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
nishit5:
20190610 19:38:12
finally solved a dp problem!!!!


aryan29:
20190607 23:56:52
My first DP problem 

howdy_1999:
20190607 16:42:11
Why is this a dp problem 

youknowwho37:
20190604 05:28:40
Dont forget to use long long int 

saurav_paul:
20190527 17:24:42
Using stl map for memorization 

man_u_13:
20190515 16:40:42
People solving this using Java must make sure to use long as the data type and also not to use long as the index of the array (typecast to int). 

kawsar_cseru:
20190513 10:44:05
Just use a recursion and a simple condition 

hetp111:
20190412 16:40:34
i get it that we have to use while(cin>>n) for input, but i didn't understand it properly... can someone provide more details about this operation? 

spojwithsaurav:
20190411 17:04:17
if number of test cases is not provided then while(cin>>n){ do the work }


bhaalu_panda:
20190409 23:14:19
You can not make a dp array of size 10^9 so make dp array of size 10^6 , precompute all values of dp array..

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 