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
distructo: 2020-09-22 17:42:06

Just declare both dp and input array globally otherwise it will give you a TLE

karankaira: 2020-09-02 14:30:39

Don't use a map gives TLE.

zbillion_: 2020-08-22 17:18:53

This was discussed in Errichto dp video 3. He called it line of wines.
//leaving this comment for those who came from the video

lakshya1st: 2020-08-20 19:41:08

AC in one go!! Use memoization technique DP

s_tank00_: 2020-08-01 19:58:40

why greedy approach is not working ?

imposter_1729: 2020-07-23 17:42:36

Go for recursion, try storing optimal action for each case, along with the max function

ayush_12349: 2020-06-30 18:24:47

First of all, if u think that dp has no application here and your greedy algorithm will work, just go through this link, for getting an example in which the greedy approach fails.

Some other tips :
1. Declare the array and the DP matrix globally, to avoid runtime error.
2. Avoid memset function.
3. Memoization technique will work fine.

deerawat: 2020-06-25 18:49:20


pradeep_7: 2020-06-02 13:40:28

Test Case :
2 3 5 1 4
Greedy - 49
ans - 50 (2,4,1,3,5)

If u get any runtime error in test case 9||10 increase dp table and array size 2009

Last edit: 2020-06-02 15:01:53
shubham7999: 2020-05-22 06:38:45

ac in third attempt because forget to memeize thr dp array dont forget tp memoize it ....nice problem

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