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) {
       
       int n = nums.size();
        vector<int> dp = vector<int>(n,0);
        int res = nums[0];
        dp[0] = nums[0];
        for(int i = 1; i < n;i++) {
            //.     要么清0 从当前值开始，要么加上当前值
            dp[i] = max(nums[i],dp[i-1]+nums[i]);
            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

class Solution {
    public int maxSubArray(int[] nums) {
        int dp[] = new int[nums.length+1];
        int max = nums[0];
        dp[0] = nums[0];
        for(int i =1;i<nums.length;i++){
            if(dp[i-1]<=0)
                dp[i] = nums[i];
            else
                dp[i] = dp[i-1]+nums[i];
            max = Math.max(dp[i],max);
        }
        return max;
    }
}