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);
}