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ByteLandian.java
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52 lines (41 loc) · 1.74 KB
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package dynamicProgramming1;
import java.util.HashMap;
/*
* Byte Landian
Byteland has 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 format :
The first and the only line of input contains a the integer value of 'n'. It is the number written on your coin.
Output format :
Print the the maximum amount of American dollars you can make.
Constraints :
0 <= n <= 10 ^ 9
Time Limit: 1 sec
Sample Input 1 :
12
Sample Output 1 :
13
Explanation of Sample Output 1 :
You can change 12 into 6, 4 and 3, and then change these into $6 + $4 + $3 = $13.
Sample Input 2 :
2
Sample Output 1 :
2
Explanation of Sample Output 2 :
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.*/
public class ByteLandian {
private static Long byteLandian(Long n, HashMap<Long, Long> dp) {
if (n <= 1) return n;
if (dp.get(n) != null) return dp.get(n);
var breakDownValue = byteLandian(n / 2, dp) + byteLandian(n / 3, dp) + byteLandian(n / 4, dp);
dp.put(n, Math.max(n, breakDownValue));
return dp.get(n);
}
public static void main(String[] args) {
var dp = new HashMap<Long, Long>();
System.out.println(byteLandian(12L, dp));
System.out.println(byteLandian(2L, dp));
}
}