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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nishit5: 2019-06-10 19:38:12

finally solved a dp problem!!!!
(had a problem in taking the input use while(cin>>a)

aryan29: 2019-06-07 23:56:52

My first DP problem

howdy_1999: 2019-06-07 16:42:11

Why is this a dp problem

youknowwho37: 2019-06-04 05:28:40

Dont forget to use long long int

saurav_paul: 2019-05-27 17:24:42

Using stl map for memorization

man_u_13: 2019-05-15 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: 2019-05-13 10:44:05

Just use a recursion and a simple condition

hetp111: 2019-04-12 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: 2019-04-11 17:04:17

if number of test cases is not provided then while(cin>>n){ do the work }
will work perfectly fine : )

Last edit: 2019-04-11 17:04:36
bhaalu_panda: 2019-04-09 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..
Then make recursive call when n >10^6 with base condition n<=10^6(because you have already computed all results).

Added by:Tomek Czajka
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Source limit:50000B
Memory limit:1536MB
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Resource:Purdue Programming Contest Training