Fast & Slow Pointers

When to use

Use for linked list cycles, finding the middle of a list, and repeated movement through a sequence at different speeds. If the problem involves a linked list and asks about position or loops, think here first.

Core intuition

One pointer moves 1 step. The other moves 2 steps. If there's a cycle, they'll eventually meet. If there's no cycle, the fast pointer hits null. When fast reaches the end, slow is near the middle.

Template

def has_cycle(head):
    slow, fast = head, head
    while fast and fast.next:
        slow = slow.next
        fast = fast.next.next
        if slow == fast:
            return True
    return False

def find_middle(head):
    slow, fast = head, head
    while fast and fast.next:
        slow = slow.next
        fast = fast.next.next
    return slow

Suggested problems