Floyd's Cycle Detection Algorithm (Tortoise and Hare)

Algorithm Overview

Use two pointers moving at different speeds:

• Slow pointer (tortoise): moves one step at a time
• Fast pointer (hare): moves two steps at a time

Implementation

function hasCycle(head) {
    if (!head || !head.next) return false;
    
    let slow = head;
    let fast = head;
    
    while (fast && fast.next) {
        slow = slow.next;        // Move 1 step
        fast = fast.next.next;   // Move 2 steps
        
        if (slow === fast) {
            return true;         // Cycle detected
        }
    }
    
    return false;               // No cycle
}

Time Complexity: O(n)

Space Complexity: O(1)