Question 51 : How to detect a loop in linked list. If linked list has loop, find the start node for the loop.

 First approach that you may think may something look like:

• Traverse through each node till end , tracking visited node using visited flag.
• If you find node that is already visited, then there is a loop in LinkedList and if you reach till end while traversing then there is no loop in LinkedList

But problem with above approach is, in most cases you can not change data structure of LinkedList node, so you won’t be able to add visited flag to it.

Efficient approach:

Efficient approach for this problem would be Floyd’s cycle detection algorithm,so steps for this algo would be:

• Use two pointer fastPtr and slowPtr and initialize both to head of linkedlist
• Move fastPtr by two nodes and slowPtr by one node in each iteration.
• If fastPtr and slowPtr meet at some iteration , then there is a loop in linkedlist.
• If fastPtr reaches to the end of linkedlist without meeting slow pointer then there is no loop in linkedlist (i.e fastPtr->next or fastPtr->next->next become null. 
• Java code for this algo will be

 public boolean ifLoopExists() {
  Node fastPtr = head;
  Node slowPtr = head;
  while (fastPtr != null && fastPtr.next != null) {
   fastPtr = fastPtr.next.next;
   slowPtr = slowPtr.next;
   if (slowPtr == fastPtr)
    return true;
 
  }
  return false;
 }
 

Above solution work with o(n) time complexity and o(1) space complexity.

Let's create a linked list without a loop :

Let's create a java program called “LinkedList.java”

public class LinkedList{
 
    private Node head;
 
    private static class Node {
        private int value;
        private Node next;
 
        Node(int value) {
            this.value = value;
 
        }
    }
 
    public void addToTheLast(Node node) {
 
        if (head == null) {
            head = node;
        } else {
            Node temp = head;
            while (temp.next != null)
                temp = temp.next;
 
            temp.next = node;
        }
    }
 
    public void printList() {
        Node temp = head;
        while (temp != null) {
            System.out.format("%d ", temp.value);
            temp = temp.next;
        }
        System.out.println();
    }
 
    public boolean ifLoopExists() {
        Node fastPtr = head;
        Node slowPtr = head;
        while (fastPtr != null && fastPtr.next != null) {
            fastPtr = fastPtr.next.next;
            slowPtr = slowPtr.next;
            if (slowPtr == fastPtr)
                return true;
 
        }
        return false;
    }
 
    public static void main(String[] args) {
        LinkedList list = new LinkedList();
        // Creating a linked list
 
        list.addToTheLast(new Node(5));
        list.addToTheLast(new Node(6));
        list.addToTheLast(new Node(7));
        list.addToTheLast(new Node(1));
        list.addToTheLast(new Node(2));
 
        list.printList();
 
        // Test if loop existed or not
        System.out.println("Loop existed-->" + list.ifLoopExists());
 
    }
}
 

Logically our linkedlist can be represented as :

Run above program, you will get following output:

5 6 7 1 2
Loop existed-->false

Let's create a loop in LinkedList

Now we will connect last node to the nodewith value 7 and it will create loop in linked list, so change above main method to this:

public static void main(String[] args) {
        LinkedList list = new LinkedList();
        // Creating a linked list
        Node loopNode=new Node(7);
        list.addToTheLast(new Node(5));
        list.addToTheLast(new Node(6));
        list.addToTheLast(loopNode);
        list.addToTheLast(new Node(1));
        list.addToTheLast(new Node(2));
 
        list.printList();
        // creating a loop
        list.addToTheLast(loopNode);
        // Test if loop existed or not
        System.out.println("Loop existed-->" + list.ifLoopExists());
 
    }
 

Logically our linkedlist with loop can be represented as :

5 6 7 1 2
Loop existed-->true

so this is how you can detect a loop in linkedlist.

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