Reverse a Singly Linked List Iterative in DSA C++ - Time & Space Complexity

Time Complexity: Reverse a Singly Linked List Iterative

O(n)

Understanding Time Complexity

We want to know how the time to reverse a linked list changes as the list gets bigger.

How does the number of steps grow when the list length increases?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

Node* reverseList(Node* head) {
    Node* prev = nullptr;
    Node* current = head;
    while (current != nullptr) {
        Node* nextNode = current->next;
        current->next = prev;
        prev = current;
        current = nextNode;
    }
    return prev;
}
    

This code reverses a singly linked list by changing the direction of the links one by one.

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 n times for n nodes.

How Execution Grows With Input

Each node is visited once, so the steps grow 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 time grows in a straight line as the list gets longer.

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 linked list takes more than linear time because of pointer changes."

[OK] Correct: Each node is visited only once, and pointer changes happen in constant time per node, so total time is linear.

Interview Connect

Understanding this linear time reversal is a key skill that shows you can work with linked lists efficiently.

Self-Check

"What if we used recursion instead of iteration? How would the time complexity change?"

Practice

1. What is the main purpose of the iterative method to reverse a singly linked list?

easy

A. To sort the nodes in ascending order

B. To change the direction of the links between nodes one by one

C. To delete all nodes from the list

D. To create a new linked list with the same elements

Solution

1. Step 1: Understand the linked list structure

   A singly linked list has nodes connected by pointers going one way only.

2. Step 2: Purpose of iterative reversal

   The iterative method changes each node's pointer to point backward, reversing the list.

3. Final Answer:

   To change the direction of the links between nodes one by one -> Option B

4. Quick Check:

   Reversing = Changing links direction [OK]

Hint: Think of flipping arrows between nodes one at a time [OK]

Common Mistakes:

• Confusing reversal with deletion
• Thinking it sorts the list
• Assuming it creates a new list

2. Which of the following is the correct syntax to initialize the previous pointer to NULL in C++ before starting the reversal?

easy

A. Node* prev = NULL;

B. Node prev = NULL;

C. Node prev* = 0;

D. Node prev = 0;

Solution

1. Step 1: Understand pointer initialization

   In C++, pointers are declared with * and can be set to NULL or nullptr.

2. Step 2: Correct pointer declaration

   "Node* prev = NULL;" correctly declares a pointer named prev and initializes it to NULL.

3. Final Answer:

   Node* prev = NULL; -> Option A

4. Quick Check:

   Pointer prev initialized to NULL [OK]

Hint: Use * for pointers and assign NULL or nullptr [OK]

Common Mistakes:

• Declaring pointer without *
• Assigning NULL to non-pointer variable
• Using 0 without pointer declaration

3. What will be the output linked list after running the iterative reverse function on the list: 1 -> 2 -> 3 -> null?

medium

A. 3 -> 2 -> 1 -> null

B. 1 -> 2 -> 3 -> null

C. null -> 1 -> 2 -> 3

D. 2 -> 3 -> 1 -> null

Solution

1. Step 1: Trace reversal of 1 -> 2 -> 3

   Start with prev = NULL, curr = 1. Change 1's next to NULL, move prev to 1, curr to 2.

2. Step 2: Continue reversing links

   Change 2's next to 1, move prev to 2, curr to 3. Then change 3's next to 2, prev to 3, curr to NULL.

3. Final Answer:

   3 -> 2 -> 1 -> null -> Option A

4. Quick Check:

   Reversed list = 3 -> 2 -> 1 [OK]

Hint: Reverse pointers one by one from head to tail [OK]

Common Mistakes:

• Not updating pointers correctly
• Leaving last node pointing to old next
• Confusing original and reversed order

4. Identify the error in this iterative reversal code snippet:

Node* reverse(Node* head) {
  Node* prev = NULL;
  Node* curr = head;
  while (curr != NULL) {
    Node* next = curr->next;
    curr->next = prev;
    prev = curr;
    // Missing update of curr here
  }
  return prev;
}

medium

A. prev is not initialized to NULL

B. The function returns head instead of prev

C. next pointer is not declared

D. The pointer curr is never updated inside the loop, causing an infinite loop

Solution

1. Step 1: Check loop pointer updates

   Inside the loop, curr must move to next node to avoid infinite loop.

2. Step 2: Identify missing update

   The code misses 'curr = next;' causing curr to never change and loop forever.

3. Final Answer:

   The pointer curr is never updated inside the loop, causing an infinite loop -> Option D

4. Quick Check:

   Missing curr update = infinite loop [OK]

Hint: Always move current pointer forward inside the loop [OK]

Common Mistakes:

• Forgetting to update curr
• Returning wrong pointer
• Not initializing prev

5. Given a singly linked list with nodes containing values [10, 20, 30, 40, 50], which of the following code snippets correctly reverses the list iteratively and returns the new head?

hard

A. Node* reverseList(Node* head) { Node* prev = nullptr; Node* curr = head; while (curr != nullptr) { curr->next = prev; prev = curr; } return prev; }

B. Node* reverseList(Node* head) { Node* curr = head; Node* prev = nullptr; while (prev) { Node* next = curr->next; curr->next = prev; prev = curr; curr = next; } return curr; }

C. Node* reverseList(Node* head) { Node* prev = nullptr; Node* curr = head; while (curr) { Node* next = curr->next; curr->next = prev; prev = curr; curr = next; } return prev; }

D. Node* reverseList(Node* head) { Node* prev = nullptr; Node* curr = head; while (curr != nullptr) { Node* next = curr->next; prev = curr; curr = next; } return prev; }

Solution

1. Step 1: Check pointer initialization and loop condition

   Node* reverseList(Node* head) { Node* prev = nullptr; Node* curr = head; while (curr) { Node* next = curr->next; curr->next = prev; prev = curr; curr = next; } return prev; } initializes prev to nullptr, curr to head, and loops while curr is not null.

2. Step 2: Verify pointer updates inside loop

   Node* reverseList(Node* head) { Node* prev = nullptr; Node* curr = head; while (curr) { Node* next = curr->next; curr->next = prev; prev = curr; curr = next; } return prev; } saves next, reverses curr->next, moves prev and curr forward correctly, then returns prev as new head.

3. Final Answer:

   Node* reverseList(Node* head) { Node* prev = nullptr; Node* curr = head; while (curr) { Node* next = curr->next; curr->next = prev; prev = curr; curr = next; } return prev; } -> Option C

4. Quick Check:

   Correct pointer updates and return [OK]

Hint: Save next, reverse link, move prev and curr forward [OK]

Common Mistakes:

• Wrong loop condition
• Not saving next before changing links
• Returning wrong pointer