The purpose is to determine whether the linked list has a cycle or not. This is the fastest method to find cycle in a linked list. The terminology of this algorithm is-

• Traverse linked list using two pointers named slow_ptr and fast_ptr.
• Move the pointer slow_ptr by 1 and fast_ptr by 2.
• If these pointers meet at the same node then there is a loop. If pointers do not meet then linked list doesn’t have a loop.

Algorithm

INPUT: Pointer to a linked list say HEAD.

OUTPUT: Return true if linked list contains loop else return false.

DATA STRUCTURE: A singly linked list.

STEPS:

    If(HEAD == NULL || HEAD->link == NULL) then
        Return false
        Exit
    Else
        // initializing staring pointers
        fast_ptr = HEAD
        slow_ptr = HEAD
        While(HEAD != NULL) do
            // move slow_ptr by 1 step and fast_ptr by 2 steps
            slow_ptr = slow_ptr->link;
            fast_ptr = fast_ptr->link->link;
            If(slow_ptr == fast_ptr)then
                Return true
            EndIf
            HEAD = HEAD->link
        EndWhile
        Return false
    EndIf

Complexity

Time complexity: O(n). Only one traversal of the loop is needed.

Auxiliary Space: O(1). There is no space required.

References

codingninjas.com, geeksforgeeks.org

Conclusion

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