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.

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Shubham Jadhav: 2017-05-19 16:44:52

use stl::map in C++

narutoumania: 2017-05-16 09:20:28

max size of array is 10^6 hence use map instead of array and u can use top-down approach but it exceeds time-limit hence use memorisation.

avar68: 2017-05-13 12:09:52

what is the input format? Do we have to scan the number of test cases or the no. of test cases is 10?

Last edit: 2017-05-13 23:26:02
hkuadithya: 2017-05-01 12:27:16

In Java, a heap of size 1,000,000,000 will throw out of memory exception. As a workaround, you can either use a Map or use an array of size 250,000,000 / 125,000,000.

aurzora24: 2017-04-16 06:00:13

Beware of edge case 0. For JAVA users, NZEC may annoy you :(

f2014044: 2017-04-08 11:01:35

0 <= n <= 1 000 000 000. thats why an array will give runtime error due to O(n) memory being used. Map will only store elements that occur in the recursion and thus use lesser space.

p3arl_03: 2017-04-07 07:21:22

I am not getting the question theory, where it is written in the question that we can exchange coins more than one time?
Please explain someone!!
Thanks in advance :)

pdn777: 2017-04-04 15:42:14

Hi @mohit_97. I have a solution. Its giving answers. I just don't know if they are correct! :-) Also, whenever I submit to this website, a working Pascal program fails. I don't know why. Finally, I don't know what dp is. Thanks!

mohit_97: 2017-04-03 22:36:00

store the values in map and use recurssion.Easy dp ,first step towards dp.

pdn777: 2017-04-03 18:58:34

Hi. Is there a list of answers, for some set of input 1..N? Thanks!

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