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
rishi_07:
20170303 12:30:59
Very Nice Question! 

hasan356:
20170302 18:27:24
My first memo!! 

vladimira:
20170225 15:44:05
Can be implemented easily with just O(n) memory without some matrix chain multiplications. But you must work first with your pen and sheet of paper a little. My solving function was 10 lines. 

nilabja16180:
20170222 19:02:54
Not easy as it seems! 

sarthakshah30:
20170127 19:49:22
AC in one Go ;)


epsilonalpha:
20161222 00:05:27
Got TLE once because I'm used to dealing with vectors instead of arrays and I forgot to pass by reference!


sayedathar11:
20161125 19:19:21
Got a tle just because forgot to memoize fixed that and Got an ac 

siddharth_0196:
20161005 10:58:49
Recursion+Memoization: AC!


davidgalehouse:
20160909 05:28:56
If you're stuck I recommend you try to solve the problem recursively in the most obvious way, study the recursive calls being made and try to make an important observation, turn the observation into memoization, then turn that into DP. 

mahmood_2000:
20160827 12:53:21
My first time I get AC on the first go on spoj :) 
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 