Question

Flavius Josephus was a famous historian of the first century, but apparently, he would not have lived to become famous without the exercise of his computational and mathematical abilities. A legend says that during the Jewish-Roman war he was part of a band of 41 rebels trapped in a cave by the Romans. To avoid capture, the rebels decided to form a circle and proceeded to kill every third remaining person until no one was left. However, Josephus quickly calculated where he and a friend should stand to avoid all this non-sense.

Write a program IN JAVA that given two positive numbers: a) the number of people in the circle, b) the elimination number, for example, if this number is exactly two, we eliminate every second person as in the original problem, determines the survivor’s position. Populate a (circular) linked list representing the band of rebels and repeatedly delete elements from it until only one remains.

Answer 1

2 3 public class GFG1 { 4 5 6 // Node class to store data static class Node 70 public int data ; public Node next; public Node ( int data) this.data = data; } } 10 110 12 13 14 15 16 170 18 19 20e 21 22 23 24 25 /* Function to find the only person left after one in every m-th node is killed in a circle of n nodes */ static void get Josephus Position(int m, int n) { // Create a circular linked list of // size N. Node head = new Node (1); Node prev = head; for(int i = 2; i <= n; i++) { prev.next = new Node (i); prev = prev.next; 26 27 28 29

/* while only one node is left in the linked list*/ Node ptrl = head, ptr2 = head; while (ptrl.next != ptrl) // Find m-th node int count = 1; while (count != m) { ptr2 = ptrl; ptrl = ptrl.next; count++; } /* Remove the m-th node */ ptr2.next = ptrl.next; ptrl = ptr2.next; } + System.out.println ("Last person left standing "(Josephus Position) is " + ptrl.data); } /* Driver program to test above functions */ public static void main(String args[]) { int n = 14, m = 2; get Josephus Position (m, n);

<terminated> GFG1 [Java Application] C:\Program Files Vava\jre 1.8.0_241\bin\javaw.exe (Jun 21, 2020, 8:19:47 AM) Last person left standing (Josephus Position) is 13

source code:

package HomeworkLib;

public class GFG1 {
  
          
       // Node class to store data
       static class Node
       {
           public int data ;
           public Node next;
           public Node( int data )
           {
               this.data = data;
           }
       }
      
       /* Function to find the only person left
       after one in every m-th node is killed
       in a circle of n nodes */
       static void getJosephusPosition(int m, int n)
       {
           // Create a circular linked list of
           // size N.
           Node head = new Node(1);
           Node prev = head;
           for(int i = 2; i <= n; i++)
           {
               prev.next = new Node(i);
               prev = prev.next;
           }
          
           // Connect last node to first
           prev.next = head;
          
           /* while only one node is left in the
           linked list*/
           Node ptr1 = head, ptr2 = head;
          
           while(ptr1.next != ptr1)
           {
              
               // Find m-th node
               int count = 1;
               while(count != m)
               {
                   ptr2 = ptr1;
                   ptr1 = ptr1.next;
                   count++;
               }
              
               /* Remove the m-th node */
               ptr2.next = ptr1.next;
               ptr1 = ptr2.next;
           }
           System.out.println ("Last person left standing " +
                   "(Josephus Position) is " + ptr1.data);
       }
      
       /* Driver program to test above functions */
       public static void main(String args[])
       {
           int n = 14, m = 2;
           getJosephusPosition(m, n);
       }
   }

if you have any doubts ask me..