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));
}