53. 最大子序和(dp)

 

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.

 

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

 

 

 

 

递归方程;

dp[i] = dp[i-1]+nums[i] ,dp[i-1]>0

dp[i] = nums[i] ,else

 1 class Solution {
 2     public int maxSubArray(int[] nums) {
 3         int dp[] = new int[nums.length+1];
 4         int max = nums[0];
 5         dp[0] = nums[0];
 6         for(int i =1;i<nums.length;i++){
 7             if(dp[i-1]<=0)
 8                 dp[i] = nums[i];
 9             else
10                 dp[i] = dp[i-1]+nums[i];
11             max = Math.max(dp[i],max);
12         }
13         return max;
14     }
15 }