TRT  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
The maximum revenue FJ can achieve by selling the treats
Example
Input: 5 1 3 1 5 2 Output: 43
hide comments
Diptesh Patel:
20140929 09:47:28
what is wrong with case:12 ? :( 

Kishlay Raj:
20140922 14:27:12
my 50th cakewalk :P 

Deepanker Aggarwal:
20140920 16:50:58
50th :)...Btw any clues on how can this be done iteratively? 

Arun Karthikeyan:
20140913 19:54:33
Java Recursion TLE, same soln AC in C++


Gaurav Ahirwar:
20140907 11:47:38
AC in go! cakewalk dp! :) :D .. 

S:
20140830 18:56:45
:S :D first attempt 

tushar aggarwal:
20140816 19:54:53
got it in 1st attempt :) 

kernel:
20140809 19:17:56
Instead of thinking it in terms of pure DP its better to approach the problem with recursion(TOPDOWN) with memoization...... AC


AmirShams:
20140808 16:19:44
nice Last edit: 20140808 16:20:38 
Added by:  Nguyen Van Quang Huy 
Date:  20060215 
Time limit:  0.165s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 VB.NET 
Resource:  USACO FEB06 Gold Division 