subject

This problem can be seen from the beginning as a dynamic programming problem , But I don't know how to write the state transition equation , But we can think about it. It should be an interval DP, And the interval DP The characteristic of state transition equation is that the state transition equation is generally related to the left node and right node or the middle breakpoint of the interval , Because we choose one of two points at a time, and the one in the original question a The value is (n-(left-right)), So we can get the state transfer equation

`dp[i][j]=max(dp[i][j-]+data[j]*(n-(j-i)),dp[i+][j]+data[i]*(n-(j-i)));`

That's the end of it , Of course not. , First we need to preprocess out dp[i][i]=data[i]

And then we look at the equation , There's a problem with the equation j The first one in the class and i It's the last one who pushed it out , So we're going to let i Push back and forth ,j Push from the front to the back . So this question gives us an inspiration , It's not enough just to get the state transfer equation , It's also important how you push .

Code ：

```#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
int data[],dp[][],maxn=;
int main()
{
int n;
scanf("%d",&n);
for(int i=;i<=n;i++)
scanf("%d",&data[i]),dp[i][i]=data[i];
for(int i=n;i>=;i--)
{
for(int j=i;j<=n;j++)
dp[i][j]=max(dp[i][j-]+data[j]*(n-(j-i)),dp[i+][j]+data[i]*(n-(j-i)));
}
cout<<dp[][n];
return ;
}```

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