Reverse a Doubly Linked List in DSA Javascript - Time & Space Complexity

Time Complexity: Reverse a Doubly Linked List

O(n)

Understanding Time Complexity

We want to understand how the time needed to reverse a doubly linked list changes as the list grows.

How does the number of steps grow when the list gets longer?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

function reverseDoublyLinkedList(head) {
  let current = head;
  let temp = null;
  while (current !== null) {
    temp = current.prev;
    current.prev = current.next;
    current.next = temp;
    current = current.prev;
  }
  if (temp !== null) {
    head = temp.prev;
  }
  return head;
}
    

This code reverses the links of a doubly linked list by swapping the previous and next pointers for each node.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The while loop that visits each node once.
• How many times: Exactly once per node, so as many times as there are nodes in the list.

How Execution Grows With Input

As the list gets longer, the number of steps grows directly with the number of nodes.

Input Size (n)	Approx. Operations
10	About 10 swaps of pointers
100	About 100 swaps of pointers
1000	About 1000 swaps of pointers

Pattern observation: The work grows in a straight line with the size of the list.

Final Time Complexity

Time Complexity: O(n)

This means the time to reverse the list grows directly in proportion to the number of nodes.

Common Mistake

[X] Wrong: "Reversing a doubly linked list takes more than linear time because of the two pointers per node."

[OK] Correct: Each node is visited only once, and swapping two pointers is a constant time operation, so the total time still grows linearly.

Interview Connect

Understanding this helps you explain how to efficiently reverse linked structures, a common task in coding challenges and real applications.

Self-Check

"What if we tried to reverse a singly linked list instead? How would the time complexity change?"

Practice

1. What does reversing a doubly linked list mean?

easy

A. Adding a new node at the end

B. Deleting all nodes from the list

C. Sorting the nodes in ascending order

D. Swapping the next and previous pointers of each node

Solution

1. Step 1: Understand doubly linked list structure

   Each node has two pointers: one to the next node and one to the previous node.

2. Step 2: Reverse means swapping pointers

   Reversing means changing each node's next pointer to previous and previous pointer to next.

3. Final Answer:

   Swapping the next and previous pointers of each node -> Option D

4. Quick Check:

   Reverse = swap next and prev pointers [OK]

Hint: Reverse means swap next and prev pointers [OK]

Common Mistakes:

• Thinking reverse means deleting nodes
• Confusing reverse with sorting
• Adding nodes instead of reversing pointers

2. Which of the following is the correct way to swap the next and prev pointers of a node in JavaScript?

easy

A. node.prev = node.next; node.next = node.prev;

B. node.next = node.prev; node.prev = node.next;

C. let temp = node.next; node.next = node.prev; node.prev = temp;

D. node.next = node.next; node.prev = node.prev;

Solution

1. Step 1: Use a temporary variable to hold one pointer

   Store node.next in temp to avoid losing its value.

2. Step 2: Swap pointers correctly

   Assign node.next = node.prev, then node.prev = temp to complete swap.

3. Final Answer:

   let temp = node.next; node.next = node.prev; node.prev = temp; -> Option C

4. Quick Check:

   Swap with temp variable = correct [OK]

Hint: Use temp variable to swap pointers safely [OK]

Common Mistakes:

• Swapping without temp loses pointer data
• Assigning both pointers to same value
• Not swapping pointers at all

3. What will be the output list after reversing this doubly linked list?

Head -> 1 <-> 2 <-> 3 <-> null

After reversal, what is the new head node's value?

medium

A. 3

B. 1

C. 2

D. null

Solution

1. Step 1: Original list order

   List is 1 <-> 2 <-> 3, head points to 1.

2. Step 2: Reverse swaps pointers, so last node becomes head

   After reversal, 3 becomes the new head, pointing backward to 2 and forward to null.

3. Final Answer:

   3 -> Option A

4. Quick Check:

   New head after reverse = last node = 3 [OK]

Hint: New head after reverse is original tail [OK]

Common Mistakes:

• Assuming head stays same after reverse
• Confusing node values order
• Thinking null becomes head

4. Identify the bug in this reverse function for a doubly linked list:

function reverse(head) {
  let current = head;
  while (current != null) {
    let temp = current.next;
    current.next = current.prev;
    current.prev = temp;
    current = current.next;
  }
  return head;
}

medium

A. The function does not update the head to the new first node

B. Swapping next and prev pointers is done incorrectly

C. The loop condition should be current.next != null

D. The function should return null instead of head

Solution

1. Step 1: Check pointer swapping

   Swapping next and prev pointers is done correctly using temp variable.

2. Step 2: Check head update after reversal

   Function returns original head, but after reversal head should be last node visited, so head is not updated.

3. Final Answer:

   The function does not update the head to the new first node -> Option A

4. Quick Check:

   Head must update to new first node [OK]

Hint: Update head to last processed node after loop [OK]

Common Mistakes:

• Not updating head after reversal
• Incorrect loop condition causing infinite loop
• Returning wrong node at end

5. Given a doubly linked list with nodes:

Head -> 10 <-> 20 <-> 30 <-> 40 <-> null

After reversing the list, what is the correct sequence of nodes starting from the new head?

hard

A. 10 <-> 20 <-> 30 <-> 40 <-> null

B. 40 <-> 30 <-> 20 <-> 10 <-> null

C. 40 <-> 20 <-> 30 <-> 10 <-> null

D. null <-> 40 <-> 30 <-> 20 <-> 10

Solution

1. Step 1: Original list order

   Nodes are linked as 10 <-> 20 <-> 30 <-> 40, head at 10.

2. Step 2: Reverse swaps pointers and changes head to last node

   After reversal, head is 40, and nodes link backward as 40 <-> 30 <-> 20 <-> 10.

3. Final Answer:

   40 <-> 30 <-> 20 <-> 10 <-> null -> Option B

4. Quick Check:

   Reverse list order = original tail to head [OK]

Hint: Reversed list order is original list backwards [OK]

Common Mistakes:

• Not reversing the order correctly
• Mixing node values in wrong order
• Confusing null placement in list