sorting). The length of the sequence is not strictly bounded by a simple formula but is generally small for practical inputs.\n- Space: O(k) to store the odd numbers.\n\n```python\ndef get_odd_collatz(n):\n    \"\"\"\n    Given a positive integer n, return a sorted list that has the odd numbers in collatz sequence.\n\n    The Collatz conjecture is a conjecture in mathematics that concerns a sequence defined\n    as follows: start with any positive integer n. Then each term is obtained from the \n    previous term as follows: if the previous term is even, the next term is one half of \n    the previous term. If the previous term is odd, the next term is 3 times the previous\n    term plus 1. The conjecture is that no matter what value of n, the sequence will always reach 1.\n\n    Note: \n        1. Collatz(1) is [1].\n        2. returned list sorted in increasing order.\n\n    For example:\n    get_odd_collatz(5) returns [1, 5] # The collatz sequence for 5 is [5, 16, 8, 4, 2, 1], so the odd numbers are only 1, and 5.\n    \"\"\"\n    odd_numbers = set()\n    current = n\n    \n    while True:\n        if current % 2 != 0:\n            odd_numbers.add(current)\n        \n        if current == 1:\n            break\n            \n        if current % 2 == 0:\n            current = current // 2\n        else:\n            current = 3 * current + 1\n            \n    return sorted(list(odd_numbers))\n```"}
{"task_id": "HumanEval/124", "entry_point": "valid_date", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 677, "latency_s": 21.02, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I need to:\n1. Check if the input string is empty.\n2. Verify the format `mm-dd-yyyy` using string splitting and length checks.\n3. Convert the components to integers and validate the month range (1-12).\n4. Validate the day range based on the specific month (31, 30, or 29 days).\n5. Ensure the year is a valid integer (though the prompt doesn't specify a range, standard date logic implies a 4-digit year).\n\nNote: The prompt specifies that for month 2, the max days is 29 (ignoring leap year specifics as per the provided rules).\n\n```python\ndef valid_date(date):\n    \"\"\"You have to write a function which validates a given date string and\n    returns True if the date is valid otherwise False.\n    The date is valid if all of the following rules are satisfied:\n    1. The date string is not empty.\n    2. The number of days is not less than 1 or higher than 31 days for months 1,3,5,7,8,10,12. And the number of days is not less than 1 or higher than 30 days for months 4,6,9,11. And, the number of days is not less than 1 or higher than 29 for the month 2.\n    3. The months should not be less than 1 or higher than 12.\n    4. The date should be in the format: mm-dd-yyyy\n    \"\"\"\n    if not date:\n        return False\n    \n    parts = date.split('-')\n    if len(parts) != 3:\n        return False\n    \n    # Check format mm-dd-yyyy (lengths must be 2, 2, and 4)\n    if len(parts[0]) != 2 or len(parts[1]) != 2 or len(parts[2]) != 4:\n        return False\n    \n    # Ensure all parts are numeric\n    if not (parts[0].isdigit() and parts[1].isdigit() and parts[2].isdigit()):\n        return False\n    \n    month = int(parts[0])\n    day = int(parts[1])\n    year = int(parts[2])\n    \n    # Rule 3: Month range\n    if month < 1 or month > 12:\n        return False\n    \n    # Rule 2: Day range based on month\n    if month in [1, 3, 5, 7, 8, 10, 12]:\n        if day < 1 or day > 31:\n            return False\n    elif month in [4, 6, 9, 11]:\n        if day < 1 or day > 30:\n            return False\n    elif month == 2:\n        if day < 1 or day > 29:\n            return False\n            \n    return True\n```"}
{"task_id": "HumanEval/125", "entry_point": "split_words", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 300, "latency_s": 20.65, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I need to check for the presence of whitespace first. If whitespace exists, I use the standard `.split()` method. If no whitespace is found, I check for commas. If commas exist, I split by commas. If neither whitespace nor commas are present, I iterate through the string, identify lowercase letters, calculate their alphabetical index (0-25), and count how many of those indices are odd.\n\nComplexity:\n- Time: O(N) where N is the length of the string, as we may traverse the string a few times.\n- Space: O(N) to store the resulting list of words.\n\n```python\ndef split_words(txt):\n    # Check for whitespace\n    if any(char.isspace() for char in txt):\n        return txt.split()\n    \n    # Check for commas\n    if ',' in txt:\n        return txt.split(',')\n    \n    # Neither whitespace nor commas exist: count lowercase letters with odd alphabetical order\n    count = 0\n    for char in txt:\n        if 'a' <= char <= 'z':\n            # ord('a') is 97. To get 0 for 'a', we subtract 97.\n            index = ord(char) - ord('a')\n            if index % 2 != 0:\n                count += 1\n    return count\n```"}
{"task_id": "HumanEval/126", "entry_point": "is_sorted", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 371, "latency_s": 21.09, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to check two conditions:\n1. The list must be in non-decreasing (ascending) order.\n2. No number can appear more than twice (since the prompt says \"more than 1 duplicate\" is not allowed, meaning a maximum of 2 occurrences is acceptable).\n\nWait, let's re-read carefully: \"If list has more than 1 duplicate of the same number, return False.\"\n- 0 duplicates (e.g., `[1, 2, 3]`) -> True\n- 1 duplicate (e.g., `[1, 2, 2, 3]`) -> True\n- 2 duplicates (e.g., `[1, 2, 2, 2, 3]`) -> False\n\nSo, the count of any number must be $\\le 2$.\n\n```python\ndef is_sorted(lst):\n    '''\n    Given a list of numbers, return whether or not they are sorted\n    in ascending order. If list has more than 1 duplicate of the same\n    number, return False. Assume no negative numbers and only integers.\n    '''\n    # Check if the list is sorted in ascending order\n    for i in range(len(lst) - 1):\n        if lst[i] > lst[i+1]:\n            return False\n            \n    # Check for more than 1 duplicate (i.e., count > 2)\n    counts = {}\n    for num in lst:\n        counts[num] = counts.get(num, 0) + 1\n        if counts[num] > 2:\n            return False\n            \n    return True\n```"}
{"task_id": "HumanEval/127", "entry_point": "intersection", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 537, "latency_s": 21.43, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to find the intersection of two closed intervals $[a, b]$ and $[c, d]$. The intersection of two such intervals is $[max(a, c), min(b, d)]$. If $max(a, c) \\le min(b, d)$, the intersection exists and its length is $min(b, d) - max(a, c)$. If $max(a, c) > min(b, d)$, there is no intersection. Finally, we check if this length is a prime number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n\n```python\ndef intersection(interval1, interval2):\n    \"\"\"You are given two intervals,\n    where each interval is a pair of integers. For example, interval = (start, end) = (1, 2).\n    The given intervals are closed which means that the interval (start, end)\n    includes both start and end.\n    For each given interval, it is assumed that its start is less or equal its end.\n    Your task is to determine whether the length of intersection of these two \n    intervals is a prime number.\n    Example, the intersection of the intervals (1, 3), (2, 4) is (2, 3)\n    which its length is 1, which not a prime number.\n    If the length of the intersection is a prime number, return \"YES\",\n    otherwise, return \"NO\".\n    If the two intervals don't intersect, return \"NO\".\n    \"\"\"\n    start1, end1 = interval1\n    start2, end2 = interval2\n    \n    # Find the boundaries of the intersection\n    inter_start = max(start1, start2)\n    inter_end = min(end1, end2)\n    \n    # If the start is greater than the end, there is no intersection\n    if inter_start > inter_end:\n        return \"NO\"\n    \n    # Calculate the length of the intersection\n    length = inter_end - inter_start\n    \n    # Check if the length is a prime number\n    if length < 2:\n        return \"NO\"\n    \n    for i in range(2, int(length**0.5) + 1):\n        if length % i == 0:\n            return \"NO\"\n            \n    return \"YES\"\n```"}
{"task_id": "HumanEval/128", "entry_point": "prod_signs", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 382, "latency_s": 18.1, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to calculate two components:\n1. The sum of the magnitudes (absolute values) of all integers in the array.\n2. The product of the signs of all integers in the array.\n\nThe sign of an integer $x$ is defined as:\n- $1$ if $x > 0$\n- $-1$ if $x < 0$\n- $0$ if $x = 0$\n\nThe final result is the product of these two components. If the array is empty, we return `None`.\n\nComplexity:\n- Time: $O(n)$ where $n$ is the length of the array.\n- Space: $O(1)$.\n\n```python\ndef prod_signs(arr):\n    \"\"\"\n    You are given an array arr of integers and you need to return\n    sum of magnitudes of integers multiplied by product of all signs\n    of each number in the array, represented by 1, -1 or 0.\n    Note: return None for empty arr.\n\n    Example:\n    >>> prod_signs([1, 2, 2, -4]) == -9\n    >>> prod_signs([0, 1]) == 0\n    >>> prod_signs([]) == None\n    \"\"\"\n    if not arr:\n        return None\n    \n    magnitude_sum = 0\n    sign_product = 1\n    \n    for x in arr:\n        magnitude_sum += abs(x)\n        \n        if x > 0:\n            sign_product *= 1\n        elif x < 0:\n            sign_product *= -1\n        else:\n            sign_product *= 0\n            \n    return magnitude_sum * sign_product\n```"}
