Detect if a Linked List is Circular in DSA Rust - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does it mean for a linked list to be circular?

A linked list is circular if its last node points back to one of the previous nodes, creating a loop instead of ending with null.

beginner

Which algorithm is commonly used to detect a cycle in a linked list?

Floyd’s Cycle Detection Algorithm, also called the "Tortoise and Hare" algorithm, uses two pointers moving at different speeds to find a loop.

beginner

In Floyd’s Cycle Detection, what happens if the fast pointer reaches null?

If the fast pointer reaches null, it means the linked list has an end and is not circular (no cycle).

intermediate

Why do we use two pointers moving at different speeds to detect a cycle?

Because if there is a cycle, the faster pointer will eventually catch up to the slower pointer inside the loop, proving the list is circular.

intermediate

What is the time complexity of detecting a cycle using Floyd’s algorithm?

The time complexity is O(n), where n is the number of nodes, because each pointer moves through the list at most a few times.

What does the fast pointer do in Floyd’s Cycle Detection Algorithm?

A Does not move

B Moves one step at a time

C Moves three steps at a time

D Moves two steps at a time

The fast pointer moves two steps at a time to quickly detect if it meets the slow pointer.

If a linked list has no cycle, what will happen to the fast pointer?

A It will eventually reach null

B It will meet the slow pointer

C It will loop forever

D It will move backwards

Without a cycle, the fast pointer will reach the end of the list (null).

What is the main sign that a linked list is circular when using Floyd’s algorithm?

A Fast pointer reaches null

B Fast and slow pointers meet at the same node

C Slow pointer reaches null

D Pointers never move

If the fast and slow pointers meet, it means there is a cycle.

What is the initial position of the slow and fast pointers in cycle detection?

A Both start at null

B Slow starts at head, fast starts at tail

C Both start at the head node

D Slow starts at tail, fast starts at head

Both pointers start at the head of the linked list.

What is the space complexity of Floyd’s Cycle Detection Algorithm?

A O(1)

B O(n)

C O(log n)

D O(n^2)

The algorithm uses only two pointers, so it requires constant extra space.

Explain how Floyd’s Cycle Detection Algorithm works to find if a linked list is circular.

Think about two runners on a track, one faster than the other.

Describe what it means for a linked list to be circular and why detecting it is important.

Imagine a train track that loops back on itself.

Practice

1. What does it mean if a linked list is circular?

easy

A. The linked list has no nodes

B. The linked list contains only one node

C. The linked list nodes are sorted in ascending order

D. The last node points back to one of the previous nodes, forming a loop

Solution

1. Step 1: Understand linked list structure

   A linked list is a chain of nodes where each node points to the next node.

2. Step 2: Define circular linked list

   If the last node points back to any previous node, it creates a loop, making the list circular.

3. Final Answer:

   The last node points back to one of the previous nodes, forming a loop -> Option D

4. Quick Check:

   Circular linked list = last node points back [OK]

Hint: Circular means last node links back to earlier node [OK]

Common Mistakes:

• Thinking circular means sorted
• Confusing empty list with circular
• Assuming single node list is always circular

2. Which Rust code snippet correctly defines a singly linked list node struct?

easy

A. struct Node { value: i32, next: Option }

B. struct Node { value: i32, next: Node }

C. struct Node { value: i32, next: &Node }

D. struct Node { value: i32, next: Box<Node> }

Solution

1. Step 1: Understand Rust ownership for linked lists

   Rust requires using Option for next to allow nullable and heap allocation.

2. Step 2: Check each option

   struct Node { value: i32, next: Option } uses Option, which is correct. Others either lack Option or use references incorrectly.

3. Final Answer:

   struct Node { value: i32, next: Option } -> Option A

4. Quick Check:

   Use Option for next pointer in Rust [OK]

Hint: Use Option for next pointer in Rust [OK]

Common Mistakes:

• Using raw Node type for next causes infinite size error
• Using references without lifetimes
• Omitting Option for nullable next

3. Given the following Rust code to detect a circular linked list, what will be printed?

fn is_circular(head: &Option) -> bool {
    let mut slow = head.as_ref();
    let mut fast = head.as_ref();
    while let (Some(s), Some(f)) = (slow, fast) {
        fast = f.next.as_ref().and_then(|n| n.next.as_ref());
        slow = s.next.as_ref();
        if slow == fast {
            return true;
        }
    }
    false
}

// List: 1 -> 2 -> 3 -> 2 (loop back to node with value 2)
// Calling is_circular returns what?

medium

A. false

B. true

C. Compilation error

D. Infinite loop

Solution

1. Step 1: Understand Floyd's cycle detection

   Two pointers move at different speeds; if they meet, list is circular.

2. Step 2: Analyze given list and code

   List loops back from node 3 to node 2, so slow and fast pointers will meet, returning true.

3. Final Answer:

   true -> Option B

4. Quick Check:

   Floyd's algorithm detects loop = true [OK]

Hint: Floyd's cycle detection returns true if pointers meet [OK]

Common Mistakes:

• Confusing pointer movement speeds
• Not checking both pointers for null
• Assuming no loop when pointers meet

4. Identify the bug in this Rust function that tries to detect a circular linked list:

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 == fast {
            return true;
        }
    }
    false
}

medium

A. Function always returns false due to wrong loop condition

B. Pointers move at the same speed, so no cycle detection

C. Using unwrap() without checking can cause panic if null

D. Missing return type causes compilation error

Solution

1. Step 1: Check unwrap usage safety

   Using unwrap() without confirming Some can panic if null is encountered.

2. Step 2: Identify risk in loop

   fast.unwrap().next.as_ref().unwrap() assumes next exists, which may not be true at list end.

3. Final Answer:

   Using unwrap() without checking can cause panic if null -> Option C

4. Quick Check:

   Unsafe unwrap causes panic [OK]

Hint: Avoid unwrap without checking Option first [OK]

Common Mistakes:

• Ignoring unwrap panic risk
• Assuming pointers move same speed
• Not checking loop exit conditions

5. You have a linked list where the last node's next pointer is mistakenly set to itself, creating a single-node loop. How should you modify the Rust cycle detection function to correctly detect this case?

hard

A. Use a hash set to store visited nodes and detect repeats

B. Ignore cases where next points to itself, treat as non-circular

C. Only check if fast pointer reaches null to decide no cycle

D. Check if slow and fast pointers meet even if they start at the same node

Solution

1. Step 1: Understand single-node loop problem

   If a node points to itself, Floyd's algorithm may detect cycle, but edge cases can be tricky.

2. Step 2: Use hash set for robust detection

   Storing visited nodes in a hash set helps detect any repeated node, including self-loop cases.

3. Final Answer:

   Use a hash set to store visited nodes and detect repeats -> Option A

4. Quick Check:

   Hash set detects all cycles including self-loops [OK]

Hint: Use hash set to catch all loops including self-pointing nodes [OK]

Common Mistakes:

• Assuming Floyd's algorithm covers all edge cases
• Ignoring self-loop as cycle
• Not handling single-node circular lists