53. Maximum subsequence sum (simple)

Ideas:

And the longest increasing subsequence and longest palindromic sequence classic example similar, they are dynamic programming

State transition equation:

dp[i] represents the largest subsequence sum before the current number

1) If dp[i-1] is a positive number, just add nums[i] directly, dp[i]=dp[i-1]+nums[i]

2) If dp[i-1] is a negative number, then dp[i] only takes nums[i], which is equivalent to reselecting a new subsequence

最终dp[i]=Math.max(dp[i-1]+nums[i],nums[i])

 

Code 1:

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

 

break down:

1) This is the second type of dp, the current value depends on all the previously calculated values

Belong to Linear Programming

 

2) Two cycles are used, which can be combined into one cycle

int res=dp[0];
for(int i=1;i<n;i++){
    dp[i]=Math.max(nums[i],nums[i]+dp[i-1]);
    res=Math.max(res,dp[i]);
}

 

3) The last state cannot be directly returned here (dp[n-1]).

Output should be all the  dp[0], , dp[1]......,dp[n - 1]  read through, whichever is greater

The same situation also applies to "Leguo" question 300: the longest ascending subsequence.