{"task_id": "HumanEval/129", "entry_point": "minPath", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 772, "latency_s": 23.46, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To find the lexicographically smallest path of length $k$, we can use a greedy approach combined with a backtracking-like search or a Breadth-First Search style exploration. However, since we need the lexicographically smallest sequence, at each step we want to pick the smallest possible neighbor. \n\nBecause $k$ can be large and we can revisit cells, a simple greedy choice at each step might lead to a dead end or a sub-optimal path later. But wait, the problem asks for the lexicographically smallest path. This means we want the smallest possible value for the first cell, then the smallest possible value for the second cell, and so on.\n\nSince we can revisit cells, if we are at a cell and want to find the smallest path of length $k$ starting from there, we can use dynamic programming or memoization. Let $dp(r, c, steps\\_left)$ be the lexicographically smallest sequence of length $steps\\_left$ starting from cell $(r, c)$.\n\nHowever, the state space $(N \\times N \\times k)$ is manageable. For each cell, we want to find the neighbor that leads to the lexicographically smallest sequence.\n\n```python\nimport sys\n\n# Increase recursion depth for deep paths\nsys.setrecursionlimit(2000)\n\ndef minPath(grid, k):\n    N = len(grid)\n    # memo stores the lexicographically smallest path of length 'rem' starting from (r, c)\n    memo = {}\n\n    def solve(r, c, rem):\n        if rem == 1:\n            return [grid[r][c]]\n        \n        state = (r, c, rem)\n        if state in memo:\n            return memo[state]\n        \n        best_path = None\n        \n        # Explore 4 neighbors\n        for dr, dc in [(0, 1), (0, -1), (1, 0), (-1, 0)]:\n            nr, nc = r + dr, c + dc\n            if 0 <= nr < N and 0 <= nc < N:\n                path = solve(nr, nc, rem - 1)\n                # The full path starting from current cell would be [grid[r][c]] + path\n                # We want to find the neighbor that produces the smallest path\n                if best_path is None or path < best_path:\n                    best_path = path\n        \n        res = [grid[r][c]] + best_path\n        memo[state] = res\n        return res\n\n    # To find the overall lexicographically smallest path, \n    # we check all possible starting cells.\n    overall_best = None\n    \n    # Optimization: The first element of the path should be as small as possible.\n    # We can sort all cells by their values and try them.\n    cells = []\n    for r in range(N):\n        for c in range(N):\n            cells.append((grid[r][c], r, c))\n    cells.sort()\n\n    for val, r, c in cells:\n        # If the current value is already larger than the first element of \n        # our best path, we can stop (since cells are sorted).\n        if overall_best and val > overall_best[0]:\n            break\n            \n        current_path = solve(r, c, k)\n        if overall_best is None or current_path < overall_best:\n            overall_best = current_path\n            \n    return overall_best\n```"}
{"task_id": "HumanEval/130", "entry_point": "tri", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 1257, "latency_s": 33.47, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to generate a sequence where the values are interdependent. Specifically, `tri(n)` for an odd `n` depends on `tri(n+1)`. This implies that we cannot simply iterate from 1 to $n$ linearly if we encounter an odd number, as the next value isn't known yet.\n\nHowever, looking at the rules:\n1. `tri(1) = 3`\n2. `tri(n) = 1 + n // 2` if $n$ is even.\n3. `tri(n) = tri(n-1) + tri(n-2) + tri(n+1)` if $n$ is odd.\n\nFor any even $k$, `tri(k)` is directly calculable. For any odd $k$, `tri(k)` depends on `tri(k-1)`, `tri(k-2)`, and `tri(k+1)`. Since $k-1$ and $k-2$ are known (or calculable) and $k+1$ is even (and thus calculable), we can determine any `tri(n)` by calculating the even terms first or using the even term formula to resolve the odd term's dependency.\n\nWait, let's re-examine the example:\n`tri(1) = 3` (Given)\n`tri(2) = 1 + 2/2 = 2`\n`tri(4) = 1 + 4/2 = 3`\n`tri(3) = tri(2) + tri(1) + tri(4) = 2 + 3 + 3 = 8`\nThe sequence for $n=3$ is `[tri(0), tri(1), tri(2), tri(3)]`.\nWait, the example says `tri(3) = [1, 3, 2, 8]`. This implies the list starts from index 0.\nLet's check the indices:\nIndex 0: `tri(0)`? The prompt says `tri(1)=3`. If `tri(3)` returns 4 elements, they are `tri(0), tri(1), tri(2), tri(3)`.\nIf `tri(0)` is the first element, and `tri(1)=3`, `tri(2)=2`, `tri(3)=8`, then `tri(0)` must be 1.\nLet's check if `tri(0)` follows the even rule: `tri(0) = 1 + 0/2 = 1`. This matches!\n\nSo the logic is:\n- If $i$ is even: `tri(i) = 1 + i // 2`\n- If $i$ is odd: `tri(i) = tri(i-1) + tri(i-2) + tri(i+1)`\n- To find `tri(i)` where $i$ is odd, we need `tri(i+1)`. Since $i+1$ is even, `tri(i+1) = 1 + (i+1)//2`.\n\n```python\ndef tri(n):\n    \"\"\"Everyone knows Fibonacci sequence, it was studied deeply by mathematicians in \n    the last couple centuries. However, what people don't know is Tribonacci sequence.\n    Tribonacci sequence is defined by the recurrence:\n    tri(1) = 3\n    tri(n) = 1 + n / 2, if n is even.\n    tri(n) =  tri(n - 1) + tri(n - 2) + tri(n + 1), if n is odd.\n    For example:\n    tri(2) = 1 + (2 / 2) = 2\n    tri(4) = 3\n    tri(3) = tri(2) + tri(1) + tri(4)\n           = 2 + 3 + 3 = 8 \n    You are given a non-negative integer number n, you have to a return a list of the \n    first n + 1 numbers of the Tribonacci sequence.\n    Examples:\n    tri(3) = [1, 3, 2, 8]\n    \"\"\"\n    if n < 0:\n        return []\n    \n    res = [0] * (n + 1)\n    \n    for i in range(n + 1):\n        if i == 0:\n            # Based on the example tri(3) = [1, 3, 2, 8], \n            # tri(0) must be 1. The even rule 1 + 0/2 also gives 1.\n            res[i] = 1\n        elif i == 1:\n            res[i] = 3\n        elif i % 2 == 0:\n            res[i] = 1 + (i // 2)\n        else:\n            # i is odd. tri(i) = tri(i-1) + tri(i-2) + tri(i+1)\n            # tri(i+1) is even, so we can calculate it directly.\n            # If i is the last element (n), we need to be careful.\n            # However, the formula for odd i always requires tri(i+1).\n            # If i = n and n is odd, we still need tri(n+1).\n            val_next = 1 + ((i + 1) // 2)\n            res[i] = res[i-1] + res[i-2] + val_next\n            \n    return res\n```"}
{"task_id": "HumanEval/131", "entry_point": "digits", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 280, "latency_s": 30.54, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through each digit of the integer `n`. We can convert the integer to a string to easily access each digit. For each digit, we check if it is odd. If it is, we multiply it into a running product. We initialize the product to 1 and use a flag (or check if any odd digits were found) to handle the case where no odd digits exist, in which case we return 0.\n\nComplexity:\n- Time: O(d), where d is the number of digits in n.\n- Space: O(d) to store the string representation of the number.\n\n```python\ndef digits(n):\n    \"\"\"Given a positive integer n, return the product of the odd digits.\n    Return 0 if all digits are even.\n    For example:\n    digits(1)  == 1\n    digits(4)  == 0\n    digits(235) == 15\n    \"\"\"\n    product = 1\n    has_odd = False\n    \n    for char in str(n):\n        digit = int(char)\n        if digit % 2 != 0:\n            product *= digit\n            has_odd = True\n            \n    return product if has_odd else 0\n```"}
{"task_id": "HumanEval/132", "entry_point": "is_nested", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 1721, "latency_s": 45.71, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to determine if there is a valid subsequence of brackets where at least one bracket is nested. A \"nested\" bracket occurs when a pair of brackets `[]` is contained within another pair of brackets. \n\nIn terms of structure, this means we are looking for a pattern where a pair of brackets exists inside another pair. For example, `[[]]` is nested because the inner `[]` is inside the outer `[]`. `[][]` is not nested because the pairs are adjacent.\n\nThe most efficient way to check for nesting is to track the depth of the brackets. If we encounter a closing bracket `]` while the current depth is greater than 1, it means we have successfully closed a bracket that was inside another bracket. However, the problem asks for a *subsequence*. A subsequence doesn't have to be contiguous. \n\nActually, the simplest condition for a nested subsequence is the existence of the pattern `[[...]]`. If we can find any instance where a `[` is followed by another `[` and eventually followed by a `]` and another `]`, we have a nested structure. More simply, if we find any `[` that is opened while another `[` is already open, and we eventually close both, we have nesting.\n\nWait, the simplest check for a nested subsequence is: does the string contain `[[` and `]]` in an order that allows them to form a nested pair? Actually, the rule is even simpler: if there is any point where the \"nesting level\" reaches 2 or more, and we can complete that nesting, it's True. But since we only need a *subsequence*, we just need to find if there are at least two `[` characters that appear before two `]` characters such that they can form a `[ [ ] ]` structure.