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
vonasj:
20160813 21:20:40
Haskell Data.Array is too slow for that. 

Mihir Saxena:
20160710 07:14:59
50th!! 

razor123:
20160627 16:39:21
'age' is not a factor for memoizing as age is (i+nj) where i and j are starting and end indices respectively. 

baadshah_:
20160626 21:40:45
AC in ONE GO!!!!!!!!!


adi_1996:
20160625 14:00:11
try TWENDS after this :) 

Tushar Singh:
20160624 22:11:32
Reading comments helped me to get AC in one go!! :D 

saurabh789:
20160623 17:59:54
nice question my 50th! 

sonali9696:
20160622 21:01:44
My first thought was a 3D array for front,rear,age. But such large arrays can't be allocated.So think how age can be expressed in terms of front and rear and make 2D array for front,rear :) Happy coding! 

saini428:
20160613 03:06:54
simple recursion+memorization ,,, 

Shivam Jha:
20160601 12:46:21
a great tutorial for this by Michal Danilák .

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 