Detect if a Linked List is Circular in DSA C - Time & Space Complexity

Time Complexity: Detect if a Linked List is Circular

O(n)

Understanding Time Complexity

We want to know how long it takes to check if a linked list loops back on itself.

How does the time needed grow as the list gets longer?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

// Detect if linked list is circular using two pointers
int isCircular(struct Node* head) {
    struct Node *slow = head, *fast = head;
    while (fast != NULL && fast->next != NULL) {
        slow = slow->next;
        fast = fast->next->next;
        if (slow == fast) {
            return 1; // Circular
        }
    }
    return 0; // Not circular
}
    

This code uses two pointers moving at different speeds to find a loop in the list.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The while loop that moves pointers through the list.
• How many times: Up to n times, where n is the number of nodes in the list.

How Execution Grows With Input

As the list grows, the number of steps to detect a loop grows roughly in a straight line.

Input Size (n)	Approx. Operations
10	About 10 steps
100	About 100 steps
1000	About 1000 steps

Pattern observation: The time grows directly with the size of the list.

Final Time Complexity

Time Complexity: O(n)

This means the time to check grows linearly with the number of nodes in the list.

Common Mistake

[X] Wrong: "The fast pointer moves twice as fast, so the time is O(n/2), which is much faster than O(n)."

[OK] Correct: We ignore constants in Big-O, so O(n/2) is still O(n). The time still grows linearly with list size.

Interview Connect

Understanding this helps you explain how to detect loops efficiently, a common real-world problem in linked list handling.

Self-Check

"What if we used only one pointer moving one step at a time? How would the time complexity change?"

Practice

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

easy

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

B. The linked list has no nodes

C. The linked list nodes are sorted in ascending order

D. The linked list has 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: Identify circular linked list property

   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 A

4. Quick Check:

   Circular linked list = last node points back [OK]

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

Common Mistakes:

• Thinking circular means sorted
• 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?

easy

A. for (int i = 0; i < 10; i++) { head = head->next; } return 0;

B. if (head == NULL) return 1; else return 0;

C. while (head->next != NULL) { head = head->next; } return 1;

D. while (head != NULL) { head = head->next; if (head == start) return 1; } return 0;

Solution

1. Step 1: Analyze code logic for circular detection

   The code moves through nodes until it finds the start node again, indicating a loop.

2. Step 2: Check other options for correctness

   if (head == NULL) return 1; else return 0; only checks if list is empty, not circular. while (head->next != NULL) { head = head->next; } return 1; stops at NULL, no loop check. for (int i = 0; i < 10; i++) { head = head->next; } return 0; blindly moves 10 steps without loop check.

3. Final Answer:

   while (head != NULL) { head = head->next; if (head == start) return 1; } return 0; -> Option D

4. Quick Check:

   Loop check by revisiting start node = while (head != NULL) { head = head->next; if (head == start) return 1; } return 0; [OK]

Hint: Check if traversal returns to start node [OK]

Common Mistakes:

• Only checking for NULL without loop detection
• Using fixed iteration count instead of loop condition
• Returning true for empty list

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

typedef struct Node {
  int data;
  struct Node* next;
} Node;

int isCircular(Node* head) {
  if (head == NULL) return 0;
  Node* temp = head->next;
  while (temp != NULL && temp != head) {
    temp = temp->next;
  }
  return (temp == head);
}

int main() {
  Node a, b, c;
  a.data = 1; b.data = 2; c.data = 3;
  a.next = &b; b.next = &c; c.next = &a;
  printf("%d", isCircular(&a));
  return 0;
}

medium

A. Runtime error

B. 0

C. 1

D. Compilation error

Solution

1. Step 1: Understand linked list setup

   Nodes a, b, c are linked in a circle: a->b->c->a.

2. Step 2: Trace isCircular function

   Function moves temp pointer until it finds head again or NULL. Here, temp will reach head again, so returns 1.

3. Final Answer:

   1 -> Option C

4. Quick Check:

   Loop detected, returns 1 [OK]

Hint: Returns 1 if traversal loops back to head [OK]

Common Mistakes:

• Assuming NULL termination means circular
• Confusing return values 0 and 1
• Not initializing temp correctly

4. Identify the bug in the following code that tries to detect if a linked list is circular:

int isCircular(Node* head) {
  Node* slow = head;
  Node* fast = head->next;
  while (fast != NULL && fast->next != NULL) {
    if (slow == fast) return 1;
    slow = slow->next;
    fast = fast->next->next;
  }
  return 0;
}

medium

A. slow pointer should move two steps, fast one step

B. fast pointer initialization should be head, not head->next

C. The loop condition should check only fast != NULL

D. Return values are reversed

Solution

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

   Both slow and fast pointers should start at head to detect cycle properly.

2. Step 2: Identify initialization error

   fast is initialized to head->next, which can miss cycle detection if list has only one node or cycle starts at head.

3. Final Answer:

   fast pointer initialization should be head, not head->next -> Option B

4. Quick Check:

   Initialize fast = head for correct cycle detection [OK]

Hint: Start both pointers at head for Floyd's cycle detection [OK]

Common Mistakes:

• Starting fast pointer one step ahead
• Swapping slow and fast pointer steps
• Ignoring null checks in loop condition

5. You have a singly linked list where the last node's next pointer is unknown. How would you modify the list to make it circular and then detect the cycle using Floyd's algorithm? Choose the correct sequence of steps.

hard

A. 1. Traverse to last node
2. Set last node's next to head
3. Use Floyd's algorithm to detect cycle

B. 1. Set head's next to NULL
2. Use Floyd's algorithm
3. Traverse list

C. 1. Reverse the list
2. Set last node's next to NULL
3. Use Floyd's algorithm

D. 1. Traverse to middle node
2. Set middle node's next to head
3. Use Floyd's algorithm

Solution

1. Step 1: Make the list circular by linking last node to head

   Traverse the list to find the last node, then set its next pointer to head to form a loop.

2. Step 2: Apply Floyd's cycle detection algorithm

   Use slow and fast pointers starting at head to detect the cycle created.

3. Final Answer:

   1. Traverse to last node 2. Set last node's next to head 3. Use Floyd's algorithm to detect cycle -> Option A

4. Quick Check:

   Make circular then detect cycle with Floyd's algorithm [OK]

Hint: Link last node to head before running cycle detection [OK]

Common Mistakes:

• Setting wrong node's next pointer
• Not traversing to last node correctly
• Using Floyd's algorithm before making list circular