24. Detect Loop in Linked List

The problem can be found at the following link: Problem Link

Problem Description

You are given the head of a singly linked list. Your task is to determine if the linked list contains a loop. A loop exists in a linked list if the next pointer of the last node points to any other node in the list (including itself), rather than being null.

Custom Input Format

• head: The head of a singly linked list.

• pos: A 1-based index denoting the position of the node to which the last node points. If pos = 0, it means the last node points to null, indicating no loop exists.

Examples:

Example 1:

Input: head: 1 -> 3 -> 4, pos = 2

Output: true

Explanation: There exists a loop as the last node points back to the second node.

image

Example 2:

Input: head: 1 -> 8 -> 3 -> 4, pos = 0

Output: false

Explanation: There exists no loop in the given linked list.

image

Example 3:

Input: head: 1 -> 2 -> 3 -> 4, pos = 1

Output: true

Explanation: There exists a loop as the last node points back to the first node.

image

Constraints:

• 1 ≤ number of nodes ≤ $10^4$

• 1 ≤ node->data ≤ $10^3$

• 0 ≤ pos ≤ Number of nodes in Linked List

My Approach

To detect a loop in a linked list, we can use the Floyd’s Cycle Detection Algorithm (Tortoise and Hare Algorithm). This algorithm uses two pointers (slow and fast) to traverse the list at different speeds. If there is a loop, the fast pointer will eventually meet the slow pointer.

Steps:

1. Initialize Two Pointers:

   • Start with slow and fast pointers, both pointing to the head of the linked list.

2. Traverse the List:

   • Move slow one step at a time.

   • Move fast two steps at a time.

   • If the fast pointer reaches null, no loop exists.

   • If the slow pointer meets the fast pointer, a loop is detected.

3. Return the Result:

   • If slow equals fast, return true.

   • Otherwise, return false.

Time and Auxiliary Space Complexity

• Expected Time Complexity: O(n), where n is the number of nodes in the linked list. Each node is visited at most twice during the traversal.

• Expected Auxiliary Space Complexity: O(1), as the algorithm only uses two pointers (slow and fast) for detection.

Code (C++)

class Solution {
public:
    bool detectLoop(Node* head) {
        Node *slow = head, *fast = head;
        while (fast && fast->next) {
            if ((slow = slow->next) == (fast = fast->next->next))
                return true;
        }
        return false;
    }
};

Code (Java)

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

Code (Python)

class Solution:
    def detectLoop(self, head):
        slow, fast = head, head
        while fast and fast.next:
            slow, fast = slow.next, fast.next.next
            if slow == fast:
                return True
        return False

Contribution and Support

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