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
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

dennislo: 2018-06-27 18:59:16

Think about the recursive approach first.

shivhek25: 2018-06-27 10:45:55

Last edit: 2018-06-27 15:34:22
kkislay20: 2018-06-08 04:59:22

A very very nice problem....variation of matrix chain multiplication but this time i did it totally by myselef.

aakash2509: 2018-06-05 14:21:19

Nothing is wrong with the test case 12 . Just make sure that you are using the storage array within bounds [2001][2001] .

Last edit: 2018-06-06 09:23:51
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


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