""" 
Given a array of length n, max_sub_array_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_sub_array_sum(array, left, right):
    """ This function finds the maximum of sum of contiguous sub-array 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_sub_array_sum(array, left, mid)
    right_half_sum = max_sub_array_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)


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