Added Bytelandian Gold coins

Author: hrishit biswas

Bytelandian-gold-coins/instructions.txt

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+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.

Bytelandian-gold-coins/solution.cpp

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+#include<bits/stdc++.h>
+using namespace std;
+map<int,long long> dp;
+long long optcoins(int n){
+    if(n<12)
+        return n;
+    if(dp.count(n))
+        return dp[n];
+    dp[n]=optcoins(n/2)+optcoins(n/3)+optcoins(n/4);
+    return dp[n];
+}
+int main(){
+    int x;
+    while(scanf("%d",&x)!=EOF)
+        printf("%lld\n",optcoins(x));
+    return 0;
+}