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?
Input
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.
Output
For each test case output a single line, containing the maximum amount of American dollars you can make.
Example
Input: 12 2 Output: 13 2
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
Shubham Jadhav:
20170519 16:44:52
use stl::map in C++ 

narutoumania:
20170516 09:20:28
max size of array is 10^6 hence use map instead of array and u can use topdown approach but it exceeds timelimit hence use memorisation.


avar68:
20170513 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: 20170513 23:26:02 

hkuadithya:
20170501 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:
20170416 06:00:13
Beware of edge case 0. For JAVA users, NZEC may annoy you :( 

f2014044:
20170408 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:
20170407 07:21:22
Hi,


pdn777:
20170404 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:
20170403 22:36:00
store the values in map and use recurssion.Easy dp ,first step towards dp.


pdn777:
20170403 18:58:34
Hi. Is there a list of answers, for some set of input 1..N? Thanks! 
Added by:  Tomek Czajka 
Date:  20050503 
Time limit:  9s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 VB.NET 
Resource:  Purdue Programming Contest Training 