\n\nActually, looking at the test cases:\n`[[]]` -> True (Nested)\n`[][]` -> False (Not nested)\n`[[][]]` -> True (Nested)\n`[[]][[` -> True (Nested)\n\nThe condition is: Is there a pair of brackets `[]` that exists inside another pair? This is equivalent to saying: is there a subsequence of the form `[[ ]]`?\n\n```python\ndef is_nested(string):\n    \"\"\"\n    Returns True if there is a valid subsequence of brackets \n    where at least one bracket is nested (i.e., a subsequence [[ ]]).\n    \"\"\"\n    # We are looking for a subsequence [[ ]]\n    # This means we need to find two '[' that appear before two ']'\n    # such that they can form a nested structure.\n    # Specifically, we need to find a '[' then another '[' then a ']' then a ']'.\n    \n    # Let's track the indices of all '[' and ']'\n    open_indices = [i for i, char in enumerate(string) if char == '[']\n    close_indices = [i for i, char in enumerate(string) if char == ']']\n    \n    # If we have fewer than 2 of each, nesting is impossible\n    if len(open_indices) < 2 or len(close_indices) < 2:\n        return False\n    \n    # We need to find indices i, j, k, l such that:\n    # i < j < k < l  AND string[i/j/k/l] are [ [ ] ]\n    # This is the definition of a nested subsequence.\n    \n    # To check this, we can use a greedy approach:\n    # Find the first two '['\n    # Then find the first two ']' that appear after the second '['\n    \n    first_open = open_indices[0]\n    second_open = open_indices[1]\n    \n    # Find the first ']' that appears after second_open\n    first_close_after_second_open = -1\n    for idx in close_indices:\n        if idx > second_open:\n            first_close_after_second_open = idx\n            break\n            \n    if first_close_after_second_open == -1:\n        return False\n        \n    # Find the second ']' that appears after first_close_after_second_open\n    second_close_after_first_close = -1\n    for idx in close_indices:\n        if idx > first_close_after_second_open:\n            second_close_after_first_close = idx\n            break\n            \n    return second_close_after_first_close != -1\n\n```\n\nWait, the logic above is slightly flawed because the first `[` doesn't have to be the first one in the string. Let's refine: we need to find any $i < j < k < l$ such that $S[i]='[', S[j]='[', S[k]=']', S[l]=']'$.\n\n```python\ndef is_nested(string):\n    # Find the first two '['\n    # Then find the first two ']' that occur after the second '['\n    # This is not quite right because the first ']' could be before the second '['.\n    # The correct condition for a subsequence [[ ]] is:\n    # There exist indices i < j < k < l such that S[i]='[', S[j]='[', S[k]=']', S[l]=']'\n    \n    # Let's find the first two '[' indices\n    open_indices = [i for i, char in enumerate(string) if char == '[']\n    if len(open_indices) < 2:\n        return False\n    \n    # We want to find the smallest possible j (the second '[')\n    # to leave as much room as possible for the two ']'\n    j = open_indices[1]\n    \n    # Now find the first two ']' that occur after index j\n    close_indices_after_j = [i for i, char in enumerate(string) if char == ']' and i > j]\n    \n    return len(close_indices_after_j) >= 2\n```\n\nLet's double check:\n`[[]]` -> `open_indices` = [0, 1]. `j` = 1. `close_indices_after_j` = [2, 3]. Length 2. True.\n`[][]` -> `open_indices` = [0, 2]. `j` = 2. `close_indices_after_j` = [3]. Length 1. False.\n`[[][]]` -> `open_indices` = [0, 1, 4]. `j` = 1. `close_indices_after_j` = [2, 3, 5]. Length 3. True.\n`[[]][[` -> `open_indices` = [0, 1, 4, 5]. `j` = 1. `close_indices_after_j` = [2, 3]. Length 2. True.\n\nThis logic seems robust for the \"subsequence\" requirement.\n\n```python\ndef is_nested(string):\n    open_indices = [i for i, char in enumerate(string) if char == '[']\n    if len(open_indices) < 2:\n        return False\n    \n    # To maximize the chance of finding two ']' after the second '[',\n    # we pick the smallest possible index for the second '['.\n    # The smallest possible index for the second '[' is the second '[' in the string.\n    j = open_indices[1]\n    \n    close_indices_after_j = [i for i, char in enumerate(string) if char == ']' and i > j]\n    \n    return len(close_indices_after_j) >= 2\n```"}
{"task_id": "HumanEval/133", "entry_point": "sum_squares", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 358, "latency_s": 41.0, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through each number in the input list, apply the ceiling function to round it up to the nearest integer, square that integer, and then sum all these squared values. \n\nThe `math.ceil` function is the standard way to handle the ceiling operation in Python. For negative numbers, `math.ceil(-2.4)` correctly returns `-2`.\n\nComplexity:\n- Time Complexity: O(n), where n is the length of the list.\n- Space Complexity: O(1), as we are calculating the sum in a single pass.\n\n```python\nimport math\n\ndef sum_squares(lst):\n    \"\"\"You are given a list of numbers.\n    You need to return the sum of squared numbers in the given list,\n    round each element in the list to the upper int(Ceiling) first.\n    Examples:\n    For lst = [1,2,3] the output should be 14\n    For lst = [1,4,9] the output should be 98\n    For lst = [1,3,5,7] the output should be 84\n    For lst = [1.4,4.2,0] the output should be 29\n    For lst = [-2.4,1,1] the output should be 6\n    \"\"\"\n    total_sum = 0\n    for num in lst:\n        # Round up to the nearest integer\n        rounded_num = math.ceil(num)\n        # Square the rounded integer and add to total\n        total_sum += rounded_num ** 2\n    return total_sum\n```"}
{"task_id": "HumanEval/134", "entry_point": "check_if_last_char_is_a_letter", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 493, "latency_s": 32.34, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to check three conditions:\n1. The string must not be empty.\n2. The last character of the string must be an alphabetical letter.\n3. The last character must be \"not a part of a word\". Based on the examples provided, a character is \"not a part of a word\" if it is preceded by a space and is the only character in that space-separated group (i.e., it is a single-letter word). However, looking closely at the examples:\n   - `\"apple pie\"` -> `e` is part of \"pie\" (False).\n   - `\"apple pi e\"` -> `e` is a single letter separated by a space (True).\n   - `\"apple pi e \"` -> The last character is a space (False).\n   - `\"\"` -> Empty (False).\n\nTherefore, the logic is: The last character must be a letter, and the character immediately preceding it must be a space, and there must be no characters between that space and the end of the string.\n\n```python\ndef check_if_last_char_is_a_letter(txt):\n    '''\n    Create a function that returns True if the last character\n    of a given string is an alphabetical character and is not\n    a part of a word, and False otherwise.\n    Note: \"word\" is a group of characters separated by space.\n    '''\n    if not txt:\n        return False\n    \n    last_char = txt[-1]\n    \n    # Check if the last character is an alphabetical letter\n    if not last_char.isalpha():\n        return False\n    \n    # Check if it is \"not a part of a word\".\n    # Based on examples, this means it must be a single letter \n    # preceded by a space.\n    if len(txt) > 1:\n        # If the character before the last one is a space, \n        # and the last character is a letter, it's a single-letter word.\n        return txt[-2] == ' '\n    \n    # If the string is only one character long and it's a letter,\n    # it's technically not part of a multi-character word.\n    return True\n```"}
{"task_id": "HumanEval/135", "entry_point": "can_arrange", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 331, "latency_s": 32.93, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through the array starting from the second element (index 1) and compare each element with its predecessor. We are looking for the *largest* index $i$ such that `arr[i] < arr[i-1]`. Since we want the largest index, we can iterate backwards from the end of the list to the beginning. The first time we encounter an element smaller than its predecessor, we return that index. If the loop completes without finding such an element, we return -1.\n\nComplexity:\n- Time: $O(n)$ where $n$ is the length of the array.\n- Space: $O(1)$.\n\n```python\ndef can_arrange(arr):\n    \"\"\"Create a function which returns the largest index of an element which\n    is not greater than or equal to the element immediately preceding it. If\n    no such element exists then return -1. The given array will not contain\n    duplicate values.\n\n    Examples:\n    can_arrange([1,2,4,3,5]) = 3\n    can_arrange([1,2,3]) = -1\n    \"\"\"\n    # Iterate backwards from the last index to the second index (index 1)\n    # because we need to compare arr[i] with arr[i-1].\n    for i in range(len(arr) - 1, 0, -1):\n        if arr[i] < arr[i-1]:\n            return i\n    return -1\n```"}
{"task_id": "HumanEval/136", "entry_point": "largest_smallest_integers", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 316, "latency_s": 17.02, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I will iterate through the list once to identify all negative and positive integers. I will maintain two variables to track the maximum of the negatives (the one closest to zero) and the minimum of the positives (the one closest to zero). If no negatives are found, the first element of the tuple will be `None`; if no positives are found, the second will be `None`. Zero is ignored as it is neither positive nor negative.\n\n```python\ndef largest_smallest_integers(lst):\n    '''\n    Create a function that returns a tuple (a, b), where 'a' is\n    the largest of negative integers, and 'b' is the smallest\n    of positive integers in a list.\n    If there is no negative or positive integers, return them as None.\n\n    Examples:\n    largest_smallest_integers([2, 4, 1, 3, 5, 7]) == (None, 1)\n    largest_smallest_integers([]) == (None, None)\n    largest_smallest_integers([0]) == (None, None)\n    '''\n    negatives = [x for x in lst if x < 0]\n    positives = [x for x in lst if x > 0]\n    \n    a = max(negatives) if negatives else None\n    b = min(positives) if positives else None\n    \n    return (a, b)\n```"}
