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
vijayrit:
20170510 11:41:58
a good question to improve in recursion and memoization 

alaa_alrayes96:
20170408 09:32:25
simple recursion + memo got acc


sirjan13:
20170328 19:51:24
simple recursion + memo did the trick!!


mddaud001:
20170325 20:02:04
TopDown + Memo


amandal799:
20170324 22:30:02
simple recursion and memorization and AC in one go 

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 ;)

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 