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
chirag2505:
20210728 12:32:11
Why map is giving TLE in this problem? But using 2D dp of fixed size got accepted? 

vatsalrocker:
20210708 18:06:14
Go for MCM! 

null12_21:
20210608 20:45:08
use recursion with memorization 

wille_25:
20210312 12:20:53
AC in two GO ..avoid memset function! 

baljot:
20201026 06:09:25
first think of n3 solution then convert it into n2 (how we get age from segment l to r) these type of problem are variation of mcm where smaller interval is processed first then we solve for bigger interval ps try to do iterative 

distructo:
20200922 17:42:06
Just declare both dp and input array globally otherwise it will give you a TLE 

karankaira:
20200902 14:30:39
Don't use a map gives TLE.


zbillion_:
20200822 17:18:53
This was discussed in Errichto dp video 3. He called it line of wines.


lakshya1st:
20200820 19:41:08
AC in one go!! Use memoization technique DP 

s_tank00_:
20200801 19:58:40
why greedy approach is not working ?

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 