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
satyabrat35:
20170613 20:38:18
simple DP try TWENDS.... :) Last edit: 20170613 20:39:14 

rishabhm123:
20170609 21:21:04
One of the very good ones in DP..Basic one but important as this type of DP algorithm (or say, method) is very much used..


saumilshah07:
20170522 21:40:54
good question and awesome comments !!!! 

da_201501181:
20170521 11:16:56
Very Nice Question..!! Learned a lot..!! 

gurjits909:
20170516 19:31:43
comments are so helpful ..thanku guyz..


vijayrit:
20170510 11:41:58
a good question to improve in recursion and memoization 

alaa_alrayes96:
20170408 09:32:25
simple recursion + memo got acc


sirjan13:
20170328 19:51:24
simple recursion + memo did the trick!!


mddaud001:
20170325 20:02:04
TopDown + Memo


amandal799:
20170324 22:30:02
simple recursion and memorization and AC in one go 
Added by:  Nguyen Van Quang Huy 
Date:  20060215 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 VB.NET 
Resource:  USACO FEB06 Gold Division 