divide-conquer-combine(4.1 from the introduction to algorithm)

this example is from chapter 4 in 《the introduction to algorithm》

the main idea is all showed in the book , i think maybe realizing the algorithm is a good way to understand it.

/*

from : introduction to algorithm chapter four

algorithm:divide and conquer

the time complexity of this algorithm is O(n * logn)



*/

#include <stdio.h>



int Find_max_crossing_subarray(int *a, int low, int mid, int high)

{

    int left_sum = -0xffff;

    int sum = 0;

    for (int i = mid; i >= low; i--)

    {

        sum += a[i];

        if (sum > left_sum)

            left_sum = sum;

    }

    int right_sum = -0xffff;

    sum = 0;

    for (int j = mid+1; j <= high; j++)

    {

        sum += a[j];

        if (sum > right_sum)

            right_sum = sum;

    }

    return left_sum + right_sum;

}



int find_maximum_subarray(int *a, int low, int high)

{

    if (high == low)

    {

        return *(a+high); // base case: only one element

    }

    else

    {

        int mid = (high + low)/2;

        if ((find_maximum_subarray(a, low, mid) >= find_maximum_subarray(a, mid+1, high))&&(find_maximum_subarray(a, low, mid)>=Find_max_crossing_subarray(a,low,mid,high)))

        {

            return find_maximum_subarray(a, low, mid);

        }

        else if ((find_maximum_subarray(a, mid+1, high) >= find_maximum_subarray(a, low, mid))&&(find_maximum_subarray(a, mid+1, high) >= Find_max_crossing_subarray(a,low,mid,high)))

        {

            return find_maximum_subarray(a, mid+1, high);

        }

        else

        {

            return Find_max_crossing_subarray(a, low, mid, high);

        }

    }

}



int main()

{

    int a[16]={13,-3,-25,20,-3,-16,-23,18,20,-7,12,-5,-22,15,-4,7};

    int b[6]={1,2,3,4,5};

    printf("%d\n",find_maximum_subarray(a,0,15));

    printf("%d\n",find_maximum_subarray(b,0,5));

}