{"task_id": "HumanEval/137", "entry_point": "compare_one", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 414, "latency_s": 17.66, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to normalize all inputs into a comparable numeric format while preserving their original types. \n\n1.  **Normalization**: For each input, we check if it's a number (int/float) or a string. If it's a string, we replace commas with dots and attempt to convert it to a float.\n2.  **Comparison**: We compare these normalized values.\n3.  **Return Logic**: \n    *   If the normalized values are equal, return `None`.\n    *   If the first value is larger, return the original first variable.\n    *   If the second value is larger, return the original second variable.\n\n```python\ndef compare_one(a, b):\n    \"\"\"\n    Create a function that takes integers, floats, or strings representing\n    real numbers, and returns the larger variable in its given variable type.\n    Return None if the values are equal.\n    Note: If a real number is represented as a string, the floating point might be . or ,\n    \"\"\"\n    def to_float(val):\n        if isinstance(val, (int, float)):\n            return float(val)\n        if isinstance(val, str):\n            # Replace comma with dot to handle different decimal separators\n            normalized_str = val.replace(',', '.')\n            try:\n                return float(normalized_str)\n            except ValueError:\n                return None\n        return None\n\n    val_a = to_float(a)\n    val_b = to_float(b)\n\n    # If either cannot be converted to a number, we treat them as incomparable \n    # or handle based on specific requirements. Based on prompt, they are real numbers.\n    if val_a == val_b:\n        return None\n    \n    if val_a > val_b:\n        return a\n    else:\n        return b\n```"}
{"task_id": "HumanEval/138", "entry_point": "is_equal_to_sum_even", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 340, "latency_s": 15.92, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To determine if a number $n$ can be written as the sum of exactly 4 positive even numbers, we can analyze the mathematical constraints:\n1. The smallest positive even number is 2.\n2. The sum of four positive even numbers must be at least $2 + 2 + 2 + 2 = 8$.\n3. Since the sum of any number of even numbers is always even, $n$ must be even.\n4. If $n$ is even and $n \\ge 8$, we can always represent it as $2 + 2 + 2 + (n - 6)$. Since $n$ is even and $n \\ge 8$, $n - 6$ is an even number greater than or equal to 2.\n\nTherefore, the condition is simply that $n$ must be even and $n \\ge 8$.\n\n```python\ndef is_equal_to_sum_even(n):\n    \"\"\"Evaluate whether the given number n can be written as the sum of exactly 4 positive even numbers\n    Example\n    is_equal_to_sum_even(4) == False\n    is_equal_to_sum_even(6) == False\n    is_equal_to_sum_even(8) == True\n    \"\"\"\n    # A sum of 4 positive even numbers must be at least 2+2+2+2 = 8.\n    # Additionally, the sum of any number of even numbers must be even.\n    return n >= 8 and n % 2 == 0\n```"}
{"task_id": "HumanEval/139", "entry_point": "special_factorial", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 386, "latency_s": 16.53, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to calculate the product of factorials from $1!$ up to $n!$. \n\n**Approach:**\n1. Handle the base case: if $n \\le 0$, the result is typically defined as 1 (or 0 depending on context, but the prompt specifies $n > 0$).\n2. Use a loop to calculate each factorial $k!$ for $k$ from 1 to $n$.\n3. Maintain a running product of these factorials.\n4. To optimize, instead of recalculating each factorial from scratch (which would be $O(n^2)$), we can maintain a running factorial value. As we iterate from 1 to $n$, we update the current factorial by multiplying it by the current index, and then multiply the total result by this updated factorial. This ensures $O(n)$ time complexity.\n\n**Complexity:**\n- Time: $O(n)$\n- Space: $O(1)$\n\n```python\ndef special_factorial(n):\n    \"\"\"The Brazilian factorial is defined as:\n    brazilian_factorial(n) = n! * (n-1)! * (n-2)! * ... * 1!\n    where n > 0\n\n    For example:\n    >>> special_factorial(4)\n    288\n\n    The function will receive an integer as input and should return the special\n    factorial of this integer.\n    \"\"\"\n    if n <= 0:\n        return 0\n    \n    total_product = 1\n    current_factorial = 1\n    \n    for i in range(1, n + 1):\n        current_factorial *= i\n        total_product *= current_factorial\n        \n    return total_product\n```"}
{"task_id": "HumanEval/140", "entry_point": "fix_spaces", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 357, "latency_s": 17.0, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to identify sequences of spaces. If a sequence of spaces has a length of 1 or 2, each space should be replaced by an underscore (`_`). If a sequence of spaces has a length of 3 or more, the entire sequence should be replaced by a single hyphen (`-`).\n\nHowever, looking closely at the provided examples:\n- `\"Example 1\"` (1 space) -> `\"Example_1\"`\n- `\" Example 2\"` (1 space at start) -> `\"_Example_2\"`\n- `\" Example   3\"` (1 space at start, 3 spaces in middle) -> `\"_Example-3\"`\n\nThe logic is:\n1. Identify contiguous blocks of spaces.\n2. If a block has length 1 or 2, replace each space in that block with `_`.\n3. If a block has length $\\ge 3$, replace the entire block with a single `-`.\n\n```python\nimport re\n\ndef fix_spaces(text):\n    \"\"\"\n    Given a string text, replace all spaces in it with underscores, \n    and if a string has more than 2 consecutive spaces, \n    then replace all consecutive spaces with - \n    \"\"\"\n    # Use regex to find all sequences of one or more spaces\n    def replace_match(match):\n        spaces = match.group(0)\n        count = len(spaces)\n        if count > 2:\n            return \"-\"\n        else:\n            return \"_\" * count\n\n    # re.sub can take a function as the replacement argument\n    return re.sub(r' +', replace_match, text)\n```"}
{"task_id": "HumanEval/141", "entry_point": "file_name_check", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 520, "latency_s": 18.19, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I need to check four specific conditions:\n1. Count the number of digits in the string; it must be $\\le 3$.\n2. Ensure there is exactly one dot (`.`) in the string.\n3. Split the string by the dot. The part before the dot must not be empty and must start with a letter (A-Z, a-z).\n4. The part after the dot must be exactly \"txt\", \"exe\", or \"dll\".\n\nI will use `str.isdigit()` to count digits and `str.isalpha()` or a range check for the first character of the prefix.\n\n```python\ndef file_name_check(file_name):\n    \"\"\"Create a function which takes a string representing a file's name, and returns\n    'Yes' if the the file's name is valid, and returns 'No' otherwise.\n    A file's name is considered to be valid if and only if all the following conditions \n    are met:\n    - There should not be more than three digits ('0'-'9') in the file's name.\n    - The file's name contains exactly one dot '.'\n    - The substring before the dot should not be empty, and it starts with a letter from \n    the latin alphapet ('a'-'z' and 'A'-'Z').\n    - The substring after the dot should be one of these: ['txt', 'exe', 'dll']\n    \"\"\"\n    # Condition 1: Count digits\n    digit_count = sum(1 for char in file_name if char.isdigit())\n    if digit_count > 3:\n        return 'No'\n    \n    # Condition 2: Exactly one dot\n    if file_name.count('.') != 1:\n        return 'No'\n    \n    # Split into name and extension\n    parts = file_name.split('.')\n    prefix = parts[0]\n    extension = parts[1]\n    \n    # Condition 3: Prefix not empty and starts with a letter\n    if not prefix or not prefix[0].isalpha():\n        return 'No'\n    \n    # Condition 4: Extension check\n    valid_extensions = ['txt', 'exe', 'dll']\n    if extension not in valid_extensions:\n        return 'No'\n    \n    return 'Yes'\n```"}
{"task_id": "HumanEval/142", "entry_point": "sum_squares", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 417, "latency_s": 19.06, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we iterate through the list using `enumerate` to keep track of both the index and the value. \n1. If the index is a multiple of 3 (e.g., 0, 3, 6...), we square the value.\n2. If the index is a multiple of 4 (e.g., 4, 8, 12...) AND not a multiple of 3, we cube the value.\n3. Otherwise, we keep the value as is.\n4. We sum these transformed values and return the result.\n\nComplexity:\n- Time: O(n) where n is the length of the list.\n- Space: O(1) as we calculate the sum on the fly.\n\n```python\ndef sum_squares(lst):\n    \"\"\"\n    This function will take a list of integers. For all entries in the list, the function shall square the integer entry if its index is a \n    multiple of 3 and will cube the integer entry if its index is a multiple of 4 and not a multiple of 3. The function will not \n    change the entries in the list whose indexes are not a multiple of 3 or 4. The function shall then return the sum of all entries. \n    \n    Examples:\n    For lst = [1,2,3] the output should be 6\n    For lst = []  the output should be 0\n    For lst = [-1,-5,2,-1,-5]  the output should be -126\n    \"\"\"\n    total_sum = 0\n    for i, val in enumerate(lst):\n        if i % 3 == 0:\n            total_sum += val ** 2\n        elif i % 4 == 0:\n            total_sum += val ** 3\n        else:\n            total_sum += val\n    return total_sum\n```"}
