Maximum Subarray

Problem

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

.

DP 来做 O（n） 的复杂度是最好的，但是这个divide and conquer 解法也值得学习

class Solution {

int helper(const vector<int>& nums, int left, int right ) {
if(left > right) return 0;
int mid = (left + right)/2;

int leftRst = helper(nums, left, mid - 1);
int rightRst = helper(nums, mid + 1, right);

int leftSum = 0, curSum = 0;
for( int i = mid - 1; i >= 0; i-- ) {
curSum += nums[i];
leftSum = max( curSum, leftSum);
}

int rightSum = 0; curSum = 0;
for( int i = mid + 1; i <= right ; i++ ) {
curSum += nums[i];
rightSum = max( curSum, rightSum);
}
int crossRst = leftSum + rightSum + nums[mid];

int rst = max(leftRst, rightRst);
rst = max(rst, crossRst);

return rst;
}
public:
int maxSubArray(vector<int>& nums) {
return helper(nums, 0, nums.size() - 1);
}
};