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
atif_11:
20160525 08:16:18
It's not a greedy problem.u consider this test case u will get the ans


vishalsingh:
20160423 18:27:43
can anyone suggest test case where greedy approach fails


Nikki:
20160320 20:28:16
For those who don't understand here is my explanation to them: All you need to do here is to find the maximum profit constraint is that you can choose either the most left or most right. 

killjee_15:
20160301 10:10:43
map+pair=>TLE


coderkoko:
20160201 14:07:24
Nice 1! My 2nd Dp! ^_^ 

dwij28:
20160111 16:56:58
It took me 1 hour to come up with a test case where the greedy approach might fail. I was totally convinced that greedy is the way to go until i used a test case where all values are not distinct. Memorized Recursion for AC. 

Akshit Johry:
20160101 16:23:04
great help sriharshaa :)) thank you


Shantanu Banerjee:
20151224 11:42:40
A must for the beginners, including me! :) 

irbis9:
20151117 19:07:09
My first dp on my own without looking for hints or solution. 

sanyamg123:
20151103 04:54:26
dont use a 2d map instead use a 2d array... 2d map gives tle while 2d array gives ac 
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 