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62 lines
1.7 KiB
Python
62 lines
1.7 KiB
Python
"""
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The maximum subarray sum problem is the task of finding the maximum sum that can be
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obtained from a contiguous subarray within a given array of numbers. For example, given
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the array [-2, 1, -3, 4, -1, 2, 1, -5, 4], the contiguous subarray with the maximum sum
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is [4, -1, 2, 1], so the maximum subarray sum is 6.
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Kadane's algorithm is a simple dynamic programming algorithm that solves the maximum
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subarray sum problem in O(n) time and O(1) space.
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Reference: https://en.wikipedia.org/wiki/Maximum_subarray_problem
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"""
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from collections.abc import Sequence
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def max_subarray_sum(
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arr: Sequence[float], allow_empty_subarrays: bool = False
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) -> float:
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"""
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Solves the maximum subarray sum problem using Kadane's algorithm.
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:param arr: the given array of numbers
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:param allow_empty_subarrays: if True, then the algorithm considers empty subarrays
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>>> max_subarray_sum([2, 8, 9])
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19
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>>> max_subarray_sum([0, 0])
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0
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>>> max_subarray_sum([-1.0, 0.0, 1.0])
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1.0
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>>> max_subarray_sum([1, 2, 3, 4, -2])
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10
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>>> max_subarray_sum([-2, 1, -3, 4, -1, 2, 1, -5, 4])
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6
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>>> max_subarray_sum([2, 3, -9, 8, -2])
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8
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>>> max_subarray_sum([-2, -3, -1, -4, -6])
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-1
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>>> max_subarray_sum([-2, -3, -1, -4, -6], allow_empty_subarrays=True)
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0
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>>> max_subarray_sum([])
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0
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"""
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if not arr:
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return 0
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max_sum = 0 if allow_empty_subarrays else float("-inf")
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curr_sum = 0.0
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for num in arr:
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curr_sum = max(0 if allow_empty_subarrays else num, curr_sum + num)
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max_sum = max(max_sum, curr_sum)
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return max_sum
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if __name__ == "__main__":
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from doctest import testmod
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testmod()
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nums = [-2, 1, -3, 4, -1, 2, 1, -5, 4]
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print(f"{max_subarray_sum(nums) = }")
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