53. Maximum Subarray

Given an integer array nums, find the contiguous subarray (containing at least one number) which has the largest sum and return its sum.

Example:

Input: [-2,1,-3,4,-1,2,1,-5,4],
Output: 6
Explanation: [4,-1,2,1] has the largest sum = 6.

Follow up:

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

 

这是一道来自84年的ACM题目,现在是easy级别,可怕

dp公式, dp[i]=max(dp[i-1] + nums[i] , nums[i])

dp[i]  代表以第i个数字结尾的子数组 , 和最大.

 

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