Reverse a Doubly Linked List in DSA Java - 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.

Specifically, how does the number of steps grow when the list has more nodes?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

public void reverse() {
    Node current = head;
    Node temp = null;
    while (current != null) {
        temp = current.prev;
        current.prev = current.next;
        current.next = temp;
        current = current.prev;
    }
    if (temp != null) {
        head = temp.prev;
    }
}
    

This code reverses the links of a doubly linked list by swapping the previous and next pointers of 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: It runs once for every node in the list, so n times if there are n nodes.

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 steps
100	About 100 steps
1000	About 1000 steps

Pattern observation: The steps increase in a straight line as the list size grows.

Final Time Complexity

Time Complexity: O(n)

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

Common Mistake

[X] Wrong: "Reversing a doubly linked list takes more than linear time because of pointer swaps."

[OK] Correct: Each node is visited once and pointers are swapped in constant time, so total time grows linearly.

Interview Connect

Understanding this helps you explain how simple pointer changes can reverse a list efficiently, a common question in interviews.

Self-Check

"What if we changed the list to a singly linked list without previous pointers? How would the time complexity change?"

Practice

1. What is the main purpose of reversing a doubly linked list?

easy

A. To change the direction of traversal so the last node becomes the first

B. To delete all nodes from the list

C. To sort the nodes in ascending order

D. To convert it into a singly linked list

Solution

1. Step 1: Understand the structure of a doubly linked list

   A doubly linked list has nodes with pointers to both previous and next nodes, allowing traversal in both directions.

2. Step 2: Purpose of reversing

   Reversing swaps the previous and next pointers of each node, making the last node the first and vice versa.

3. Final Answer:

   To change the direction of traversal so the last node becomes the first -> Option A

4. Quick Check:

   Reversing means swapping directions [OK]

Hint: Reversing flips the list direction, last becomes first [OK]

Common Mistakes:

• Confusing reversing with deleting nodes
• Thinking reversing sorts the list
• Assuming it converts to singly linked list

2. Which of the following Java code snippets correctly swaps the next and prev pointers of a node curr in a doubly linked list?

easy

A. curr.next = curr.prev; curr.prev = null;

B. Node temp = curr.prev; curr.prev = curr.next; curr.next = null;

C. curr.next = curr.prev; curr.prev = curr.next;

D. Node temp = curr.next; curr.next = curr.prev; curr.prev = temp;

Solution

1. Step 1: Identify correct swapping logic

   Swapping two pointers requires a temporary variable to hold one pointer before overwriting it.

2. Step 2: Check each option

   A temporary variable is required to swap pointers without data loss. curr.next = curr.prev; curr.prev = null; incorrectly sets prev to null. Node temp = curr.prev; curr.prev = curr.next; curr.next = null; uses temp but wrongly sets next to null. curr.next = curr.prev; curr.prev = curr.next; overwrites without preserving original values. Node temp = curr.next; curr.next = curr.prev; curr.prev = temp; correctly swaps the pointers.

3. Final Answer:

   Node temp = curr.next; curr.next = curr.prev; curr.prev = temp; -> Option D

4. Quick Check:

   Use temp variable to swap pointers [OK]

Hint: Always use a temp variable to swap two pointers [OK]

Common Mistakes:

• Swapping without a temporary variable
• Setting one pointer to null accidentally
• Swapping pointers in wrong order

3. Given the following doubly linked list nodes and code to reverse it, what will be the printed output after reversal?

class Node {
  int data;
  Node prev, next;
  Node(int d) { data = d; prev = next = null; }
}

// List: 1 <-> 2 <-> 3
Node head = new Node(1);
Node second = new Node(2);
Node third = new Node(3);
head.next = second; second.prev = head;
second.next = third; third.prev = second;

// Reverse code snippet
Node curr = head;
Node temp = null;
while (curr != null) {
  temp = curr.prev;
  curr.prev = curr.next;
  curr.next = temp;
  curr = curr.prev;
}
if (temp != null) head = temp.prev;

// Print list forward
Node ptr = head;
while (ptr != null) {
  System.out.print(ptr.data + " ");
  ptr = ptr.next;
}

medium

A. 1 2 3

B. 3 2 1

C. 3 1 2

D. 2 3 1

Solution

1. Step 1: Understand reversal logic

   The code swaps prev and next for each node, then moves curr to the original next node (now prev after swap).

2. Step 2: Trace the list after reversal

   Original list: 1 <-> 2 <-> 3
   After reversal, head points to node with data 3.
   Printing from head forward prints: 3 2 1

3. Final Answer:

   3 2 1 -> Option B

4. Quick Check:

   Reversed list prints nodes backward [OK]

Hint: After reversal, head points to original tail node [OK]

Common Mistakes:

• Not updating head after reversal
• Confusing prev and next pointers
• Printing from old head instead of new head

4. Identify the error in the following code snippet that attempts to reverse a doubly linked list:

Node curr = head;
while (curr != null) {
  Node temp = curr.next;
  curr.next = curr.prev;
  curr.prev = temp;
  curr = curr.next;
}

medium

A. The pointers next and prev are not swapped correctly

B. The temp variable should store curr.prev, not curr.next

C. The loop moves curr to curr.next instead of curr.prev after swapping

D. The loop condition should be curr.next != null

Solution

1. Step 1: Analyze pointer swapping

   The code swaps next and prev correctly using temp.

2. Step 2: Check loop iteration step

   After swapping, curr.next points to the original prev. To move forward in the original list, curr should move to curr.prev (which is original next). The code incorrectly moves to curr.next, causing wrong traversal.

3. Final Answer:

   The loop moves curr to curr.next instead of curr.prev after swapping -> Option C

4. Quick Check:

   Move curr to curr.prev after swapping [OK]

Hint: After swapping, move curr to curr.prev to continue traversal [OK]

Common Mistakes:

• Moving curr to wrong pointer after swap
• Confusing temp usage
• Incorrect loop condition

5. You have a doubly linked list with nodes containing integer data. After reversing the list using the standard pointer swap method, you want to find the middle node efficiently. Which approach is best to find the middle node after reversal?

hard

A. Use two pointers starting from the new head: one moves one step, the other moves two steps until the faster reaches null

B. Traverse from the original head before reversal to find the middle

C. Count nodes from the tail and divide by two to find middle index

D. Reverse the list again and then find the middle node

Solution

1. Step 1: Understand list reversal effect

   After reversal, the head points to the original tail. The list is still doubly linked and can be traversed forward.

2. Step 2: Efficient middle node finding

   The two-pointer technique (slow and fast pointers) starting from the new head finds the middle in one pass efficiently.

3. Final Answer:

   Use two pointers starting from the new head: one moves one step, the other moves two steps until the faster reaches null -> Option A

4. Quick Check:

   Two-pointer method finds middle in O(n) [OK]

Hint: Use slow and fast pointers from new head to find middle [OK]

Common Mistakes:

• Trying to find middle from old head after reversal
• Counting nodes from tail which is inefficient
• Reversing list again unnecessarily