Why Detect Cycle in Linked List Floyd's Algorithm in DSA Rust?

The Big Idea

What if you could find hidden loops in your data without getting stuck forever?

The Scenario

Imagine you have a long chain of paper clips linked together. Sometimes, by mistake, the chain loops back on itself, creating a circle. If you try to count the clips one by one, you might get stuck going around forever without realizing it.

The Problem

Manually checking if the chain loops means you have to remember every clip you saw before. This is slow and easy to forget, especially if the chain is very long. You might never finish counting because you keep going in circles.

The Solution

Floyd's Algorithm uses two pointers moving at different speeds along the chain. If there is a loop, the faster pointer will eventually catch up to the slower one. This clever trick quickly tells us if a cycle exists without extra memory or endless counting.

Before vs After

✗ Before

let mut visited = Vec::new();
let mut current = head.as_deref();
while let Some(node) = current {
    if visited.contains(&(node as *const Node)) {
        return true; // cycle found
    }
    visited.push(node as *const Node);
    current = node.next.as_deref();
}
return false;

✓ After

let mut slow = head.as_deref();
let mut fast = head.as_deref();
while fast.is_some() && fast.unwrap().next.is_some() {
    slow = slow.unwrap().next.as_deref();
    fast = fast.unwrap().next.as_deref().unwrap().next.as_deref();
    if slow == fast {
        return true; // cycle found
    }
}
return false;

What It Enables

This method lets us detect loops in linked lists quickly and efficiently, preventing endless processing and bugs in programs.

Real Life Example

In social networks, detecting cycles helps find groups of friends who keep referencing each other, avoiding infinite loops in friend suggestions.

Key Takeaways

Manual cycle detection is slow and error-prone.

Floyd's Algorithm uses two pointers moving at different speeds.

It detects cycles efficiently without extra memory.

Practice

1. What is the main idea behind Floyd's Cycle Detection Algorithm in a linked list?

easy

A. Use two pointers moving at different speeds to detect a cycle

B. Count the number of nodes and check if it exceeds a limit

C. Reverse the linked list and check if it matches the original

D. Use a hash set to store visited nodes and check for repeats

Solution

1. Step 1: Understand Floyd's algorithm concept

   It uses two pointers, one moving faster (fast) and one slower (slow) through the list.

2. Step 2: Detect cycle by pointer meeting

   If the fast pointer meets the slow pointer, a cycle exists; otherwise, no cycle.

3. Final Answer:

   Use two pointers moving at different speeds to detect a cycle -> Option A

4. Quick Check:

   Two pointers at different speeds = cycle detection [OK]

Hint: Two pointers at different speeds detect cycle fast [OK]

Common Mistakes:

• Thinking counting nodes detects cycle
• Assuming reversing list helps detect cycle
• Using extra memory instead of pointers

2. Which Rust code snippet correctly initializes the slow and fast pointers for Floyd's cycle detection in a linked list named head?

easy

A. let mut slow = head.as_ref(); let mut fast = head.as_ref();

B. let mut slow = head.clone(); let mut fast = head.clone();

C. let mut slow = &head.next; let mut fast = &head.next.next;

D. let mut slow = &head; let mut fast = &head.next;

Solution

1. Step 1: Initialize both pointers at head

   Floyd's algorithm starts both slow and fast pointers at the head node.

2. Step 2: Correct Rust reference usage

   Using head.as_ref() for both slow and fast is correct; fast moves faster later.

3. Final Answer:

   let mut slow = head.as_ref(); let mut fast = head.as_ref(); -> Option A

4. Quick Check:

   Both pointers start at head [OK]

Hint: Start both pointers at head node [OK]

Common Mistakes:

• Starting fast pointer at head.next before loop
• Cloning nodes unnecessarily
• Using wrong references causing borrow errors

3. What will be the output of the following Rust code snippet detecting a cycle in a linked list?

struct Node { val: i32, next: Option }

fn has_cycle(head: &Option) -> bool {
    let mut slow = head.as_ref();
    let mut fast = head.as_ref();
    while fast.is_some() && fast.unwrap().next.is_some() {
        slow = slow.unwrap().next.as_ref();
        fast = fast.unwrap().next.as_ref().unwrap().next.as_ref();
        if slow.map(|n| n as *const ()) == fast.map(|n| n as *const ()) {
            return true;
        }
    }
    false
}

// List: 1 -> 2 -> 3 -> 4 -> 2 (cycle back to node with value 2)

medium

A. Infinite loop

B. false

C. true

D. Compilation error

Solution

1. Step 1: Understand the list structure

   The list has a cycle starting at node with value 2, so cycle exists.

2. Step 2: Trace Floyd's pointers

   Slow and fast pointers will eventually meet inside the cycle, returning true.

3. Final Answer:

   true -> Option C

4. Quick Check:

   Cycle present = true [OK]

Hint: Cycle in list means pointers meet = true [OK]

Common Mistakes:

• Assuming no cycle returns true
• Confusing Option with references
• Missing unwrap() causing panic

4. Identify the bug in this Rust code snippet for detecting a cycle using Floyd's algorithm:

fn has_cycle(head: &Option) -> bool {
    let mut slow = head.as_ref();
    let mut fast = head.as_ref();
    while fast.is_some() && fast.unwrap().next.is_some() {
        slow = slow.unwrap().next.as_ref();
        fast = fast.unwrap().next.as_ref(); // Bug here
        if slow.map(|n| n as *const ()) == fast.map(|n| n as *const ()) {
            return true;
        }
    }
    false
}

medium

A. slow pointer moves two steps instead of one

B. fast pointer moves only one step instead of two

C. Missing check for slow being None

D. Incorrect comparison of slow and fast pointers

Solution

1. Step 1: Analyze fast pointer movement

   Fast pointer should move two steps each loop, but here it moves only one step.

2. Step 2: Understand impact on cycle detection

   Moving fast only one step breaks Floyd's logic, so cycle detection fails or slows.

3. Final Answer:

   fast pointer moves only one step instead of two -> Option B

4. Quick Check:

   Fast pointer must move two steps [OK]

Hint: Fast pointer must jump two nodes each iteration [OK]

Common Mistakes:

• Moving fast pointer one step only
• Not checking fast pointer's next before moving
• Comparing pointers incorrectly

5. Given a linked list where the last node points back to the head (forming a cycle), how can you modify Floyd's algorithm to find the exact node where the cycle begins?

hard

A. Use a hash set to store nodes and find first repeated node

B. Count nodes until slow and fast meet, then return that count as cycle start

C. Reverse the list and check where reversal breaks

D. After detecting cycle, reset slow to head and move both pointers one step until they meet

Solution

1. Step 1: Detect cycle using Floyd's algorithm

   First, detect if cycle exists by moving slow and fast pointers.

2. Step 2: Find cycle start node

   Reset slow to head, then move slow and fast one step each until they meet; meeting point is cycle start.

3. Final Answer:

   After detecting cycle, reset slow to head and move both pointers one step until they meet -> Option D

4. Quick Check:

   Reset slow and move both pointers to find cycle start [OK]

Hint: Reset slow to head after cycle detection to find start [OK]

Common Mistakes:

• Trying to count nodes instead of pointer moves
• Using extra memory instead of pointer reset
• Reversing list which breaks cycle detection