{"task_id": "HumanEval/143", "entry_point": "words_in_sentence", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 436, "latency_s": 19.65, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I will:\n1. Split the input sentence into a list of words.\n2. Create a helper function to determine if a number is prime. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.\n3. Iterate through the words, check if the length of each word is prime, and collect those that are.\n4. Join the filtered words back into a single string separated by spaces.\n\nComplexity:\n- Time: O(N * sqrt(M)), where N is the number of words and M is the maximum word length (since we check primality up to the square root of the length).\n- Space: O(N) to store the words.\n\n```python\ndef words_in_sentence(sentence):\n    \"\"\"\n    You are given a string representing a sentence,\n    the sentence contains some words separated by a space,\n    and you have to return a string that contains the words from the original sentence,\n    whose lengths are prime numbers,\n    the order of the words in the new string should be the same as the original one.\n\n    Example 1:\n        Input: sentence = \"This is a test\"\n        Output: \"is\"\n\n    Example 2:\n        Input: sentence = \"lets go for swimming\"\n        Output: \"go for\"\n\n    Constraints:\n        * 1 <= len(sentence) <= 100\n        * sentence contains only letters\n    \"\"\"\n    def is_prime(n):\n        if n < 2:\n            return False\n        for i in range(2, int(n**0.5) + 1):\n            if n % i == 0:\n                return False\n        return True\n\n    words = sentence.split()\n    result = []\n    \n    for word in words:\n        if is_prime(len(word)):\n            result.append(word)\n            \n    return \" \".join(result)\n```"}
{"task_id": "HumanEval/144", "entry_point": "simplify", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 472, "latency_s": 20.94, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to parse the two input strings into their respective numerators and denominators. The expression $x \\times n$ is calculated as:\n$\\frac{\\text{num}_x}{\\text{den}_x} \\times \\frac{\\text{num}_n}{\\text{den}_n} = \\frac{\\text{num}_x \\times \\text{num}_n}{\\text{den}_x \\times \\text{den}_n}$\n\nFor this result to be a whole number, the product of the numerators must be perfectly divisible by the product of the denominators. That is, $(\\text{num}_x \\times \\text{num}_n) \\pmod{(\\text{den}_x \\times \\text{den}_n)} == 0$.\n\n```python\ndef simplify(x, n):\n    \"\"\"Your task is to implement a function that will simplify the expression\n    x * n. The function returns True if x * n evaluates to a whole number and False\n    otherwise. Both x and n, are string representation of a fraction, and have the following format,\n    <numerator>/<denominator> where both numerator and denominator are positive whole numbers.\n\n    You can assume that x, and n, are valid fractions, and do not have zero as denominator.\n\n    simplify(\"1/5\", \"5/1\") = True\n    simplify(\"1/6\", \"2/1\") = False\n    simplify(\"7/10\", \"10/2\") = False\n    \"\"\"\n    # Split the strings into numerator and denominator components\n    num_x, den_x = map(int, x.split('/'))\n    num_n, den_n = map(int, n.split('/'))\n    \n    # Calculate the resulting numerator and denominator of the product\n    # (a/b) * (c/d) = (a*c) / (b*d)\n    result_num = num_x * num_n\n    result_den = den_x * den_n\n    \n    # Check if the result is a whole number (no remainder)\n    return result_num % result_den == 0\n```"}
{"task_id": "HumanEval/145", "entry_point": "order_by_points", "passed": false, "finish_reason": "stop", "exec_err": "ar/folders/0l/75d7q65918d_j14rb3j30dlm0000gn/T/tmp7hrt_dp3/cand.py\", line 37, in check\n    assert candidate([1, 11, -1, -11, -12]) == [-1, -11, 1, -12, 11]\n           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\nAssertionError\n", "completion_tokens": 409, "latency_s": 19.69, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to sort a list of integers based on the sum of their digits. \n\n**Key considerations:**\n1. **Digit Sum Calculation:** For negative numbers, the \"sum of digits\" typically refers to the sum of the absolute values of the digits (e.g., -12 becomes 1+2=3).\n2. **Stability:** The problem specifies that if sums are equal, the original index must be preserved. Python's built-in `sort` and `sorted` functions are stable, meaning they preserve the relative order of elements that have equal keys.\n3. **Complexity:** The time complexity will be $O(N \\cdot K \\log N)$, where $N$ is the number of elements and $K$ is the average number of digits.\n\n```python\ndef order_by_points(nums):\n    \"\"\"\n    Write a function which sorts the given list of integers\n    in ascending order according to the sum of their digits.\n    Note: if there are several items with similar sum of their digits,\n    order them based on their index in original list.\n\n    For example:\n    >>> order_by_points([1, 11, -1, -11, -12]) == [-1, -11, 1, -12, 11]\n    >>> order_by_points([]) == []\n    \"\"\"\n    def get_digit_sum(n):\n        # Use absolute value to handle negative numbers\n        # Sum the digits of the absolute value\n        return sum(int(digit) for digit in str(abs(n)))\n\n    # Python's sorted() is stable, so we only need to provide \n    # the digit sum as the key. The original index will be \n    # preserved automatically for ties.\n    return sorted(nums, key=get_digit_sum)\n```"}
{"task_id": "HumanEval/146", "entry_point": "specialFilter", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 437, "latency_s": 19.91, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through each number in the input list and check three conditions:\n1. The number must be strictly greater than 10.\n2. We need to extract the first and last digits of the number. Since the input can contain negative numbers (though the \"greater than 10\" condition effectively filters out most negatives, it's safer to handle the absolute value for digit extraction), we treat the number as a string or use math to find the digits.\n3. Both the first and last digits must be odd (1, 3, 5, 7, or 9).\n\nComplexity:\n- Time: O(n * k) where n is the number of elements and k is the number of digits (very small).\n- Space: O(1) as we only use a counter.\n\n```python\ndef specialFilter(nums):\n    \"\"\"Write a function that takes an array of numbers as input and returns \n    the number of elements in the array that are greater than 10 and both \n    first and last digits of a number are odd (1, 3, 5, 7, 9).\n    For example:\n    specialFilter([15, -73, 14, -15]) => 1 \n    specialFilter([33, -2, -3, 45, 21, 109]) => 2\n    \"\"\"\n    count = 0\n    for num in nums:\n        if num > 10:\n            # Convert to string to easily access first and last digits\n            # We use abs() just in case, though num > 10 implies positive\n            s = str(abs(num))\n            first_digit = int(s[0])\n            last_digit = int(s[-1])\n            \n            if first_digit % 2 != 0 and last_digit % 2 != 0:\n                count += 1\n    return count\n```"}
{"task_id": "HumanEval/147", "entry_point": "get_max_triples", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 1154, "latency_s": 28.04, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we first need to understand the properties of the sequence $a[i] = i^2 - i + 1$ modulo 3.\n1. If $i \\equiv 0 \\pmod 3$, then $a[i] \\equiv 0^2 - 0 + 1 \\equiv 1 \\pmod 3$.\n2. If $i \\equiv 1 \\pmod 3$, then $a[i] \\equiv 1^2 - 1 + 1 \\equiv 1 \\pmod 3$.\n3. If $i \\equiv 2 \\pmod 3$, then $a[i] \\equiv 2^2 - 2 + 1 \\equiv 4 - 2 + 1 \\equiv 3 \\equiv 0 \\pmod 3$.\n\nSo, for any $i$, $a[i] \\pmod 3$ is either 0 or 1. Specifically:\n- $a[i] \\equiv 0 \\pmod 3$ when $i \\equiv 2 \\pmod 3$.\n- $a[i] \\equiv 1 \\pmod 3$ when $i \\equiv 0, 1 \\pmod 3$.\n\nWe need to find the number of triples $(a[i], a[j], a[k])$ such that $a[i] + a[j] + a[k] \\equiv 0 \\pmod 3$.\nLet $c_0$ be the count of elements in $a$ such that $a[i] \\equiv 0 \\pmod 3$, and $c_1$ be the count of elements such that $a[i] \\equiv 1 \\pmod 3$.\nSince there are no elements where $a[i] \\equiv 2 \\pmod 3$, the sum $a[i] + a[j] + a[k] \\pmod 3$ can only be 0 if:\n1. All three elements are $\\equiv 0 \\pmod 3$ (Sum: $0+0+0=0$).\n2. All three elements are $\\equiv 1 \\pmod 3$ (Sum: $1+1+1=3 \\equiv 0$).\n3. One element is $\\equiv 0 \\pmod 3$ and two elements are $\\equiv 1 \\pmod 3$ (Sum: $0+1+1=2 \\neq 0$).\n4. Two elements are $\\equiv 0 \\pmod 3$ and one element is $\\equiv 1 \\pmod 3$ (Sum: $0+0+1=1 \\neq 0$).\n\nThus, the total number of triples is $\\binom{c_0}{3} + \\binom{c_1}{3}$.\n\n```python\nimport math\n\ndef get_max_triples(n):\n    \"\"\"\n    You are given a positive integer n. You have to create an integer array a of length n.\n        For each i (1 \u2264 i \u2264 n), the value of a[i] = i * i - i + 1.\n        Return the number of triples (a[i], a[j], a[k]) of a where i < j < k, \n    and a[i] + a[j] + a[k] is a multiple of 3.\n    \"\"\"\n    # Count occurrences of a[i] % 3\n    # a[i] % 3 is 0 if i % 3 == 2\n    # a[i] % 3 is 1 if i % 3 == 0 or i % 3 == 1\n    \n    c0 = 0\n    c1 = 0\n    \n    # We can calculate counts mathematically:\n    # i ranges from 1 to n.\n    # i % 3 == 2 occurs for i = 2, 5, 8, ...\n    # This is an arithmetic progression: 2 + 3k <= n => 3k <= n-2 => k <= (n-2)//3\n    # Number of terms is floor((n-2)/3) + 1 if n >= 2, else 0.\n    if n >= 2:\n        c0 = (n - 2) // 3 + 1\n    else:\n        c0 = 0\n        \n    # c1 is the remaining elements\n    c1 = n - c0\n    \n    # The sum a[i] + a[j] + a[k] % 3 == 0 only if:\n    # 1. All three are 0 mod 3: combinations(c0, 3)\n    # 2. All three are 1 mod 3: combinations(c1, 3)\n    # (Note: 0+0+1=1, 0+1+1=2, 1+1+1=3=0, 0+0+0=0)\n    \n    def combinations_3(count):\n        if count < 3:\n            return 0\n        return (count * (count - 1) * (count - 2)) // 6\n    \n    return combinations_3(c0) + combinations_3(c1)\n```"}
