COINS - Bytelandian gold coins

In Byteland they have a very strange monetary system.

Each Bytelandian gold coin has an integer number written on it. A coin n can be exchanged in a bank into three coins: n/2, n/3 and n/4. But these numbers are all rounded down (the banks have to make a profit).

You can also sell Bytelandian coins for American dollars. The exchange rate is 1:1. But you can not buy Bytelandian coins.

You have one gold coin. What is the maximum amount of American dollars you can get for it?


The input will contain several test cases (not more than 10). Each testcase is a single line with a number n, 0 <= n <= 1 000 000 000. It is the number written on your coin.


For each test case output a single line, containing the maximum amount of American dollars you can make.




You can change 12 into 6, 4 and 3, and then change these into $6+$4+$3 = $13. If you try changing the coin 2 into 3 smaller coins, you will get 1, 0 and 0, and later you can get no more than $1 out of them. It is better just to change the 2 coin directly into $2.

hide comments
shubh809: 2016-10-18 15:33:36

AC in one go.Boosted my confidence for dp.

rajat7: 2016-09-05 11:20:51

AC in one go

karan_batra: 2016-08-29 14:42:00

Easy one. AC in one go. :D

rishabh_nitw: 2016-08-25 16:49:46

My 1st DP :)

manish_hacked: 2016-08-24 21:58:42

AC in first go
Use recursion

suraj_: 2016-08-19 20:56:57

finally ac

monish007: 2016-08-19 19:47:12

Highly recommended for Beginners like me ;)

ravi shankar: 2016-08-07 11:13:51

boom boom :) must try for every beginners

tushar091: 2016-07-27 21:26:27

how to take input in python as number of testcases is not defined .... gives NZEC error

sharath_111: 2016-07-22 13:23:51

good dp problem :) use long long and recursion for numbers greater than 1000000

Added by:Tomek Czajka
Time limit:9s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS PERL 6
Resource:Purdue Programming Contest Training