Detect if a Linked List is Circular in DSA Javascript - 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.

function isCircular(head) {
  let slow = head;
  let fast = head;
  while (fast !== null && fast.next !== null) {
    slow = slow.next;
    fast = fast.next.next;
    if (slow === fast) {
      return true;
    }
  }
  return false;
}
    

This code checks if a linked list has a cycle by moving two pointers at different speeds.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The while loop that moves slow and fast pointers through the list.
• How many times: At most, each pointer moves through the list nodes once until they meet or reach the end.

How Execution Grows With Input

As the list grows, the number of steps increases roughly in a straight line with the number of nodes.

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

Pattern observation: The steps grow directly with the list size, not faster or slower.

Final Time Complexity

Time Complexity: O(n)

This means the time to check grows in a straight line with the number of nodes in the list.

Common Mistake

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

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

Interview Connect

Understanding this helps you explain how to detect loops efficiently, a common linked list question.

Self-Check

"What if we used only one pointer and checked visited nodes with extra memory? How would the time complexity change?"

Practice

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

easy

A. The linked list has only one node

B. The linked list has no nodes

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 list
• Confusing empty list with circular list
• Assuming single node list is always circular

2. Which of the following is the correct way to check if a linked list is circular in JavaScript?

easy

A. Count nodes and compare with array length

B. Use two pointers moving at different speeds and check if they meet

C. Check if head is null only

D. Sort the linked list nodes

Solution

1. Step 1: Understand Floyd's cycle detection

   Use two pointers: slow moves one step, fast moves two steps. If they meet, list is circular.

2. Step 2: Eliminate wrong options

   Checking head null only doesn't detect loops. Counting nodes or sorting is unrelated.

3. Final Answer:

   Use two pointers moving at different speeds and check if they meet -> Option B

4. Quick Check:

   Two-pointer cycle detection = correct method [OK]

Hint: Two pointers meeting means circular list [OK]

Common Mistakes:

• Only checking if head is null
• Trying to sort linked list to detect cycle
• Counting nodes without loop detection

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

class Node {
  constructor(value) {
    this.value = value;
    this.next = null;
  }
}

const head = new Node(1);
const second = new Node(2);
const third = new Node(3);
head.next = second;
second.next = third;
third.next = second; // creates a loop

function isCircular(head) {
  let slow = head;
  let fast = head;
  while (fast && fast.next) {
    slow = slow.next;
    fast = fast.next.next;
    if (slow === fast) return true;
  }
  return false;
}

console.log(isCircular(head));

medium

A. false

B. undefined

C. true

D. TypeError

Solution

1. Step 1: Analyze linked list structure

   Nodes 1 -> 2 -> 3, and third node points back to second, creating a loop.

2. Step 2: Trace two-pointer loop detection

   Slow and fast pointers will eventually meet inside the loop, so function returns true.

3. Final Answer:

   true -> Option C

4. Quick Check:

   Loop detected = true [OK]

Hint: Loop causes pointers to meet, returning true [OK]

Common Mistakes:

• Assuming no loop because list looks linear
• Confusing pointer equality check
• Expecting false without tracing pointers

4. Find the error in this code that tries to detect a circular linked list:

function isCircular(head) {
  let slow = head;
  let fast = head;
  while (fast.next && fast.next.next) {
    slow = slow.next;
    fast = fast.next.next;
    if (slow == fast) return true;
  }
  return false;
}

medium

A. The while condition should check if fast and fast.next exist

B. The comparison should use === instead of ==

C. The slow pointer should move two steps instead of one

D. The function should return false inside the loop

Solution

1. Step 1: Check while loop condition safety

   fast.next.next is accessed without confirming fast is not null, can cause error if fast is null.

2. Step 2: Correct condition to avoid runtime error

   Condition should be while (fast && fast.next) to safely access fast.next.next.

3. Final Answer:

   The while condition should check if fast and fast.next exist -> Option A

4. Quick Check:

   Check fast and fast.next before accessing next nodes [OK]

Hint: Always check fast and fast.next before fast.next.next [OK]

Common Mistakes:

• Not checking if fast is null before accessing fast.next.next
• Using == instead of === (not critical here)
• Moving slow pointer two steps incorrectly

5. Given a linked list where the last node points back to the head, how can you modify the detection function to also return the node where the loop starts?

function detectLoopStart(head) {
  let slow = head;
  let fast = head;
  while (fast && fast.next) {
    slow = slow.next;
    fast = fast.next.next;
    if (slow === fast) {
      // Loop detected
      slow = head;
      while (slow !== fast) {
        slow = slow.next;
        fast = fast.next;
      }
      return slow;
    }
  }
  return null;
}

hard

A. The function returns the node where the loop starts by resetting slow to head and moving both pointers one step

B. The function returns true if a loop exists but does not find the start node

C. The function incorrectly moves fast pointer one step after detection

D. The function will always return null because slow and fast never meet

Solution

1. Step 1: Detect loop using two pointers

   Slow and fast pointers meet inside the loop confirming a cycle.

2. Step 2: Find loop start node

   Reset slow to head, move slow and fast one step at a time until they meet again; this node is loop start.

3. Final Answer:

   The function returns the node where the loop starts by resetting slow to head and moving both pointers one step -> Option A

4. Quick Check:

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

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

Common Mistakes:

• Returning true instead of loop start node
• Moving fast pointer incorrectly after detection
• Assuming slow and fast never meet