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
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

chawla_1209: 2016-07-20 11:52:35

Must do for beginners.

Saif : 2016-07-19 16:48:57

Problem can also be done without maps
First use dp for nos upto 10^7 and for larger nos use normal recursion

Wumbolo: 2016-07-19 03:12:07

wa and sigfxsxxxz because %I64d modificator instead of %lld

prashant_kn: 2016-07-18 10:57:03

Last edit: 2016-07-18 11:10:57
nikita204: 2016-07-17 21:08:41

my 50th and first dp!...A good one!

liuxueyang: 2016-07-17 10:30:28

Use Integer as key and BigInteger as value in JAVA HashMap... test with 1000000000, output should be: 4243218150
thanks for @vstepano 's comment.

sujoy_3: 2016-07-06 12:12:29

1st dp problem

Ameya: 2016-06-22 23:58:11

I used memoization by hashmap. I'm getting TLC.

edit: Got it. I didn't make the map global. Was initializing it every time the method was called.

Last edit: 2016-06-23 00:26:08

Added by:Tomek Czajka
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Source limit:50000B
Memory limit:1536MB
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