Create JOSHEPHUS_ALGO.cpp

JOSHEPHUS_ALGO.cpp

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+// THERE ARE N PEOPLE AND 1 KNIFE AND 1ST PERSON STARTS GAME AND ATLERNATE PEOPLE ARE KILLED TELL WHICH PERSON IS ALIVE
+//IDEA IS TO REPRESENT N IN FORM OF 2^X +L 
+//AND THE ANS WILL BE 2*L +1
+/*EG:
+   ALIVE    |  N
+   1           1
+   1           1 2
+   3           1 2 3
+   1           1 2 3 4
+   3           1 2 3 4 5
+   5           1 2 3 4 5 6
+   7           1 2 3 4 5 6 7
+   1           1 2 3 4 5 6 7 8
+   3           1 2 3 4 5 6 7 8 9 
+
+   SO 1 = 2^0+0 L=0 2L+1= 1 
+      2 = 2^1+0 L=0 2L+1= 1 
+      3 = 2^1+1 L=1 2L+1= 3
+      4 = 2^2+0 L=0 2L+1= 1 
+      5 = 2^2+1 L=1 2L+1= 3
+      6 = 2^2+2 L=2 2L+1= 5
+      7 = 2^2+3 L=3 2L+1= 7
+      8 = 2^3+0 L=0 2L+1= 1 
+      9 = 2^3+1 L=1 2L+1= 3
+*/
+
+#include <iostream>
+using namespace std;
+int power_of_2(int n)
+{
+    int i=1;
+    while(i*2<=n)
+    {
+        i=i*2;
+    }
+    return i;
+}
+int alive(int n)
+{
+    int m=power_of_2(n);
+    int r=n-m;
+    return (2*r+1);
+}
+
+int main() 
+{
+    int n=9;
+    cout<<alive(n);
+    return 0;
+}