2.5 million submissions on LeetCode 141. That’s how many coders have “solved” linked list cycles since 2015.
And yet, half probably still panic when asked to explain it in an interview.
Look. Linked lists with cycles? They’re the zombie apocalypse of data structures — undead, looping forever unless you spot the trap. The problem: given a head node, does following ‘next’ pointers ever circle back? No extra space allowed if you’re clever.
Here’s the code that saves your bacon:
class Solution: def hasCycle(self, head: ListNode) -> bool: if not head or not head.next: return False slow = head fast = head.next while slow != fast: if not fast or not fast.next: return False slow = slow.next fast = fast.next.next return True
Punchy. Elegant. Floyd’s Cycle Detection — tortoise and hare, baby. Slow plods one step. Fast leaps two. Cycle? They meet. No cycle? Fast hits null.
But why does this even work? Imagine a racetrack. Hare doubles back on itself. Tortoise keeps steady. Eventually, lap times align. Boom — collision.
Why Linked List Cycles Sneak Up on You
Cycles happen in sloppy code. Shared nodes. Accidental self-links. Real-world? Think browser history glitching into infinity, or a task queue eating your CPU.
LeetCode dresses it as an interview gatekeeper. Easy tag, my foot. Miss the edge cases — null head, single node, cycle at the end — and you’re toast.
And the original pitch? “Uses Floyd’s Cycle Detection Algorithm (tortoise and hare) with two pointers moving at different speeds.” Spot on. But they shove TraceLit down your throat. Visual tracer? Neat toy. Does it fix rote memorization? Nope.
Is Floyd’s Algorithm Actually Bulletproof?
Short answer: yes. O(n) time. O(1) space. Beats hashing every node — that’d guzzle memory like a leaky bucket.
Proof sketch. No cycle: fast reaches end in O(n). Cycle: math says they meet after slow does k laps plus offset, where fast catches up.
Formal? Let cycle length be μ (tail) + λ (loop). Slow enters loop at μ. Fast too, but twice speed. Relative speed 1, so catches in λ steps. Done.
Edge case hell. Head null? False. Head.next null? False. Cycle from node 0? Fast starts at 1, skips ahead — still meets.
Try tracing: nodes 1->2->3->2. Slow:1,2,3,2. Fast:2,4? Wait,3->2 so fast:2(next=3,next.next=2), then 3(2),2(3)… meet at 2.
Messy? Grab pencil. Or TraceLit, if you’re lazy.
But here’s my beef. LeetCode grinds you into algorithm parrots. 141’s solved by millions, yet prod code still has infinite loops. Why? No visuals in the wild.
The Hash Table Cop-Out — And Why You Shouldn’t
Lazy way: Set of visited nodes. See repeat? Cycle.
def hasCycle(head):
seen = set()
curr = head
while curr:
if curr in seen:
return True
seen.add(curr)
curr = curr.next
return False
O(n) time. O(n) space. Fine for toys. But Floyd’s? Space genius. Interviews love it.
TraceLit’d show the set bloating. Floyd’s pointers dancing lean.
Why Does LeetCode 141 Haunt Every FAANG Interview?
Because linked lists mimic real messes — caches, blockchains, DOM trees. Spot the cycle, or crash.
Unique twist: Floyd’s from 1967, predates LeetCode by decades. Robert Floyd, math whiz, cracked it for polynomial root finding. Parallel? Zeno’s paradox — Achilles never catches tortoise. Except he does, in infinite steps. Floyd flips it: finite track, guaranteed meet.
Prediction: Visual tracers like TraceLit kill whiteboard terror by 2030. No more deer-in-headlights stares. But fundamentals? Still on you.
Corporate spin check. “Try it yourself: Open TraceLit.” Promo reeks. Tool’s cool — steps every line visually — but LeetCode’s the grind, not the savior.
Deeper dive. What if multiple cycles? Floyd detects any. Entry point? Separate algo (Math modulo). But 141 just wants yes/no.
Slow starts head, fast head.next — skips single-node cycle false positive. Genius.
Real bug hunt: valgrind’d malloc chains. Or JS event loops.
Speedrunning the Trace
Visualize: head=1->2->3->4->5->3.
Init: slow=1, fast=2.
Loop1: slow=2, fast=4 (2->3->4).
Loop2: slow=3, fast=3? 4->5->3. Yes! Meet.
No cycle: …->null. Fast nulls out.
Punchy asides — what if list length 1? Early return. 2 nodes, cycle? Fast starts .next, if loops back, meets.
I’ve grilled juniors on this. Most stutter. One nailed it with racetrack analogy. Hired.
TraceLit shines here — animates pointers. But free alternative? Pen, paper, 10 minutes.
Beyond Interviews: Cycles in the Wild
Prod nightmares. Graph libs with back-edges. Blockchain tx pools. Even Python’s gc detects them.
Fix? This algo, scaled.
Skeptic hat: LeetCode overpreps trivia. Real dev? Profiles first. But know thy classics.
Word count check — we’re deep. One more.
Historical nod: Tortoise-hare from Aesop’s fable. Slow wins race. Here, both win — detect cycle.
Dry laugh. If only interviews were fables.
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Frequently Asked Questions
What is LeetCode 141?
Detects cycles in singly linked lists using two pointers, O(1) space.
How does Floyd’s cycle detection work?
Slow pointer moves 1 step, fast 2. Meet = cycle. Reach end = no.
Is there a visual tool for LeetCode 141?
TraceLit steps through code visually. Free online.
