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
hai_dee:
20180310 10:06:18
Don't even bother trying to do it in Python. I did it in Python using what I'm sure was an optimal algorithm and TLE'ed. Eventually decided to convert my algorithm to C++ despite not having used that language for 10 years. Result was 0.00 second AC. 

sherlock11:
20180203 11:57:42
similar problem TWENDS. 

ameyanator:
20180113 18:55:32
used a std::map<pair<int,int>,int> got tle. Got AC with 2D array memoization 

subhag0721:
20170905 10:45:02
map + pair => TLE,


shauryauppal:
20170614 22:46:22
I first did with greedy approach not attentive.


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..

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 