Create and Initialize Doubly Linked List in DSA C++ - Time & Space Complexity

Time Complexity: Create and Initialize Doubly Linked List

O(n)

Understanding Time Complexity

We want to understand how long it takes to create and set up a doubly linked list as it grows.

How does the time needed change when we add more nodes?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

Node* createList(int n) {
    if (n == 0) return nullptr;
    Node* head = new Node{1, nullptr, nullptr};
    Node* current = head;
    for (int i = 2; i <= n; i++) {
        Node* newNode = new Node{i, current, nullptr};
        current->next = newNode;
        current = newNode;
    }
    return head;
}
    

This code creates a doubly linked list with n nodes, linking each node to the previous and next.

Identify Repeating Operations

• Primary operation: The for-loop that creates and links each new node.
• How many times: It runs (n - 1) times, once for each node after the first.

How Execution Grows With Input

Each new node requires a fixed number of steps to create and link.

Input Size (n)	Approx. Operations
10	About 9 node creations and linkings
100	About 99 node creations and linkings
1000	About 999 node creations and linkings

Pattern observation: The work grows directly with the number of nodes; doubling nodes doubles the work.

Final Time Complexity

Time Complexity: O(n)

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

Common Mistake

[X] Wrong: "Creating a doubly linked list takes constant time regardless of size."

[OK] Correct: Each node must be created and linked, so more nodes mean more work, not the same.

Interview Connect

Understanding this helps you explain how data structures grow and why efficient creation matters in real projects.

Self-Check

"What if we added a nested loop to link nodes in both directions after creation? How would the time complexity change?"

Practice

1. What is the main purpose of a doubly linked list in data structures?

easy

A. To allow traversal in both forward and backward directions

B. To store data in a fixed-size array

C. To sort elements automatically

D. To store data only at the beginning

Solution

1. Step 1: Understand doubly linked list structure

   A doubly linked list has nodes with pointers to both previous and next nodes.

2. Step 2: Identify traversal capability

   This structure allows moving forward and backward through the list easily.

3. Final Answer:

   To allow traversal in both forward and backward directions -> Option A

4. Quick Check:

   Doubly linked list = forward and backward traversal [OK]

Hint: Remember: doubly means two directions [OK]

Common Mistakes:

• Confusing doubly linked list with arrays
• Thinking it sorts data automatically
• Assuming it only allows forward traversal

2. Which of the following is the correct way to declare a node structure for a doubly linked list in C++?

easy

A. struct Node { int data; Node prev; Node next; };

B. struct Node { int data; Node next; Node prev; };

C. struct Node { int data; Node* next; };

D. struct Node { int data; Node* next; Node* prev; };

Solution

1. Step 1: Check pointer usage in node structure

   Each node must have pointers to next and previous nodes, so use Node* for both.

2. Step 2: Verify syntax correctness

   struct Node { int data; Node* next; Node* prev; }; correctly uses pointers (Node*) for next and prev, while others use incorrect types.

3. Final Answer:

   struct Node { int data; Node* next; Node* prev; }; -> Option D

4. Quick Check:

   Node pointers use * for next and prev [OK]

Hint: Use pointers (*) for next and prev nodes [OK]

Common Mistakes:

• Using Node instead of Node* for pointers
• Missing prev pointer in node
• Incorrect order of members

3. What will be the output of the following code snippet that creates a doubly linked list with two nodes and prints their data?

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

int main() {
  Node* head = new Node{10, nullptr, nullptr};
  Node* second = new Node{20, nullptr, head};
  head->next = second;
  std::cout << head->data << " -> " << second->data << " -> null";
  return 0;
}

medium

A. 20 -> 10 -> null

B. 10 -> 20 -> null

C. 10 -> null

D. Compilation error

Solution

1. Step 1: Analyze node creation and linking

   First node has data 10, second node has data 20 and points back to first node. Head's next points to second.

2. Step 2: Trace output statement

   Prints head data (10), then second data (20), then "-> null" string.

3. Final Answer:

   10 -> 20 -> null -> Option B

4. Quick Check:

   Print order matches linked list nodes [OK]

Hint: Follow pointers to print nodes in order [OK]

Common Mistakes:

• Confusing prev and next pointers
• Printing second node first
• Forgetting to set head->next

4. Identify the error in the following code that attempts to create a doubly linked list with one node:

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

int main() {
  Node* head = new Node;
  head->data = 5;
  head->next = head->prev = nullptr;
  head->prev = head;
  return 0;
}

medium

A. head->prev should not point to head itself

B. Missing initialization of head->data

C. head->next should point to head

D. Node structure is incomplete

Solution

1. Step 1: Review pointer assignments

   head->next and head->prev are set to nullptr, then head->prev is set to head itself.

2. Step 2: Identify logical error

   head->prev pointing to head creates a circular reference which is incorrect for a single node list.

3. Final Answer:

   head->prev should not point to head itself -> Option A

4. Quick Check:

   Single node prev = nullptr, not self [OK]

Hint: Single node prev and next must be nullptr [OK]

Common Mistakes:

• Setting prev or next to self causing loops
• Forgetting to initialize data
• Confusing next and prev pointers

5. You want to create a doubly linked list with three nodes containing values 1, 2, and 3 respectively. Which of the following code snippets correctly initializes the list and links all nodes properly?

hard

A. Node* first = new Node{1, nullptr, nullptr};
Node* second = new Node{2, nullptr, first};
first->prev = second;
Node* third = new Node{3, nullptr, second};
second->prev = third;

B. Node* first = new Node{1, nullptr, nullptr};
Node* second = new Node{2, first, nullptr};
first->next = second;
Node* third = new Node{3, second, nullptr};
second->next = third;

C. Node* first = new Node{1, nullptr, nullptr};
Node* second = new Node{2, nullptr, first};
first->next = second;
Node* third = new Node{3, nullptr, second};
second->next = third;

D. Node* first = new Node{1, nullptr, nullptr};
Node* second = new Node{2, first, nullptr};
first->prev = second;
Node* third = new Node{3, second, nullptr};
second->prev = third;

Solution

1. Step 1: Check node creation and pointer assignments

   Node* first = new Node{1, nullptr, nullptr}; Node* second = new Node{2, nullptr, first}; first->next = second; Node* third = new Node{3, nullptr, second}; second->next = third; creates nodes with correct data and sets next and prev pointers properly: second's prev points to first, first's next points to second, third's prev points to second, second's next points to third.

2. Step 2: Verify linkage correctness

   All nodes are linked forward and backward correctly, forming a proper doubly linked list.

3. Final Answer:

   Node* first = new Node{1, nullptr, nullptr}; Node* second = new Node{2, nullptr, first}; first->next = second; Node* third = new Node{3, nullptr, second}; second->next = third; -> Option C

4. Quick Check:

   Next and prev pointers set correctly in Node* first = new Node{1, nullptr, nullptr}; Node* second = new Node{2, nullptr, first}; first->next = second; Node* third = new Node{3, nullptr, second}; second->next = third; [OK]

Hint: Prev points backward, next points forward in order [OK]

Common Mistakes:

• Swapping next and prev pointers
• Not linking nodes both ways
• Setting prev or next to nullptr incorrectly