Detect if a Linked List is Circular in DSA C# - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the output of this code detecting circular linked list?

Given the linked list created and checked below, what will be printed?

DSA C#

public class Node {
    public int Value;
    public Node Next;
    public Node(int value) { Value = value; Next = null; }
}

public class LinkedList {
    public Node Head;
    public bool IsCircular() {
        if (Head == null) return false;
        Node slow = Head;
        Node fast = Head.Next;
        while (fast != null && fast.Next != null) {
            if (slow == fast) return true;
            slow = slow.Next;
            fast = fast.Next.Next;
        }
        return false;
    }
}

var list = new LinkedList();
list.Head = new Node(1);
list.Head.Next = new Node(2);
list.Head.Next.Next = new Node(3);
list.Head.Next.Next.Next = list.Head; // Circular link

System.Console.WriteLine(list.IsCircular());

A NullReferenceException

B False

C Compilation error

D True

💡 Hint

Think about how the fast and slow pointers move and meet in a circular list.

The fast pointer moves two steps and slow moves one step. In a circular list, they will meet, so IsCircular returns true.

❓ Predict Output

intermediate

What is the output when the linked list is not circular?

Consider the linked list below without any cycle. What will the IsCircular method print?

DSA C#

public class Node {
    public int Value;
    public Node Next;
    public Node(int value) { Value = value; Next = null; }
}

public class LinkedList {
    public Node Head;
    public bool IsCircular() {
        if (Head == null) return false;
        Node slow = Head;
        Node fast = Head.Next;
        while (fast != null && fast.Next != null) {
            if (slow == fast) return true;
            slow = slow.Next;
            fast = fast.Next.Next;
        }
        return false;
    }
}

var list = new LinkedList();
list.Head = new Node(1);
list.Head.Next = new Node(2);
list.Head.Next.Next = new Node(3);
// No circular link

System.Console.WriteLine(list.IsCircular());

A True

B False

C NullReferenceException

D Compilation error

💡 Hint

If the fast pointer reaches the end, the list is not circular.

Since the list ends with null, fast pointer reaches null and the method returns false.

🔧 Debug

advanced

Why does this code cause an infinite loop when checking circularity?

Examine the code below. Why does it cause an infinite loop when the list is circular?

DSA C#

public class Node {
    public int Value;
    public Node Next;
    public Node(int value) { Value = value; Next = null; }
}

public class LinkedList {
    public Node Head;
    public bool IsCircular() {
        Node slow = Head;
        Node fast = Head;
        while (fast != null && fast.Next != null) {
            slow = slow.Next;
            fast = fast.Next.Next;
            if (slow == fast) return true;
        }
        return false;
    }
}

var list = new LinkedList();
list.Head = new Node(1);
list.Head.Next = new Node(2);
list.Head.Next.Next = new Node(3);
list.Head.Next.Next.Next = list.Head; // Circular

System.Console.WriteLine(list.IsCircular());

A The slow and fast pointers start at the same node, so they meet immediately causing infinite loop.

B The slow pointer moves too fast causing it to skip the fast pointer.

C The slow and fast pointers start at the same node and the check happens after moving pointers, so they never meet.

D The fast pointer moves two steps but slow pointer is not updated causing infinite loop.

💡 Hint

Check when the pointers are compared and when they move.

Since slow and fast start at the same node and comparison happens after moving, they skip meeting at start and loop forever.

🧠 Conceptual

advanced

What is the time complexity of detecting a circular linked list using Floyd's algorithm?

Consider Floyd's cycle detection algorithm for a linked list of length n. What is its time complexity?

A O(n)

B O(n^2)

C O(log n)

D O(1)

💡 Hint

Think about how many times the pointers move through the list.

Both pointers traverse the list at most a few times, so the time complexity is linear O(n).

🚀 Application

expert

How many nodes are in the cycle of this linked list?

Given the linked list below with a cycle, how many nodes are in the cycle?

DSA C#

public class Node {
    public int Value;
    public Node Next;
    public Node(int value) { Value = value; Next = null; }
}

public class LinkedList {
    public Node Head;
    public int CycleLength() {
        Node slow = Head;
        Node fast = Head;
        while (fast != null && fast.Next != null) {
            slow = slow.Next;
            fast = fast.Next.Next;
            if (slow == fast) {
                int length = 1;
                Node current = slow.Next;
                while (current != slow) {
                    length++;
                    current = current.Next;
                }
                return length;
            }
        }
        return 0;
    }
}

var list = new LinkedList();
list.Head = new Node(1);
list.Head.Next = new Node(2);
list.Head.Next.Next = new Node(3);
list.Head.Next.Next.Next = new Node(4);
list.Head.Next.Next.Next.Next = new Node(5);
list.Head.Next.Next.Next.Next.Next = list.Head.Next.Next; // Cycle starts at node with value 3

System.Console.WriteLine(list.CycleLength());

A 3

B 4

C 5

D 2

💡 Hint

Count nodes starting from the meeting point until you reach it again.

The cycle includes nodes with values 3, 4, and 5, so length is 3.

