Cycle in a Linked List? Detect It Before You Loop Forever!

Detect a Cycle in a Linked List – Find the Loop!

Linked lists are a fundamental data structure, but they come with a tricky challenge—cycles. If a cycle exists, traversing the list can become an infinite loop. Today’s problem is to detect whether a given linked list contains a cycle.

The Best Data Structure for Solving It (and Why!)

To detect a cycle, no additional complex data structures are needed. The best solutions rely on:

  • Hashing (HashSet/HashMap) – Keeps track of visited nodes.

  • Two-pointer technique (Floyd’s Cycle Detection Algorithm) – Detects cycles efficiently using minimal space.

Different Approaches – Brute Force to Optimized Solutions

1)HashMap Approach – Track Visited Nodes

Idea: Store each visited node in a HashSet. If a node is visited again, a cycle is detected.

import java.util.HashSet;

class Solution {
    public boolean hasCycle(ListNode head) {
        HashSet<ListNode> visited = new HashSet<>();
        while (head != null) {
            if (visited.contains(head)) return true;
            visited.add(head);
            head = head.next;
        }
        return false;
    }
}

Why It’s Not Optimal: This approach uses additional space, making it inefficient for large lists.

2)Optimized Approach – Floyd’s Cycle Detection (Hare & Tortoise)

Idea: Use two pointers, one moving slow (one step at a time) and one moving fast (two steps at a time). If they ever meet, a cycle exists.

class Solution {
    public boolean hasCycle(ListNode head) {
        if (head == null || head.next == null) return false;
        
        ListNode slow = head, fast = head;
        while (fast != null && fast.next != null) {
            slow = slow.next;
            fast = fast.next.next;
            if (slow == fast) return true;
        }
        return false;
    }
}

Why This is the Best Approach:

  • Uses constant space (O(1)).

  • Fast and efficient – Works in a single traversal.

  • Does not modify the linked list structure.

⚠️ Common Mistakes & Pitfalls to Avoid

  • Forgetting to check for null – If the list is empty, return false immediately.

  • Not handling fast pointer reaching null – Always check fast.next to prevent null pointer exceptions.

  • Assuming slow and fast will always meet – If there’s no cycle, fast will reach null.

📊 Time & Space Complexity Analysis

  • HashSet Method – O(N) time, O(N) space.

  • Floyd’s Cycle Detection – O(N) time, O(1) space. ✅

🌍 Real-World Applications

  • Operating Systems – Detecting circular dependencies in process scheduling.

  • Networking – Finding loops in packet routing or network topology.

  • Blockchain & Cryptography – Identifying repeated patterns in blockchain structures.


I hope you found this article insightful! Keep exploring, keep learning, and don’t forget to check back daily for more exciting problem breakdowns. If you know someone who would benefit from this, share it with them and help them grow too! That’s it for today—see you in the next post!

                                                                                                                                         Signing off!! 

                                                                                                Master DSA One Problem at a Time :)

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