Fast & Slow Pointers

Two pointers moving at different speeds to detect patterns

Algorithm Code

Time: O(n) | Space: O(1)

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

Algorithm Steps

Step 1 of 5

1

Initialize Pointers

Set both slow and fast pointers to head (index 0)

2

Move Pointers

Slow pointer at index 1, Fast pointer at index 2

3

Move Pointers

Slow pointer at index 2, Fast pointer at index 4

4

Move Pointers

Slow pointer at index 3, Fast pointer at index 5

5

No Cycle Detected

Fast pointer reached the end - no cycle in the list

Linked List

0
1
Slow
Fast
→
1
2
→
2
3
→
3
4
→
4
5
→
5
6

Fast & Slow Pointers Technique

Slow Pointer: Moves 1 step at a time
Fast Pointer: Moves 2 steps at a time
Use Case: Cycle detection, finding middle element
Slow
Fast
Both
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