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Fast & Slow Pointers

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Floyd’s Cycle Detection

• Slow pointer moves 1 step at a time
• Fast pointer moves 2 steps at a time
• If there’s a cycle, they will meet
• If fast reaches the end, there’s no cycle

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Finding the Cycle Start

1. Reset one pointer to the head
2. Move both pointers one step at a time
3. They meet at the cycle start

def detect_cycle(head):
    slow = fast = head
    while fast and fast.next:
        slow = slow.next
        fast = fast.next.next
        if slow == fast:
            # Find cycle start
            slow = head
            while slow != fast:
                slow = slow.next
                fast = fast.next
            return slow  # cycle start
    return None  # no cycle

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Finding the Middle

def find_middle(head):
    slow = fast = head
    while fast and fast.next:
        slow = slow.next
        fast = fast.next.next
    return slow  # middle node

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Classic Problems

• Linked List Cycle I & II
• Find the Duplicate Number (array as linked list)
• Middle of the Linked List
• Palindrome Linked List (find middle + reverse second half)
• Happy Number (cycle in digit-square sequence)
• Reorder List

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How It Differs from Two Pointers

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When to Use

• Detecting cycles in linked lists or sequences
• Finding the middle element in one pass
• Problems where the structure “loops back” (e.g., Happy Number)
• Linked list problems requiring O(1) space