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* Improve documentation and educational comments in find_max.py - Added clear explanation of Divide and Conquer approach - Improved parameter descriptions for better understanding - Enhanced comments to explain the algorithm steps - Better documentation for educational purposes * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: Christian Clauss <cclauss@me.com>
89 lines
2.9 KiB
Python
89 lines
2.9 KiB
Python
from __future__ import annotations
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def find_max_iterative(nums: list[int | float]) -> int | float:
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"""
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>>> for nums in ([3, 2, 1], [-3, -2, -1], [3, -3, 0], [3.0, 3.1, 2.9]):
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... find_max_iterative(nums) == max(nums)
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True
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True
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True
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True
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>>> find_max_iterative([2, 4, 9, 7, 19, 94, 5])
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94
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>>> find_max_iterative([])
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Traceback (most recent call last):
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...
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ValueError: find_max_iterative() arg is an empty sequence
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"""
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if len(nums) == 0:
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raise ValueError("find_max_iterative() arg is an empty sequence")
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max_num = nums[0]
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for x in nums:
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if x > max_num: # noqa: PLR1730
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max_num = x
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return max_num
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# Divide and Conquer algorithm
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# Using Divide and Conquer approach:
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# 1. Divide the array into two halves
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# 2. Recursively find the maximum in each half
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# 3. Combine the results by comparing the two maximums
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def find_max_recursive(nums: list[int | float], left: int, right: int) -> int | float:
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"""
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Find the maximum value in a list using Divide and Conquer approach
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:param nums: list of numbers to search through
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:param left: starting index of the current subarray (inclusive)
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:param right: ending index of the current subarray (inclusive)
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:return: maximum value found in the subarray nums[left:right+1]
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>>> for nums in ([3, 2, 1], [-3, -2, -1], [3, -3, 0], [3.0, 3.1, 2.9]):
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... find_max_recursive(nums, 0, len(nums) - 1) == max(nums)
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True
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True
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True
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True
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>>> nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]
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>>> find_max_recursive(nums, 0, len(nums) - 1) == max(nums)
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True
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>>> find_max_recursive([], 0, 0)
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Traceback (most recent call last):
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...
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ValueError: find_max_recursive() arg is an empty sequence
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>>> find_max_recursive(nums, 0, len(nums)) == max(nums)
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Traceback (most recent call last):
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...
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IndexError: list index out of range
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>>> find_max_recursive(nums, -len(nums), -1) == max(nums)
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True
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>>> find_max_recursive(nums, -len(nums) - 1, -1) == max(nums)
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Traceback (most recent call last):
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...
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IndexError: list index out of range
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"""
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if len(nums) == 0:
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raise ValueError("find_max_recursive() arg is an empty sequence")
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if (
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left >= len(nums)
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or left < -len(nums)
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or right >= len(nums)
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or right < -len(nums)
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):
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raise IndexError("list index out of range")
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if left == right:
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return nums[left]
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mid = (left + right) >> 1 # Equivalent to (left + right) // 2 - finds middle index
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left_max = find_max_recursive(nums, left, mid) # find max in range[left, mid]
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right_max = find_max_recursive(
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nums, mid + 1, right
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) # find max in range[mid + 1, right]
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return left_max if left_max >= right_max else right_max
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if __name__ == "__main__":
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import doctest
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doctest.testmod(verbose=True)
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