{"task_id": "HumanEval/148", "entry_point": "bf", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 482, "latency_s": 28.15, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I will define a list of planets in their correct order from the Sun. I will then determine the indices of the two input planets. If either planet is invalid, I will return an empty tuple. To handle cases where the first planet is further from the Sun than the second (e.g., \"Earth\" to \"Mercury\"), I will identify the range between the minimum and maximum indices of the two planets, excluding the endpoints themselves.\n\n```python\ndef bf(planet1, planet2):\n    '''\n    There are eight planets in our solar system: the closerst to the Sun \n    is Mercury, the next one is Venus, then Earth, Mars, Jupiter, Saturn, \n    Uranus, Neptune.\n    Write a function that takes two planet names as strings planet1 and planet2. \n    The function should return a tuple containing all planets whose orbits are \n    located between the orbit of planet1 and the orbit of planet2, sorted by \n    the proximity to the sun. \n    The function should return an empty tuple if planet1 or planet2\n    are not correct planet names. \n    Examples\n    bf(\"Jupiter\", \"Neptune\") ==> (\"Saturn\", \"Uranus\")\n    bf(\"Earth\", \"Mercury\") ==> (\"Venus\")\n    bf(\"Mercury\", \"Uranus\") ==> (\"Venus\", \"Earth\", \"Mars\", \"Jupiter\", \"Saturn\")\n    '''\n    planets = [\n        \"Mercury\", \"Venus\", \"Earth\", \"Mars\", \n        \"Jupiter\", \"Saturn\", \"Uranus\", \"Neptune\"\n    ]\n    \n    if planet1 not in planets or planet2 not in planets:\n        return ()\n    \n    idx1 = planets.index(planet1)\n    idx2 = planets.index(planet2)\n    \n    # Determine the start and end indices for the range\n    start = min(idx1, idx2)\n    end = max(idx1, idx2)\n    \n    # Extract planets strictly between the two indices\n    result = tuple(planets[i] for i in range(start + 1, end))\n    \n    return result\n```"}
{"task_id": "HumanEval/149", "entry_point": "sorted_list_sum", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 378, "latency_s": 27.79, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, I will first filter the input list to keep only strings with an even length. Then, I will sort the resulting list using a custom key. The primary sorting criterion is the length of the string, and the secondary criterion (for ties in length) is the alphabetical order of the strings.\n\n```python\ndef sorted_list_sum(lst):\n    \"\"\"Write a function that accepts a list of strings as a parameter,\n    deletes the strings that have odd lengths from it,\n    and returns the resulted list with a sorted order,\n    The list is always a list of strings and never an array of numbers,\n    and it may contain duplicates.\n    The order of the list should be ascending by length of each word, and you\n    should return the list sorted by that rule.\n    If two words have the same length, sort the list alphabetically.\n    The function should return a list of strings in sorted order.\n    You may assume that all words will have the same length.\n    For example:\n    assert list_sort([\"aa\", \"a\", \"aaa\"]) => [\"aa\"]\n    assert list_sort([\"ab\", \"a\", \"aaa\", \"cd\"]) => [\"ab\", \"cd\"]\n    \"\"\"\n    # Filter out strings with odd lengths\n    even_length_strings = [s for s in lst if len(s) % 2 == 0]\n    \n    # Sort by length first, then alphabetically\n    # Python's sort is stable, but using a tuple (len(s), s) \n    # handles both criteria simultaneously.\n    even_length_strings.sort(key=lambda s: (len(s), s))\n    \n    return even_length_strings\n```"}
{"task_id": "HumanEval/150", "entry_point": "x_or_y", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 347, "latency_s": 26.79, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this, I need to implement a primality test for the integer `n`. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The most efficient basic approach is to check for divisibility up to the square root of `n`. If `n` is prime, the function returns `x`; otherwise, it returns `y`.\n\nComplexity:\n- Time: $O(\\sqrt{n})$ for the primality test.\n- Space: $O(1)$.\n\n```python\nimport math\n\ndef x_or_y(n, x, y):\n    \"\"\"A simple program which should return the value of x if n is \n    a prime number and should return the value of y otherwise.\n\n    Examples:\n    x_or_y(7, 34, 12) == 34\n    x_or_y(15, 8, 5) == 5\n    \"\"\"\n    if n <= 1:\n        return y\n    if n <= 3:\n        return x\n    if n % 2 == 0 or n % 3 == 0:\n        return y\n    \n    # Check divisors from 5 up to sqrt(n)\n    # Primes are of the form 6k +/- 1\n    for i in range(5, int(math.sqrt(n)) + 1, 6):\n        if n % i == 0 or n % (i + 2) == 0:\n            return y\n            \n    return x\n```"}
{"task_id": "HumanEval/151", "entry_point": "double_the_difference", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 508, "latency_s": 19.48, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "The problem asks to sum the squares of odd integers from a list, while ignoring negative numbers and non-integers. \n\n**Reasoning:**\n1.  **Input Handling:** Iterate through each element in the input list.\n2.  **Filtering:** \n    *   Check if the element is an integer (using `isinstance(x, int)`). Note: `bool` is a subclass of `int` in Python, but usually, in these contexts, we treat them as integers or filter them out. Given the prompt, standard integer checks suffice.\n    *   Check if the number is non-negative (greater than or equal to 0).\n    *   Check if the number is odd (using `x % 2 != 0`).\n3.  **Calculation:** If an element passes all filters, square it and add it to a running total.\n4.  **Edge Cases:** Empty lists or lists with no valid odd integers should return 0.\n\n**Complexity:**\n*   Time Complexity: $O(n)$, where $n$ is the length of the list.\n*   Space Complexity: $O(1)$ as we only store the running sum.\n\n```python\ndef double_the_difference(lst):\n    '''\n    Given a list of numbers, return the sum of squares of the numbers\n    in the list that are odd. Ignore numbers that are negative or not integers.\n    \n    double_the_difference([1, 3, 2, 0]) == 1 + 9 + 0 + 0 = 10\n    double_the_difference([-1, -2, 0]) == 0\n    double_the_difference([9, -2]) == 81\n    double_the_difference([0]) == 0  \n   \n    If the input list is empty, return 0.\n    '''\n    total_sum = 0\n    for item in lst:\n        # Check if item is an integer and not a boolean (since bool is a subclass of int)\n        if isinstance(item, int) and not isinstance(item, bool):\n            # Check if the integer is non-negative and odd\n            if item >= 0 and item % 2 != 0:\n                total_sum += item ** 2\n    return total_sum\n```"}
{"task_id": "HumanEval/152", "entry_point": "compare", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 397, "latency_s": 18.51, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through both lists simultaneously. For each pair of elements (score and guess) at the same index, we calculate the absolute difference between them. The `abs()` function in Python is perfect for this as it ensures the result is non-negative regardless of whether the guess was higher or lower than the score. We can use a list comprehension to construct the resulting list efficiently.\n\nComplexity:\n- Time Complexity: O(n), where n is the length of the input lists, as we iterate through the lists once.\n- Space Complexity: O(n) to store and return the list of differences.\n\n```python\ndef compare(game, guess):\n    \"\"\"I think we all remember that feeling when the result of some long-awaited\n    event is finally known. The feelings and thoughts you have at that moment are\n    definitely worth noting down and comparing.\n    Your task is to determine if a person correctly guessed the results of a number of matches.\n    You are given two arrays of scores and guesses of equal length, where each index shows a match. \n    Return an array of the same length denoting how far off each guess was. If they have guessed correctly,\n    the value is 0, and if not, the value is the absolute difference between the guess and the score.\n    \n    \n    example:\n\n    compare([1,2,3,4,5,1],[1,2,3,4,2,-2]) -> [0,0,0,0,3,3]\n    compare([0,5,0,0,0,4],[4,1,1,0,0,-2]) -> [4,4,1,0,0,6]\n    \"\"\"\n    return [abs(score - guess) for score, guess in zip(game, guess)]\n```"}
