Mbpp

MBPP

Write a Python function that satisfies the given tests. Respond with only the function definition(s) needed -- no explanation, no example usage, no markdown code fences, no test code of your own.

General Strategies

• Carefully analyze the test cases to infer the expected behavior, including edge cases.
• Handle edge cases explicitly, such as empty inputs, zero, negative numbers, or single-element inputs.
• Use built-in functions and libraries (e.g., math, re, zip, map, lambda) when appropriate for clarity and correctness.
• For list or string manipulation, consider list comprehensions, slicing, and built-in methods like split, join, strip, replace, or isdigit.
• When processing sequences, iterate carefully and maintain state (e.g., using sets or dictionaries) to track seen elements or counts.
• For mathematical functions, ensure correct formulas and use floating-point arithmetic when needed.
• When working with recursion, ensure base cases are correct and recursive calls progress toward termination.
• For sorting and dynamic programming problems, sort input if order is not guaranteed, and use DP arrays to store intermediate results.
• When using regular expressions, anchor patterns (e.g., ^, \b) and escape special characters when matching literals.
• Return values exactly as specified (e.g., strings, tuples, lists) and ensure no syntax errors (e.g., unclosed strings, missing returns).
• Avoid off-by-one errors in loops and indexing, especially when using ranges or slicing.
• For bit manipulation, use bitwise operators (|, &, ^, <<, >>) and understand binary representations.
• When flattening or transforming nested structures, use nested loops or comprehensions with zip(*...) for transposition.
• Always validate input constraints (e.g., IP address octets in [0,255]) and return correct error responses.
• For geometric or trigonometric calculations, use math.pi and correct formulas (e.g., area, arc length, lateral surface).
• In recursive or iterative sequences (e.g., Fibonacci-like), initialize base values correctly and iterate from known states.
• When comparing floating-point results, rely on exact decimal matches as per test expectations.
• For problems involving pairs or combinations, use nested loops with proper indexing to avoid duplicates.
• Ensure string matching patterns correctly handle zero or one occurrence using ? and full string coverage.