From 463ae4285a8041f751d48a882e83e398c2db24b6 Mon Sep 17 00:00:00 2001
From: Raghav Agarwal <raghav.agarwalqw77@gmail.com>
Date: Fri, 2 Oct 2020 16:28:00 +0530
Subject: [PATCH] added solution to problem Bytelandian gold coins of codechef
 with explanation

---
 .../code.cpp                                  | 43 +++++++++++++++++++
 1 file changed, 43 insertions(+)
 create mode 100644 DP/Bytelandian_gold_coins_problem_codechef/code.cpp

diff --git a/DP/Bytelandian_gold_coins_problem_codechef/code.cpp b/DP/Bytelandian_gold_coins_problem_codechef/code.cpp
new file mode 100644
index 00000000..79031422
--- /dev/null
+++ b/DP/Bytelandian_gold_coins_problem_codechef/code.cpp
@@ -0,0 +1,43 @@
+#include<bits/stdc++.h>
+using namespace std;
+#define ull unsigned long long int
+/*
+Problem Statement: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?
+
+Example: input = 12 output = 13
+            -> you can change 12 into 6 , 4 , 3 which sums up to 13.
+
+Explanation:
+        let input = n
+        so output = max(n,( (output of n/2) + (output of n/3) + (output of n/4) ))
+        to store the output of n/2 , n/3 , n/4 , i use an array to reduce the time for multiple calculation of output of n/2 , n/3 , n/4 in sub steps.
+
+*/
+
+ull check(ull n,ull *a)
+{
+    if(n<12)
+        return n;
+    if(a[n])
+        return a[n];
+    return a[n]= max(n,check((n/2),a)+check((n/3),a)+check((n/4),a));
+
+}
+int main()
+{
+    ull n;
+    while(cin>>n)
+    {
+        ull *a = new ull[n+1];
+        ull ans= check(n,a);
+        cout<<ans<<endl;
+    }
+    return 0;
+}