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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lotus_guy: 2017-03-08 09:33:04

Think a bit different :D

shadow10: 2017-03-07 07:51:07

Use dictionary in python

jamesx_: 2017-02-26 20:01:12

Nice one. Recommended for beginners looking for practicing DP problems.

anmol23: 2017-02-24 22:52:30

Why does array give runtime error but map does not?

taiken: 2017-02-04 16:26:06

I was getting SIGSEGV. As it turns out I was using simple arrays (to check if the value had already been calculated) in C++ (not std ones) but I failed to initialize them so when I tried to compare to a -1 or 0 or whatever, it failed. Then it was just a matter of initializing the array and AC.

sahil_420420: 2017-01-31 08:03:12

pre-comp upto 1000000 , cakewalk :p :p for several testcases use while(cin>>n) c++ :D :D

vineetpratik: 2017-01-26 12:00:51

solved using array and recursion after max array size AC in 0.00 3.4M

Last edit: 2017-01-26 12:04:24
arpit_1996: 2017-01-23 16:23:34

In c++ don't use while (!cin.eof()) gave me many WAs.

soumavo769: 2017-01-14 05:56:00

can anyone provide any test case other than the ones given here which may be critical

simran07: 2017-01-11 20:10:02

solved from top down.. but getting tle or runtime error without map in bottom up?? why??

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