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.


Line 1: A single integer, N

Lines 2..N+1: Line i+1 contains the value of treat v(i)


The maximum revenue FJ can achieve by selling the treats




hide comments
iamthewalrus: 2011-10-04 09:50:07

I'm using recursion, gives TLE !!

Kunal Kapadia: 2011-06-15 17:47:53

Done :)

The Financier: 2011-03-05 09:30:48

Tornike Mandzulashvili, isn't. Try 6 98 98 98 98 1 99 , correct is 1865

What is the optimal logik ? I solved using bruteforce with caching. But it's too slow

Tornike Mandzulashvili: 2012-01-16 13:53:18

if c[l]<=c[r] then take c[l]*a and l++; else choose c[r]*a and r--; this is o(n) solution . isnt it right???

yyf: 2010-12-19 02:42:14

The treats are numbered 1..N and stored sequentially in single file in a long box that is open at both ends

pantop: 2010-05-26 11:34:53

@ ~!(*(@*!@^&
why did he sell the treats ( values 1,3,1,5,2) in this order (1,5,2,3,4)of indices....why not in (1,3,5,2,4) making 1*1 + 2*1 + 3*2 + 4*3 + 5*5 = 46 > 43 ...??????????

Pls read the problem statement carefully !!

Last edit: 2010-05-27 05:56:13
~!(*(@*!@^&: 2009-03-27 06:36:10

Explanation of the sample:

Five treats. On the first day FJ can sell either treat #1 (value 1) or treat #5 (value 2).

FJ sells the treats (values 1, 3, 1, 5, 2) in the following order of indices: 1, 5, 2, 3, 4, making 1x1 + 2x2 + 3x3 + 4x1 + 5x5 = 43 - Insert example explaination pls.

Added by:Nguyen Van Quang Huy
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