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
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.

https://www.quora.com/Are-there-any-good-resources-or-tutorials-for-dynamic-programming-DP-besides-the-TopCoder-tutorial/answer/Michal-Danil%C3%A1k

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

AC IN one GO, EASY DP!!

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
Date:2006-02-15
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