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.
该题最简单的方法当然是枚举所有情况，然后选出最大的和。但是此题可以采用分治的算法。

• 把数组分成左右两部分
• 整体和、左侧和、右侧和只中取最大的
• 再把左侧和右侧递归下去
• 最后得出最大和

class Solution {public:     int maxSubArray(vector<int>& nums) {        int n = nums.size();        return maxSub(nums, 0, n - 1);    }private:    int maxSub(vector<int>& nums, int l, int r) {        if (l > r) return INT_MIN;        int m = l + ((r - l) /2);        int lm = maxSub(nums, l, m - 1); // left half        int rm = maxSub(nums, m + 1, r); // right half        int i, sum, ml = 0, mr = 0;        // Move leftwards        for (i = m - 1, sum = 0; i >= l; i--) {            sum += nums[i];            ml = max(sum, ml);        }        // Move rightwards        for (i = m + 1, sum = 0; i <= r; i++) {            sum += nums[i];            mr = max(sum, mr);        }        return max(ml + mr + nums[m], max(lm, rm));    }};