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
sandeepd: 2019-12-02 15:32:54

I must admit I got the dreaded CE when I submitted my first solution that I cranked out without thinking much of the approach. Mind is blown after realising how sub-optimally I was thinking as well as the simplicity of it all. Nice problem indeed.

sumantopal07: 2019-09-15 08:01:09

This is a popular DP question but the scenario known as "LINE OF WINE"

nikhil_sarda: 2019-08-31 12:15:54

A suggestion:
Do not use map STL, you would get TLE, so use a 2-D array to get AC.

moulikbhardwaj: 2019-06-27 17:15:09

Nice Question for DP beginners, AC in one GO!

suraj_13: 2019-03-20 19:38:50

Refer to this - ( https://www.quora.com/Are-there-any-good-resources-or-tutorials-for-dynamic-programming-DP-besides-the-TopCoder-tutorial/answer/Michal-Danilák ) if you are having trouble.

manas173: 2019-01-10 15:38:25

Last edit: 2019-01-11 07:42:58
pavanjupalli: 2019-01-10 14:46:57

my code runs up to 11 then it shows wrong answer,help me out?

harry_shit: 2018-10-29 14:34:25

feeling i just got is awesome :))))))

Last edit: 2018-10-29 14:40:54
adipat: 2018-10-12 10:46:03

There are two things of significance in this problem. First, find a way to represent age in terms of start and end indices so that you don't need it during memoization. Second, something very subtle, using unordered_map gave me TLE, switched to a 2D vector and it passed probably because finding if a key exists is not constant time in all cases whereas if you initialise a 2D vector with dummy values, checking if the key exists is a constant time operation.

Sampath Ravolaparthi: 2018-08-17 11:55:08

For Newbies out there, I've written a very detailed editorial for this. Check it out
https://www.stopstalk.com/problems/read_editorial/31

P.S: The overall complexity is number of pairs (i, j) for 1 to n. ans = n^2


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