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Floyd's Cycle Detection Algorithm

Tortoise & Hare — Two-Pointer Technique

LeetCode 142 • Medium • Linked Lists

Time O(n) at most 2n steps

Space O(1) only 2 pointers

Steps: 0 Phase: —

Slow (Tortoise) — 1 step

Fast (Hare) — 2 steps

Meeting Point

Cycle Start

Speed:

Ready

Press Play to watch the algorithm run, or Step to advance one move at a time.
The linked list has 10 nodes with a cycle starting at node 3.

✎ Whiteboard

Size: 3

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Practice until you don't need to look. Use the guide comments below as scaffolding. Type the full implementation in the editor. The green highlights are the nuances to burn into memory.

# ─── FLOYD'S CYCLE DETECTION (LeetCode 142) ───

# Pattern: Fast & slow pointers (two phases)

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

# 1. Define: detectCycle(self, head)

# 2. Init both pointers at head:

# slow = head

# fast = head

# 3. Phase 1 — Detect cycle:

# Loop: while fast and fast.next:

# slow = slow.next ← 1 step

# fast = fast.next.next ← 2 steps

# if slow == fast: ← they meet = cycle!

# 4. Phase 2 — Find cycle start:

# slow = head ← reset slow only

# Loop: while slow != fast:

# slow = slow.next ← both move 1 step

# fast = fast.next ← both move 1 step

# return slow ← cycle start node

# 5. No cycle: return None

# Vars: slow, fast

# Key: Phase 2 works because distance from head to

# cycle start == distance from meeting point to start

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