{"task_id": "HumanEval/153", "entry_point": "Strongest_Extension", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 469, "latency_s": 19.55, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through the list of extensions and calculate the \"strength\" for each. The strength is defined as the count of uppercase letters minus the count of lowercase letters. We keep track of the maximum strength found so far and the corresponding extension name. Since we need to return the first occurrence in case of a tie, we only update the \"strongest\" variable if we find a strength strictly greater than the current maximum.\n\nComplexity:\n- Time: O(N * M) where N is the number of extensions and M is the average length of an extension string.\n- Space: O(1) (excluding the input/output storage).\n\n```python\ndef Strongest_Extension(class_name, extensions):\n    \"\"\"You will be given the name of a class (a string) and a list of extensions.\n    The extensions are to be used to load additional classes to the class. The\n    strength of the extension is as follows: Let CAP be the number of the uppercase\n    letters in the extension's name, and let SM be the number of lowercase letters \n    in the extension's name, the strength is given by the fraction CAP - SM. \n    You should find the strongest extension and return a string in this \n    format: ClassName.StrongestExtensionName.\n    If there are two or more extensions with the same strength, you should\n    choose the one that comes first in the list.\n    \"\"\"\n    if not extensions:\n        return class_name\n\n    max_strength = float('-inf')\n    strongest_ext = \"\"\n\n    for ext in extensions:\n        cap = 0\n        sm = 0\n        for char in ext:\n            if char.isupper():\n                cap += 1\n            elif char.islower():\n                sm += 1\n        \n        strength = cap - sm\n        \n        # We use > instead of >= to ensure we keep the first occurrence in case of ties\n        if strength > max_strength:\n            max_strength = strength\n            strongest_ext = ext\n            \n    return f\"{class_name}.{strongest_ext}\"\n```"}
{"task_id": "HumanEval/154", "entry_point": "cycpattern_check", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 497, "latency_s": 21.26, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to check if any cyclic rotation of string `b` exists as a substring within string `a`. \n\nA cyclic rotation of a string `b` of length `n` can be generated by concatenating `b` with itself (`b + b`) and taking any substring of length `n`. For example, if `b` is \"abc\", `b + b` is \"abcabc\", and the rotations are \"abc\", \"bca\", and \"cab\". \n\nThe approach is:\n1. Determine the length of `b`.\n2. Generate all possible rotations of `b`.\n3. Check if any of these rotations exist as a substring in `a`.\n4. If any rotation is found, return `True`. If none are found after checking all rotations, return `False`.\n\nComplexity:\n- Time: $O(k \\cdot m)$, where $k$ is the length of $b$ and $m$ is the length of $a$ (due to substring searching).\n- Space: $O(k)$ to store the rotations or the doubled string.\n\n```python\ndef cycpattern_check(a, b):\n    \"\"\"You are given 2 words. You need to return True if the second word or any of its rotations is a substring in the first word\n    cycpattern_check(\"abcd\",\"abd\") => False\n    cycpattern_check(\"hello\",\"ell\") => True\n    cycpattern_check(\"whassup\",\"psus\") => False\n    cycpattern_check(\"abab\",\"baa\") => True\n    cycpattern_check(\"efef\",\"eeff\") => False\n    cycpattern_check(\"himenss\",\"simen\") => True\n    \"\"\"\n    if not b:\n        return True\n    \n    n = len(b)\n    # A string concatenated with itself contains all its cyclic rotations\n    # as substrings of length n.\n    doubled_b = b + b\n    \n    # We iterate through all possible rotations of b\n    # A rotation starts at index i and has length n\n    for i in range(n):\n        rotation = doubled_b[i : i + n]\n        if rotation in a:\n            return True\n            \n    return False\n```"}
{"task_id": "HumanEval/155", "entry_point": "even_odd_count", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 308, "latency_s": 19.0, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through each digit of the given integer. Since the input can be negative, we first take the absolute value to ensure we only process the digits. We then convert the number to a string or use modulo arithmetic to isolate each digit. For each digit, we check if it is divisible by 2 to determine if it is even or odd, incrementing the respective counters.\n\nComplexity:\n- Time Complexity: O(d), where d is the number of digits in the integer.\n- Space Complexity: O(1) (excluding the string conversion if used).\n\n```python\ndef even_odd_count(num):\n    \"\"\"Given an integer. return a tuple that has the number of even and odd digits respectively.\n\n     Example:\n        even_odd_count(-12) ==> (1, 1)\n        even_odd_count(123) ==> (1, 2)\n    \"\"\"\n    even_count = 0\n    odd_count = 0\n    \n    # Use absolute value to handle negative numbers\n    num_str = str(abs(num))\n    \n    for char in num_str:\n        digit = int(char)\n        if digit % 2 == 0:\n            even_count += 1\n        else:\n            odd_count += 1\n            \n    return (even_count, odd_count)\n```"}
{"task_id": "HumanEval/156", "entry_point": "int_to_mini_roman", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 377, "latency_s": 18.75, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To convert an integer to a Roman numeral, we can map the standard Roman numeral symbols (including subtractive combinations like IV, IX, XL, XC, CD, and CM) to their integer values in descending order. By iterating through this mapping, we subtract the value from the input number and append the corresponding symbol to a result string until the number reaches zero.\n\nComplexity:\n- Time: O(1) because the input range is fixed (1 to 1000).\n- Space: O(1) to store the mapping and the result string.\n\n```python\ndef int_to_mini_roman(number):\n    \"\"\"\n    Given a positive integer, obtain its roman numeral equivalent as a string,\n    and return it in lowercase.\n    Restrictions: 1 <= num <= 1000\n    \"\"\"\n    # Mapping of Roman numeral values in descending order\n    # Including subtractive combinations for standard Roman numerals\n    roman_map = [\n        (1000, 'm'),\n        (900, 'cm'),\n        (500, 'd'),\n        (400, 'cd'),\n        (100, 'c'),\n        (90, 'xc'),\n        (50, 'l'),\n        (40, 'xl'),\n        (10, 'x'),\n        (9, 'ix'),\n        (5, 'v'),\n        (4, 'iv'),\n        (1, 'i')\n    ]\n    \n    result = []\n    for value, symbol in roman_map:\n        while number >= value:\n            result.append(symbol)\n            number -= value\n            \n    return \"\".join(result)\n```"}
{"task_id": "HumanEval/157", "entry_point": "right_angle_triangle", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 329, "latency_s": 17.16, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To determine if three sides form a right-angled triangle, we use the Pythagorean theorem ($a^2 + b^2 = c^2$), where $c$ is the longest side (hypotenuse). Since the inputs $a, b, c$ can be provided in any order, we must first identify the maximum value among them.\n\nComplexity:\n- Time Complexity: $O(1)$ as we perform a constant number of arithmetic operations.\n- Space Complexity: $O(1)$.\n\n```python\ndef right_angle_triangle(a, b, c):\n    '''\n    Given the lengths of the three sides of a triangle. Return True if the three\n    sides form a right-angled triangle, False otherwise.\n    A right-angled triangle is a triangle in which one angle is right angle or \n    90 degree.\n    Example:\n    right_angle_triangle(3, 4, 5) == True\n    right_angle_triangle(1, 2, 3) == False\n    '''\n    # Put sides in a list and sort them to find the hypotenuse (the largest side)\n    sides = sorted([a, b, c])\n    \n    # Check the Pythagorean theorem: a^2 + b^2 = c^2\n    # Using sides[0] and sides[1] as legs, and sides[2] as the hypotenuse\n    return sides[0]**2 + sides[1]**2 == sides[2]**2\n```"}
{"task_id": "HumanEval/158", "entry_point": "find_max", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 414, "latency_s": 16.21, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to iterate through the list of strings and determine the count of unique characters for each word. We can use a `set` to find the unique characters of a string. \n\nTo handle the tie-breaking condition (lexicographical order), we can use a custom key for the `max` function. The key will be a tuple: `(number_of_unique_characters, negative_lexicographical_order)`. However, a cleaner way is to use the `max` function with a key that returns the count of unique characters, and then handle the lexicographical order by sorting the list first or by using a custom comparison. \n\nActually, the most efficient way is to use `max()` with a key that returns the count of unique characters. To handle the lexicographical tie-break (where we want the *smallest* string alphabetically among those with the *maximum* count), we can sort the list lexicographically first, then find the max based on unique counts. Since `max()` returns the first occurrence of the maximum value, the lexicographically first word will be preserved.\n\n```python\ndef find_max(words):\n    \"\"\"Write a function that accepts a list of strings.\n    The list contains different words. Return the word with maximum number\n    of unique characters. If multiple strings have maximum number of unique\n    characters, return the one which comes first in lexicographical order.\n    \"\"\"\n    if not words:\n        return \"\"\n    \n    # Sort lexicographically first to handle the tie-break condition.\n    # max() returns the first occurrence of the maximum value.\n    sorted_words = sorted(words)\n    \n    # Find the word with the maximum number of unique characters.\n    # The key is the length of the set of characters in the word.\n    result = max(sorted_words, key=lambda w: len(set(w)))\n    \n    return result\n```"}
