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
Input: 5 1 3 1 5 2 Output: 43
feeling i just got is awesome :))))))Last edit: 2018-10-29 14:40:54
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.
For Newbies out there, I've written a very detailed editorial for this. Check it out
Think about the recursive approach first.
Last edit: 2018-06-27 15:34:22
A very very nice problem....variation of matrix chain multiplication but this time i did it totally by myselef.
Nothing is wrong with the test case 12 . Just make sure that you are using the storage array within bounds  .
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.
similar problem TWENDS.
used a std::map<pair<int,int>,int> got tle. Got AC with 2D array memoization