Below diagram shows a linked list with a loop

Following are different ways of doing this
Use Hashing:
Traverse the list one by one and keep putting the node addresses in a Hash Table. At any point, if NULL is reached then return false and if next of current node points to any of the previously stored nodes in Hash then return true.

Mark Visited Nodes:
This solution requires modifications to basic linked list data structure.  Have a visited flag with each node.  Traverse the linked list and keep marking visited nodes.  If you see a visited node again then there is a loop. This solution works in O(n) but requires additional information with each node.
A variation of this solution that doesn’t require modification to basic data structure can be implemented using hash.  Just store the addresses of visited nodes in a hash and if you see an address that already exists in hash then there is a loop.

Floyd’s Cycle-Finding Algorithm:
This is the fastest method. Traverse linked list using two pointers.  Move one pointer by one and other pointer by two.  If these pointers meet at some node then there is a loop.  If pointers do not meet then linked list doesn’t have loop.

Implementation of Floyd’s Cycle-Finding Algorithm:

#include<stdio.h>
#include<stdlib.h>

/* Link list node */
struct node
{
  int data;
  struct node* next;
};

void push(struct node** head_ref, int new_data)
{
  /* allocate node */
  struct node* new_node =
  (struct node*) malloc(sizeof(struct node));

  /* put in the data  */
  new_node->data  = new_data;

  /* link the old list off the new node */
  new_node->next = (*head_ref);

  /* move the head to point to the new node */
  (*head_ref)    = new_node;
}

int detectloop(struct node *list)
{
  struct node  *slow_p = list, *fast_p = list;

  while(slow_p && fast_p &&
          fast_p->next )
  {
    slow_p = slow_p->next;
    fast_p  = fast_p->next->next;
    if (slow_p == fast_p)
    {
       printf("Found Loop");
       return 1;
    }
  }
  return 0;
}

/* Drier program to test above function*/
int main()
{
  /* Start with the empty list */
  struct node* head = NULL;

  push(&head, 20);
  push(&head, 4);
  push(&head, 15);
  push(&head, 10);

  /* Create a loop for testing */
  head->next->next->next->next = head;
  detectloop(head);

  getchar();
}

Time Complexity: O(n)
Auxiliary Space: O(1)

References:
http://en.wikipedia.org/wiki/Cycle_detection
http://ostermiller.org/find_loop_singly_linked_list.html

         

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