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
little_finger: 2018-06-15 09:28:09

Do we know the no of test cases?

vgupta1127: 2018-06-04 07:38:31

how do i take variable inputs in java??? Because the question does not specify the no of test cases?

alwerty: 2018-06-02 04:15:02

First time on this site, how are you supposed to handle the input if you don't know how long it is? should I look for EOF?

thunderbird18: 2018-06-01 06:17:07

nice dp problem,be careful with input and size of array in dp.

caro_linda2018: 2018-05-28 04:50:47

Getting SIGABRT, problably because I don't know how to stop reading the input... Just made "while (cin>>n)". Does someone know how can I fix it? Thank you a lot!!

akash13s: 2018-05-24 13:49:16

dp array,and recursion for n>1000000

ayushtopper: 2018-05-20 22:19:09

How map<int, long long> works fine here for input 10^9? Isn't 10^9 very large to fit into int??

ankitk2909: 2018-05-16 12:44:43

watch out for the test case for 0 if your program is working otherwise and you are getting nzec runtime error

nitish235: 2018-05-09 12:54:22

u can not make a dp array of size 10^9 so make dp array of size 10^6 , precompute all values of dp array..
Then make recursive call when n >10^6 with base condition n<=10^6(because you have already computed all results).

abualy: 2018-03-13 11:17:06

recursion, and memory array, solved with GO

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