Python/divide_and_conquer/max_subarray_sum.py

"""
Given a array of length n, max_subarray_sum() finds
the maximum of sum of contiguous sub-array using divide and conquer method.

Time complexity : O(n log n)

Ref : INTRODUCTION TO ALGORITHMS THIRD EDITION
(section : 4, sub-section : 4.1, page : 70)

"""


def max_sum_from_start(array):
    """This function finds the maximum contiguous sum of array from 0 index

    Parameters :
    array (list[int]) : given array

    Returns :
    max_sum (int) : maximum contiguous sum of array from 0 index

    """
    array_sum = 0
    max_sum = float("-inf")
    for num in array:
        array_sum += num
        if array_sum > max_sum:
            max_sum = array_sum
    return max_sum


def max_cross_array_sum(array, left, mid, right):
    """This function finds the maximum contiguous sum of left and right arrays

    Parameters :
    array, left, mid, right (list[int], int, int, int)

    Returns :
    (int) :  maximum of sum of contiguous sum of left and right arrays

    """

    max_sum_of_left = max_sum_from_start(array[left : mid + 1][::-1])
    max_sum_of_right = max_sum_from_start(array[mid + 1 : right + 1])
    return max_sum_of_left + max_sum_of_right


def max_subarray_sum(array, left, right):
    """Maximum contiguous sub-array sum, using divide and conquer method

    Parameters :
    array, left, right (list[int], int, int) :
    given array, current left index and current right index

    Returns :
    int :  maximum of sum of contiguous sub-array

    """

    # base case: array has only one element
    if left == right:
        return array[right]

    # Recursion
    mid = (left + right) // 2
    left_half_sum = max_subarray_sum(array, left, mid)
    right_half_sum = max_subarray_sum(array, mid + 1, right)
    cross_sum = max_cross_array_sum(array, left, mid, right)
    return max(left_half_sum, right_half_sum, cross_sum)


if __name__ == "__main__":
    array = [-2, -5, 6, -2, -3, 1, 5, -6]
    array_length = len(array)
    print(
        "Maximum sum of contiguous subarray:",
        max_subarray_sum(array, 0, array_length - 1),
    )