Practice

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

easy

A. The linked list nodes are sorted in ascending order

B. The linked list has no nodes

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

D. The linked list contains only one node

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 C

4. Quick Check:

   Circular linked list = loop in nodes [OK]

Hint: Circular means last node links back inside list [OK]

Common Mistakes:

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

2. Which of the following C# code snippets correctly checks if a linked list is circular using two pointers?

easy

A. if (head == null) return true; else return false;

B. while (slow != null) { slow = slow.Next; if (slow == null) return true; } return false;

C. for (int i = 0; i < length; i++) { if (list[i] == list[length - 1]) return true; } return false;

D. while (fast != null && fast.Next != null) { slow = slow.Next; fast = fast.Next.Next; if (slow == fast) return true; } return false;

Solution

1. Step 1: Identify Floyd's cycle detection logic

   Two pointers move at different speeds: slow moves one step, fast moves two steps.

2. Step 2: Check for pointer meeting

   If slow and fast meet, a cycle exists; otherwise, if fast reaches null, no cycle.

3. Final Answer:

   while (fast != null && fast.Next != null) { slow = slow.Next; fast = fast.Next.Next; if (slow == fast) return true; } return false; -> Option D

4. Quick Check:

   Two-pointer cycle detection = while (fast != null && fast.Next != null) { slow = slow.Next; fast = fast.Next.Next; if (slow == fast) return true; } return false; [OK]

Hint: Use two pointers moving at different speeds [OK]

Common Mistakes:

• Checking only one pointer for null
• Using for loop on linked list nodes
• Returning true when list is empty

3. What will be the output of the following C# code snippet?

class Node { public int Data; public Node Next; public Node(int d) { Data = d; Next = null; } }
Node head = new Node(1);
head.Next = new Node(2);
head.Next.Next = new Node(3);
head.Next.Next.Next = head.Next;
bool IsCircular(Node node) {
  Node slow = node, fast = node;
  while (fast != null && fast.Next != null) {
    slow = slow.Next;
    fast = fast.Next.Next;
    if (slow == fast) return true;
  }
  return false;
}
Console.WriteLine(IsCircular(head));

medium

A. true

B. false

C. Compilation error

D. Runtime exception

Solution

1. Step 1: Analyze linked list structure

   Nodes 1 -> 2 -> 3, then 3 points back to node 2, creating a loop.

2. Step 2: Trace Floyd's cycle detection

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

3. Final Answer:

   true -> Option A

4. Quick Check:

   Loop detected = true [OK]

Hint: Loop means pointers meet inside list [OK]

Common Mistakes:

• Assuming no loop because list looks linear
• Confusing pointer equality with data equality
• Expecting false because of missing null check

4. Identify the bug in this C# method that tries to detect if a linked list is circular:

bool IsCircular(Node head) {
  Node slow = head, fast = head;
  while (fast != null) {
    slow = slow.Next;
    fast = fast.Next.Next;
    if (slow == fast) return true;
  }
  return false;
}

medium

A. Missing check for fast.Next being null before accessing fast.Next.Next

B. Slow pointer should move two steps instead of one

C. Should return false inside the loop instead of after

D. Head node should be initialized to null

Solution

1. Step 1: Review pointer movement and null checks

   fast moves two steps: fast = fast.Next.Next; must check fast.Next != null to avoid null reference.

2. Step 2: Identify missing null check

   Loop condition only checks fast != null, but fast.Next could be null causing runtime error.

3. Final Answer:

   Missing check for fast.Next being null before accessing fast.Next.Next -> Option A

4. Quick Check:

   Check fast.Next != null before fast.Next.Next [OK]

Hint: Always check fast and fast.Next for null before moving fast [OK]

Common Mistakes:

• Ignoring fast.Next null check
• Moving slow pointer two steps incorrectly
• Returning false too early inside loop

5. Given a linked list where some nodes may form multiple loops, which approach correctly detects if the list is circular and why?

public bool IsCircular(Node head) {
  Node slow = head, fast = head;
  while (fast != null && fast.Next != null) {
    slow = slow.Next;
    fast = fast.Next.Next;
    if (slow == fast) return true;
  }
  return false;
}

hard

A. It fails because it only detects the first loop and misses others

B. Floyd's cycle detection works because fast pointer will eventually meet slow pointer in any loop

C. It requires extra memory to store visited nodes to detect multiple loops

D. It only works if the list has exactly one loop

Solution

1. Step 1: Understand Floyd's cycle detection behavior

   Fast and slow pointers move at different speeds; if any loop exists, they will meet inside it.

2. Step 2: Consider multiple loops scenario

   In a singly linked list, multiple loops cannot exist independently; any loop causes pointers to meet.

3. Final Answer:

   Floyd's cycle detection works because fast pointer will eventually meet slow pointer in any loop -> Option B

4. Quick Check:

   Any loop causes pointer meeting = true [OK]

Hint: One loop detection suffices; multiple loops can't exist singly [OK]

Common Mistakes:

• Thinking multiple loops can exist in singly linked list
• Believing extra memory is needed for loop detection
• Assuming method detects all loops separately