leetcode_question_53 Maximum Subarray

Find the contiguous subarray within an array (containing at least one number) which has the largest sum.

For example, given the array [−2,1,−3,4,−1,2,1,−5,4],
the contiguous subarray [4,−1,2,1] has the largest sum = 6.

More practice:

If you have figured out the O(n) solution, try coding another solution using the divide and conquer approach, which is more subtle.

dp:

int maxSubArray(int A[], int n) {        // Start typing your C/C++ solution below        // DO NOT write int main() function        int max = A[0];        int currentsum = A[0];        for(int i = 1; i < n; ++i){            if(currentsum < 0) currentsum = 0;            currentsum += A[i];            if(currentsum > max) max = currentsum;        }        return max;    }

Divide and Conquer:

int calmaxsubarr(int A[], int begin, int end){        if(begin == end) return A[begin];                int mid = (end-begin)/2 + begin;                int left = calmaxsubarr(A, begin, mid);        int right = calmaxsubarr(A, mid+1, end);                int lefthalf = A[mid];        int tmp = A[mid];        for(int i = mid -1; i >= begin; i--){            tmp += A[i];            if(tmp > lefthalf) lefthalf = tmp;        }                int righthalf = A[mid+1];        tmp = A[mid+1];        for(int i = mid +2; i <= end; ++i){            tmp += A[i];            if(tmp > righthalf)righthalf = tmp;        }        int middle = lefthalf + righthalf;        int res = left > right ? left : right;        res = res > middle ? res : middle;        return res;    }    int maxSubArray(int A[], int n) {        // Start typing your C/C++ solution below        // DO NOT write int main() function        return calmaxsubarr(A, 0, n-1);    }