Poj3186treats for the cows (interval DP)

Description

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 has es over a given period time.

The treats are interesting for each 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.

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

513152

Sample output

43

Hint

Explanation of the sample:

Five treats. On the first day FJ can have 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. only the two ends can be retrieved.

#include<stdio.h>int dp[2005][2005];int max(int a,int b){    return a>b?a:b;}int main(){    int n,a[2005],ans[2005];    while(scanf("%d",&n)>0)    {        ans[0]=0;        for(int i=1;i<=n;i++)        {            scanf("%d",&a[i]);            ans[i]=ans[i-1]+a[i];            for(int j=1;j<=n;j++)            dp[i][j]=0;        }        for(int r=0;r<n;r++)        for(int i=1;i<=n-r;i++)        {            int j=i+r;            dp[i][j]=max(dp[i][j-1]+a[j]+ans[j-1]-ans[i-1],a[i]+ans[j]-ans[i]+dp[i+1][j]);        }        printf("%d\n",dp[1][n]);    }}

Poj3186treats for the cows (interval DP)