core pattern

Fast & Slow Pointers

Two pointers moving at different speeds through a sequence. Fast pointer moves 2x speed of slow. They meet if there's a cycle, or fast reaches the end for middle-finding.

Time

O(n)

Space

O(1)

🧠Mental Model

“Tortoise and hare on a circular track — if there's a loop, the hare will lap the tortoise.”

Verbal cue: Slow moves 1 step, fast moves 2 steps

🎯Recognition Triggers

When you see these patterns in a problem, consider this approach:

Cycle detectionFind middle of linked listHappy numberLinked list loop startPalindrome linked listCircular array loop

📝Code Template

Fast & Slow Pointers Template

1function hasCycle(head) {
2  if (!head || !head.next) return false;
3  
4  let slow = head;
5  let fast = head;
6  
7  while (fast && fast.next) {
8    slow = slow.next;        // Move 1 step
9    fast = fast.next.next;   // Move 2 steps
10    
11    if (slow === fast) {
12      return true;  // Cycle detected
13    }
14  }
15  
16  return false;  // No cycle
17}

Complexity rationale: At most n iterations until cycle found or end reached

💡Interview Tips

1Explain WHY they meet: fast "gains" one node per iteration
2For cycle start: reset slow to head, move both at same speed
3This pattern proves O(1) space is possible for many linked list problems
4Draw the linked list and trace through with arrows

⚠️Common Mistakes

✕Not checking if fast.next exists before fast.next.next
✕Starting both pointers at head vs head.next for some variants
✕Confusing cycle detection with finding cycle start
✕Forgetting edge cases: null head, single node