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
hai_dee: 2018-03-10 10:06:18

Don't even bother trying to do it in Python. I did it in Python using what I'm sure was an optimal algorithm and TLE'ed. Eventually decided to convert my algorithm to C++ despite not having used that language for 10 years. Result was 0.00 second AC.

sherlock11: 2018-02-03 11:57:42

similar problem TWENDS.

ameyanator: 2018-01-13 18:55:32

used a std::map<pair<int,int>,int> got tle. Got AC with 2D array memoization

subhag0721: 2017-09-05 10:45:02

map + pair => TLE,
2-d array => AC

shauryauppal: 2017-06-14 22:46:22

I first did with greedy approach not attentive.
Got WA
thought of tc->
4
6 1 5 5

then did this with memoization in attempt two and got success

Last edit: 2017-06-14 22:46:49
satyabrat35: 2017-06-13 20:38:18

simple DP try TWENDS.... :)

Last edit: 2017-06-13 20:39:14
rishabhm123: 2017-06-09 21:21:04

One of the very good ones in DP..Basic one but important as this type of DP algorithm (or say, method) is very much used..
Good one and along with it...A must one in DP..
No recursion.. done with a 2-D array..

saumilshah07: 2017-05-22 21:40:54

good question and awesome comments !!!!

da_201501181: 2017-05-21 11:16:56

Very Nice Question..!! Learned a lot..!!

gurjits909: 2017-05-16 19:31:43

comments are so helpful ..thanku guyz..
learned a lot . my first memorization problem

Last edit: 2017-05-16 19:33:22

Added by:Nguyen Van Quang Huy
Date:2006-02-15
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