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77 lines
2.0 KiB
Python
77 lines
2.0 KiB
Python
"""
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Given a array of length n, max_subarray_sum() finds
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the maximum of sum of contiguous sub-array using divide and conquer method.
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Time complexity : O(n log n)
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Ref : INTRODUCTION TO ALGORITHMS THIRD EDITION
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(section : 4, sub-section : 4.1, page : 70)
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"""
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def max_sum_from_start(array):
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""" This function finds the maximum contiguous sum of array from 0 index
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Parameters :
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array (list[int]) : given array
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Returns :
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max_sum (int) : maximum contiguous sum of array from 0 index
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"""
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array_sum = 0
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max_sum = float("-inf")
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for num in array:
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array_sum += num
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if array_sum > max_sum:
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max_sum = array_sum
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return max_sum
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def max_cross_array_sum(array, left, mid, right):
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""" This function finds the maximum contiguous sum of left and right arrays
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Parameters :
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array, left, mid, right (list[int], int, int, int)
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Returns :
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(int) : maximum of sum of contiguous sum of left and right arrays
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"""
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max_sum_of_left = max_sum_from_start(array[left : mid + 1][::-1])
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max_sum_of_right = max_sum_from_start(array[mid + 1 : right + 1])
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return max_sum_of_left + max_sum_of_right
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def max_subarray_sum(array, left, right):
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""" Maximum contiguous sub-array sum, using divide and conquer method
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Parameters :
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array, left, right (list[int], int, int) :
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given array, current left index and current right index
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Returns :
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int : maximum of sum of contiguous sub-array
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"""
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# base case: array has only one element
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if left == right:
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return array[right]
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# Recursion
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mid = (left + right) // 2
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left_half_sum = max_subarray_sum(array, left, mid)
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right_half_sum = max_subarray_sum(array, mid + 1, right)
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cross_sum = max_cross_array_sum(array, left, mid, right)
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return max(left_half_sum, right_half_sum, cross_sum)
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array = [-2, -5, 6, -2, -3, 1, 5, -6]
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array_length = len(array)
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print(
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"Maximum sum of contiguous subarray:", max_subarray_sum(array, 0, array_length - 1)
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)
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