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

When we create and initialize a doubly linked list, we want to know how the time needed grows as we add more nodes.

We ask: How long does it take to build the list as its size increases?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

struct Node* createList(int n) {
    struct Node* head = NULL;
    struct Node* temp = NULL;
    for (int i = 0; i < n; i++) {
        struct Node* newNode = malloc(sizeof(struct Node));
        newNode->data = i;
        newNode->prev = temp;
        newNode->next = NULL;
        if (temp != NULL) temp->next = newNode;
        else head = newNode;
        temp = newNode;
    }
    return head;
}
    

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

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop that runs n times to create and link nodes.
• How many times: Exactly once for each node from 0 to n-1, so n times.

How Execution Grows With Input

Each new node requires a fixed number of steps to create and link it. So, as n grows, the total steps grow in a straight line.

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

Pattern observation: The work grows directly with n; doubling n doubles the work.

Final Time Complexity

Time Complexity: O(n)

This means the time to create the list grows linearly with the number of nodes.

Common Mistake

[X] Wrong: "Creating each node takes constant time, so the whole list creation is constant time."

[OK] Correct: Even though each node is made quickly, you must do it n times, so total time grows with n, not stays the same.

Interview Connect

Understanding how list creation scales helps you explain efficiency clearly and shows you know how data structures behave as they grow.

Self-Check

"What if we added nodes at the head instead of the tail? 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 data automatically

D. To store data only in one direction

Solution

1. Step 1: Understand doubly linked list structure

   A doubly linked list has nodes with pointers to both next and previous 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 = bidirectional traversal [OK]

Hint: Remember: doubly means two directions [OK]

Common Mistakes:

• Confusing doubly linked list with singly linked list
• Thinking it sorts data automatically
• Assuming it uses arrays internally

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; struct Node* next; };

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

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

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

Solution

1. Step 1: Check node structure for doubly linked list

   Each node must have data, a pointer to next node, and a pointer to previous node.

2. Step 2: Identify correct syntax

   struct Node { int data; struct Node* prev; struct Node* next; }; correctly declares pointers to next and prev nodes using struct Node*.

3. Final Answer:

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

4. Quick Check:

   Node has data + prev pointer + next pointer [OK]

Hint: Pointers to prev and next must be struct Node* [OK]

Common Mistakes:

• Using int instead of pointer for next/prev
• Missing prev pointer in node
• Declaring next/prev as struct Node instead of pointer

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

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

int main() {
  Node* head = (Node*)malloc(sizeof(Node));
  Node* second = (Node*)malloc(sizeof(Node));

  head->data = 10;
  head->prev = NULL;
  head->next = second;

  second->data = 20;
  second->prev = head;
  second->next = NULL;

  printf("%d -> %d -> NULL", head->data, second->data);
  return 0;
}

medium

A. Compilation error

B. 20 -> 10 -> NULL

C. 10 -> 20 -> NULL

D. 10 -> NULL

Solution

1. Step 1: Analyze node creation and linking

   Two nodes are created: head with data 10, second with data 20. head->next points to second, second->prev points to head.

2. Step 2: Understand print statement

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

3. Final Answer:

   10 -> 20 -> NULL -> Option C

4. Quick Check:

   Prints data in order: 10 then 20 [OK]

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

Common Mistakes:

• Confusing order of nodes
• Forgetting to set next or prev pointers
• Assuming print shows backward traversal

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

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

int main() {
  struct Node* node = malloc(sizeof(struct Node));
  node->data = 5;
  node->prev = NULL;
  node->next = NULL;
  free(node);
  printf("%d", node->data);
  return 0;
}

medium

A. Accessing freed memory after free(node)

B. Missing #include

C. Incorrect struct declaration

D. No error, code runs fine

Solution

1. Step 1: Review memory allocation and freeing

   Memory is allocated for node, initialized, then freed with free(node).

2. Step 2: Identify invalid access

   After freeing, code tries to print node->data, which accesses freed memory causing undefined behavior.

3. Final Answer:

   Accessing freed memory after free(node) -> Option A

4. Quick Check:

   Using pointer after free = error [OK]

Hint: Never use pointer after free() [OK]

Common Mistakes:

• Ignoring use-after-free errors
• Forgetting to include stdlib.h (but not main error here)
• Assuming free deletes pointer variable

5. You want to create a doubly linked list with nodes containing values 1, 2, and 3 in that order. Which code snippet correctly initializes this list with proper prev and next pointers?

hard

A. Node* n1 = malloc(sizeof(Node)); n1->data=1; n1->prev=NULL; n1->next=NULL;
Node* n2 = malloc(sizeof(Node)); n2->data=2; n2->prev=NULL; n2->next=NULL;
n1->next=n2;
Node* n3 = malloc(sizeof(Node)); n3->data=3; n3->prev=NULL; n3->next=NULL;
n2->next=n3;

B. Node* n1 = malloc(sizeof(Node)); n1->data=1; n1->prev=NULL; n1->next=NULL;
Node* n2 = malloc(sizeof(Node)); n2->data=2; n2->prev=n1; n2->next=NULL;
n1->next=n2;
Node* n3 = malloc(sizeof(Node)); n3->data=3; n3->prev=n2; n3->next=n1;
n2->next=n3;

C. Node* n1 = malloc(sizeof(Node)); n1->data=1; n1->prev=NULL; n1->next=NULL;
Node* n2 = malloc(sizeof(Node)); n2->data=2; n2->prev=n1; n2->next=NULL;
n1->next=n2;
Node* n3 = malloc(sizeof(Node)); n3->data=3; n3->prev=NULL; n3->next=NULL;
n2->next=n3;

D. Node* n1 = malloc(sizeof(Node)); n1->data=1; n1->prev=NULL; n1->next=NULL;
Node* n2 = malloc(sizeof(Node)); n2->data=2; n2->prev=n1; n2->next=NULL;
n1->next=n2;
Node* n3 = malloc(sizeof(Node)); n3->data=3; n3->prev=n2; n3->next=NULL;
n2->next=n3;

Solution

1. Step 1: Check initialization of first node

   n1 has data=1, prev=NULL, next=NULL initially.

2. Step 2: Link second node correctly

   n2 has data=2, prev=n1, next=NULL; n1->next points to n2.

3. Step 3: Link third node correctly

   n3 has data=3, prev=n2, next=NULL; n2->next points to n3.

4. Final Answer:

   Code snippet B correctly sets prev and next pointers for all nodes -> Option D

5. Quick Check:

   Each node's prev and next link neighbors properly [OK]

Hint: Prev of first is NULL; next of last is NULL [OK]

Common Mistakes:

• Not setting prev pointers for nodes after first
• Setting next pointers incorrectly
• Making circular links unintentionally