There are n people standing in a circle waiting to be executed. The counting out begins at some point in the circle and proceeds around the circle in a fixed direction. In each step, a certain number of people are skipped and the next person is executed. The elimination proceeds around the circle (which is becoming smaller and smaller as the executed people are removed), until only the last person remains, who is given freedom. Given the total number of persons n and a number m which indicates that m-1 persons are skipped and m-th person is killed in circle. The task is to choose the place in the initial circle so that you are the last one remaining and so survive.
Examples :
Input : Length of circle : n = 4
Count to choose next : m = 2
Output : 1
Input : n = 5
m = 3
Output : 4
We have discussed different solutions of this problem (here and here). In this post a simple circular linked list based solution is discussed.
1) Create a circular linked list of size n.
2) Traverse through linked list and one by one delete every m-th node until there is one node left.
3) Return value of the only left node.
C++
// CPP program to find last man standing #include<bits/stdc++.h> using namespace std; /* structure for a node in circular linked list */struct Node { int data; struct Node *next; }; // To create a new node of circular // linked list Node *newNode(int data) { Node *temp = new Node; temp->next = temp; temp->data = data; } /* Function to find the only person left after one in every m-th node is killed in a circle of n nodes */void getJosephusPosition(int m, int n) { // Create a circular linked list of // size N. Node *head = newNode(1); Node *prev = head; for (int i = 2; i <= n; i++) { prev->next = newNode(i); prev = prev->next; } prev->next = head; // Connect last // node to first /* 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; } printf ("Last person left standing " "(Josephus Position) is %d
", ptr1->data); } /* Driver program to test above functions */int main() { int n = 14, m = 2; getJosephusPosition(m, n); return 0; } |
Java
// Java Code to find the last man Standing public class GFG { // 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); } } |
C#
// C# Code to find the last man Standing using System; public class GFG { // Node class to store data 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; } Console.WriteLine ("Last person left standing " + "(Josephus Position) is " + ptr1.data); } /* Driver program to test above functions */ static public void Main(String []args) { int n = 14, m = 2; getJosephusPosition(m, n); } } //contributed by Arnab Kundu |
Output :
Last person left standing (Josephus Position) is 13
Time complexity: O(m * n)
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
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