Adding Josephus Algorithm

Author: Sun-0321

Dynamic Programming/josephus_algorithm.cpp

@@ -0,0 +1,43 @@
+// Author : Sundar
+
+/*Problem : N people are standing in a circle and we continuously eliminate the M th person 
+starting from the first. Find the peson who is not eliminated and is still standing in the circle
+
+    Sample Input: 5 2
+    Ans : 3
+    The 3rd person is the person who is not eliminated.
+*/
+
+#include<iostream>
+using namespace std;
+int josephus_iterative(int N,int M)
+{
+    int res=0;
+    for(int i=1;i<=N;i++)
+    {
+        res=(res+M)%i;
+    }
+    return res+1;
+}
+int josephus_recursive(int N,int M)
+{
+    if(N==1)
+        return 1;
+    int a=josephus_recursive(N-1,M);
+    return (a+M-1)%N+1;
+}
+
+
+
+int main()
+{
+    int N,M;
+    //N - number of people in the circle
+    //M - people from the current location to be eliminated
+    cin>>N>>M;
+    
+    
+    cout<<"The Last Standing person derived using ITERATION : "<<josephus_iterative(N,M)<<'\n';
+    cout<<"The Last Standing person derived using RECURSION : "<<josephus_recursive(N,M)<<'\n';
+    return 0;
+}