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
sandeepd:
20191202 15:32:54
I must admit I got the dreaded CE when I submitted my first solution that I cranked out without thinking much of the approach. Mind is blown after realising how suboptimally I was thinking as well as the simplicity of it all. Nice problem indeed. 

sumantopal07:
20190915 08:01:09
This is a popular DP question but the scenario known as "LINE OF WINE" 

nikhil_sarda:
20190831 12:15:54
A suggestion:


moulikbhardwaj:
20190627 17:15:09
Nice Question for DP beginners, AC in one GO! 

suraj_13:
20190320 19:38:50
Refer to this  ( https://www.quora.com/ArethereanygoodresourcesortutorialsfordynamicprogrammingDPbesidestheTopCodertutorial/answer/MichalDanilák ) if you are having trouble. 

manas173:
20190110 15:38:25
Last edit: 20190111 07:42:58 

pavanjupalli:
20190110 14:46:57
my code runs up to 11 then it shows wrong answer,help me out? 

harry_shit:
20181029 14:34:25
feeling i just got is awesome :)))))) Last edit: 20181029 14:40:54 

adipat:
20181012 10:46:03
There are two things of significance in this problem. First, find a way to represent age in terms of start and end indices so that you don't need it during memoization. Second, something very subtle, using unordered_map gave me TLE, switched to a 2D vector and it passed probably because finding if a key exists is not constant time in all cases whereas if you initialise a 2D vector with dummy values, checking if the key exists is a constant time operation. 

Sampath Ravolaparthi:
20180817 11:55:08
For Newbies out there, I've written a very detailed editorial for this. Check it out

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 