{"task_id": "HumanEval/159", "entry_point": "eat", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 472, "latency_s": 18.09, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to determine how many carrots the rabbit can actually eat based on the `need` and the `remaining` stock. \n\n1. The rabbit wants to eat `need` carrots.\n2. However, the rabbit can only eat what is available in the `remaining` stock. Therefore, the actual amount eaten is the minimum of `need` and `remaining`.\n3. The total number of carrots eaten will be the initial `number` plus the amount actually eaten.\n4. The remaining stock will be the initial `remaining` minus the amount actually eaten.\n\nComplexity:\n- Time Complexity: O(1) as we are performing basic arithmetic.\n- Space Complexity: O(1) as we are returning a fixed-size list.\n\n```python\ndef eat(number, need, remaining):\n    \"\"\"\n    You're a hungry rabbit, and you already have eaten a certain number of carrots,\n    but now you need to eat more carrots to complete the day's meals.\n    you should return an array of [ total number of eaten carrots after your meals,\n                                    the number of carrots left after your meals ]\n    if there are not enough remaining carrots, you will eat all remaining carrots, but will still be hungry.\n    \n    Variables:\n    @number : integer\n        the number of carrots that you have eaten.\n    @need : integer\n        the number of carrots that you need to eat.\n    @remaining : integer\n        the number of remaining carrots thet exist in stock\n    \n    Constrain:\n    * 0 <= number <= 1000\n    * 0 <= need <= 1000\n    * 0 <= remaining <= 1000\n\n    Have fun :)\n    \"\"\"\n    # Determine how many carrots the rabbit actually eats\n    # It is the smaller of what is needed and what is available\n    eaten_now = min(need, remaining)\n    \n    # Calculate final totals\n    total_eaten = number + eaten_now\n    left_in_stock = remaining - eaten_now\n    \n    return [total_eaten, left_in_stock]\n```"}
{"task_id": "HumanEval/160", "entry_point": "do_algebra", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 900, "latency_s": 24.01, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to evaluate an algebraic expression where the order of operations (PEMDAS/BODMAS) applies. Specifically, exponentiation (`**`) has the highest precedence, followed by multiplication (`*`) and floor division (`//`), and finally addition (`+`) and subtraction (`-`).\n\nSince the expression is provided as a sequence of operands and operators, we can use a stack-based approach or a two-pass approach to handle precedence. A common way to handle this is to first process all multiplications and divisions from left to right, and then process all additions and subtractions from left to right. However, because exponentiation is right-associative in Python (e.g., `2**3**2` is `2**(3**2)`), but the problem implies a linear sequence of operations, we will treat the sequence as a standard left-to-right evaluation for operators of the same precedence, while respecting the standard hierarchy.\n\nActually, the standard way to evaluate such a sequence is to treat it like a mathematical string. We can convert the lists into a list of tokens and use a standard expression evaluator or a simplified two-pass approach:\n1. Handle `**` (Exponentiation).\n2. Handle `*` and `//` (Multiplication and Floor Division).\n3. Handle `+` and `-` (Addition and Subtraction).\n\n```python\ndef do_algebra(operator, operand):\n    \"\"\"\n    Given two lists operator, and operand. The first list has basic algebra operations, and \n    the second list is of integers. Use the two given lists to build the algebric \n    expression and return the evaluation of this expression.\n    \"\"\"\n    # Combine operands and operators into a list of tokens\n    # Example: [2, '+', 3, '*', 4, '-', 5]\n    tokens = []\n    for i in range(len(operand)):\n        tokens.append(operand[i])\n        if i < len(operator):\n            tokens.append(operator[i])\n\n    # Pass 1: Handle Exponentiation (**)\n    # Note: In standard math, ** is right-associative. \n    # However, in most \"list of operators\" problems, left-to-right is expected \n    # unless specified. We will follow standard Python precedence.\n    i = 0\n    while i < len(tokens):\n        if tokens[i] == '**':\n            # To handle right-associativity correctly for **:\n            # We look for the next ** to the right.\n            # But for simplicity in this specific format, we'll process left-to-right.\n            left = tokens[i-1]\n            right = tokens[i+1]\n            res = int(left ** right)\n            tokens[i-1:i+2] = [res]\n            # Don't increment i because the list shifted\n        else:\n            i += 1\n\n    # Pass 2: Handle Multiplication (*) and Floor Division (//)\n    i = 0\n    while i < len(tokens):\n        if tokens[i] == '*' or tokens[i] == '//':\n            left = tokens[i-1]\n            right = tokens[i+1]\n            if tokens[i] == '*':\n                res = int(left * right)\n            else:\n                res = int(left // right)\n            tokens[i-1:i+2] = [res]\n        else:\n            i += 1\n\n    # Pass 3: Handle Addition (+) and Subtraction (-)\n    i = 0\n    while i < len(tokens):\n        if tokens[i] == '+' or tokens[i] == '-':\n            left = tokens[i-1]\n            right = tokens[i+1]\n            if tokens[i] == '+':\n                res = int(left + right)\n            else:\n                res = int(left - right)\n            tokens[i-1:i+2] = [res]\n        else:\n            i += 1\n\n    return tokens[0]\n```"}
{"task_id": "HumanEval/161", "entry_point": "solve", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 377, "latency_s": 24.56, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to check two conditions:\n1. Does the string contain any alphabetic characters?\n2. If it does, iterate through the string and swap the case of each letter while keeping non-letters unchanged.\n3. If it contains no letters, return the reversed string.\n\nComplexity:\n- Time: O(n), where n is the length of the string, as we iterate through the string at most twice.\n- Space: O(n) to store the resulting string.\n\n```python\ndef solve(s):\n    \"\"\"You are given a string s.\n    if s[i] is a letter, reverse its case from lower to upper or vise versa, \n    otherwise keep it as it is.\n    If the string contains no letters, reverse the string.\n    The function should return the resulted string.\n    Examples\n    solve(\"1234\") = \"4321\"\n    solve(\"ab\") = \"AB\"\n    solve(\"#a@C\") = \"#A@c\"\n    \"\"\"\n    # Check if there is at least one letter in the string\n    has_letter = any(char.isalpha() for char in s)\n    \n    if not has_letter:\n        # If no letters, return the reversed string\n        return s[::-1]\n    else:\n        # If letters exist, swap the case of each letter\n        result = []\n        for char in s:\n            if char.isalpha():\n                if char.isupper():\n                    result.append(char.lower())\n                else:\n                    result.append(char.upper())\n            else:\n                result.append(char)\n        return \"\".join(result)\n```"}
{"task_id": "HumanEval/162", "entry_point": "string_to_md5", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 232, "latency_s": 22.49, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To implement this, I will use the built-in `hashlib` library. Since `hashlib.md5()` requires a bytes-like object, I must encode the input string (defaulting to UTF-8). I will also include a check for the empty string as specified.\n\n```python\nimport hashlib\n\ndef string_to_md5(text):\n    \"\"\"\n    Given a string 'text', return its md5 hash equivalent string.\n    If 'text' is an empty string, return None.\n\n    >>> string_to_md5('Hello world') == '3e25960a79dbc69b674cd4ec67a72c62'\n    \"\"\"\n    if text == \"\":\n        return None\n    \n    # Encode the string to bytes before hashing\n    encoded_text = text.encode('utf-8')\n    # Generate the md5 hash\n    md5_hash = hashlib.md5(encoded_text).hexdigest()\n    \n    return md5_hash\n```"}
{"task_id": "HumanEval/163", "entry_point": "generate_integers", "passed": true, "finish_reason": "stop", "exec_err": "", "completion_tokens": 445, "latency_s": 22.17, "served_model": "gemma-4-12b-it-UD-Q8_K_XL.gguf", "raw": "To solve this problem, we need to identify the range between `a` and `b` (regardless of which is larger), iterate through every integer in that range, and check if the integer itself is an even digit. \n\nWait, looking at the examples:\n- `generate_integers(2, 8)` returns `[2, 4, 6, 8]`. These are even numbers.\n- `generate_integers(10, 14)` returns `[]`. Even though 10, 12, and 14 are even numbers, they are not \"digits\" (digits are 0-9).\n\nTherefore, the logic is:\n1. Determine the minimum and maximum of `a` and `b`.\n2. Iterate through the range from `min` to `max` inclusive.\n3. Check if the number is a single digit (0-9) AND if it is even.\n4. Return the list of such numbers in ascending order.\n\n```python\ndef generate_integers(a, b):\n    \"\"\"\n    Given two positive integers a and b, return the even digits between a\n    and b, in ascending order.\n\n    For example:\n    generate_integers(2, 8) => [2, 4, 6, 8]\n    generate_integers(8, 2) => [2, 4, 6, 8]\n    generate_integers(10, 14) => []\n    \"\"\"\n    start = min(a, b)\n    end = max(a, b)\n    result = []\n    \n    for num in range(start, end + 1):\n        # A \"digit\" is a single-digit number (0-9)\n        # The problem specifies positive integers, but we check 0-9 for safety\n        if 0 <= num <= 9 and num % 2 == 0:\n            result.append(num)\n            \n    return sorted(result)\n```"}