Treats for the Cows

FJ has purchased N (1 <= N <= 2000) yummy treats for the cows who get money for giving vast amounts of milk. FJ sells one treat per day and wants to maximize the money he receives over a given period time.

The treats are interesting for many reasons:

• The treats are numbered 1..N and stored sequentially in single file in a long box that is open at both ends. On any day, FJ can retrieve one treat from either end of his stash of treats.
• Like fine wines and delicious cheeses, the treats improve with age and command greater prices.
• The treats are not uniform: some are better and have higher intrinsic value. Treat i has value v(i) (1 <= v(i) <= 1000).
• Cows pay more for treats that have aged longer: a cow will pay v(i)*a for a treat of age a.

Given the values v(i) of each of the treats lined up in order of the index i in their box, what is the greatest value FJ can receive for them if he orders their sale optimally?

The first treat is sold on day 1 and has age a=1. Each subsequent day increases the age by 1.

Input

Line 1: A single integer, N

Lines 2..N+1: Line i+1 contains the value of treat v(i)

Output

Line 1: The maximum revenue FJ can achieve by selling the treats

Sample Input

5
1
3
1
5
2

Sample Output

43

Hint

Explanation of the sample:

Five treats. On the first day FJ can sell either treat #1 (value 1) or treat #5 (value 2).

FJ sells the treats (values 1, 3, 1, 5, 2) in the following order of indices: 1, 5, 2, 3, 4, making 1x1 + 2x2 + 3x3 + 4x1 + 5x5 = 43.

 

这题要么从左边取，要么从右边取，也是一道DP;

 

#include<stdio.h>
#include<algorithm>
#include<iostream>
#include<string.h>

using namespace std;
 int a[2100];
 int dp[2100][2100]={0};
 int N;

 int dfs(int i,int l,int r)
 {
     if(l==r)
        return a[l]*i;
     if(dp[l][r]!=0)
        return dp[l][r];
     dp[l][r]=max(dfs(i+1,l+1,r)+a[l]*i,dfs(i+1,l,r-1)+a[r]*i);
     return dp[l][r];
 }

int main()
{

    scanf("%d",&N);
    for(int i=1;i<=N;i++)
        scanf("%d",&a[i]);
    int t=dfs(1,1,N);
    printf("%d",t);
    return 0;
}