53. Maximum Subarray(动态规划）

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.

分析：

创建了dp数组，dp[i]表示以array[i]结尾的最大子数组和为dp[i]，动态转移方程为dp[i]=max(dp[i-1]+array[i],array[i]);

class Solution {
public:
    int maxSubArray(vector<int>& nums) {
        int dp[nums.size()]={0};
        dp[0]=nums[0];
        int maxsum=nums[0];
        for(int i=1;i<nums.size();i++){
            dp[i]=max(dp[i-1]+nums[i],nums[i]);
            maxsum=max(maxsum,dp[i]);
        }
        return maxsum;
    }
};