Floyd slow and fast pointers
Detect a Looping Relay
01. The question
Starting at node 0, detect a repeated node by identity. Input is an acyclic JSON list, or {"values":[...],"cycle":null|index} linking the tail to an index, or {"values":[...],"next":[null|index,...]} specifying every pointer. Explicit-pointer nodes must all be reachable from node 0.
Before revealing the idea, predict the result and describe what information you would need to track.
02. Worked example
Input{"values":[8,3,8,5],"cycle":1}
Outputtrue
- Move slow one edge and fast two edges at a time.
- They eventually meet at the same node in the loop.
- The two 8 readings alone are not evidence of a cycle.
Try your code
Define solve(data, parameter="") and return your result. Your code runs locally, not on a server.
Edit your test cases
Use 1-10 objects with data and an optional string parameter. Expected outputs are computed from the lesson. An optional expected field must be correct.
Input contract & reference code
Example data: {"values":[8,3,8,5],"cycle":1}. Parameter: "". Numeric parameters arrive as strings; convert them with int(parameter) when needed.
The example and generated cases use the question’s exact variant. This checks behavior on a small test batch—not performance on every possible input.
Python downloads only when you run code, using compressed runtime assets. Code is not saved or uploaded. Enable JavaScript to run it.
Printed output
Five-second execution limit per batch. Standard-library Python only; additional packages and network access are unavailable. Stop ends execution without blocking the lesson.
03. The idea
Try sketching your own approach first. What would you track, and why would it work?
Reveal the idea
- Construct nodes and their next references from the validated input.
- Advance slow by one and fast by two while fast can move.
- Compare node objects, not values; falling off the chain proves no loop.
04. Watch it happen
Use Step to move slowly, or Play to follow the whole trace. Change a preset or load your own input.
Input & settings
Red = current item / blue = active window or cells / green = completed work. A value docks at its actual destination; the original input stays unchanged. Positions start at 0.
Working state / what changes
Ready to begin
Enable JavaScript to step through the animation. The worked example and solution below remain readable without it.
Python / why it changes
The line behind the step
class Node:
def __init__(self, value):
self.value = value
self.next = None
def solve(data, parameter=''):
readings = data if isinstance(data, list) else data["values"]
nodes = [Node(value) for value in readings]
links = list(range(1, len(nodes))) + [None] if nodes else []
if isinstance(data, dict):
if "next" in data:
links = data["next"]
elif nodes:
links[-1] = data["cycle"]
for index, following in enumerate(links):
nodes[index].next = None if following is None else nodes[following]
slow = fast = nodes[0] if nodes else None
while fast is not None and fast.next is not None:
slow = slow.next
fast = fast.next.next
if slow is fast:
return True
return FalseHow to use this walkthrough
Hover or focus a control for its label. Play forms the input and follows values into the working state. Step shows one change; Back and the slider restore exact snapshots. Reduced motion uses instant updates. Saved snapshots and sorted heap displays are teaching overhead, not algorithm complexity.
05. Python solution
class Node:
def __init__(self, value):
self.value = value
self.next = None
def solve(data, parameter=''):
readings = data if isinstance(data, list) else data["values"]
nodes = [Node(value) for value in readings]
links = list(range(1, len(nodes))) + [None] if nodes else []
if isinstance(data, dict):
if "next" in data:
links = data["next"]
elif nodes:
links[-1] = data["cycle"]
for index, following in enumerate(links):
nodes[index].next = None if following is None else nodes[following]
slow = fast = nodes[0] if nodes else None
while fast is not None and fast.next is not None:
slow = slow.next
fast = fast.next.next
if slow is fast:
return True
return False06. Cost & edge cases
- Time
- O(n)
- Space
- O(1) algorithm workspace; O(n) JSON-to-node construction
- An empty chain has no cycle.
- A one-node self-loop is a cycle.
- Out-of-range pointers, contradictory cycle/next fields and detached nodes are invalid.