Doubly Linked List Structure and Node Design in DSA C - Time & Space Complexity

Time Complexity: Doubly Linked List Structure and Node Design

O(1)

Understanding Time Complexity

We want to understand how the time to work with a doubly linked list changes as it grows.

Specifically, how fast can we access or change nodes based on the list size?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

// Define a node in a doubly linked list
struct Node {
    int data;
    struct Node* prev;
    struct Node* next;
};

// Create a new node
struct Node* createNode(int value) {
    struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));
    newNode->data = value;
    newNode->prev = NULL;
    newNode->next = NULL;
    return newNode;
}
    

This code creates a single node with pointers to the previous and next nodes.

Identify Repeating Operations

In this snippet, there are no loops or recursion.

• Primary operation: Allocating and initializing one node.
• How many times: Exactly once per call.

How Execution Grows With Input

Since this creates only one node at a time, the work does not grow with the list size.

Input Size (n)	Approx. Operations
10	1 node creation
100	1 node creation
1000	1 node creation

Pattern observation: The time to create a node stays the same no matter how big the list is.

Final Time Complexity

Time Complexity: O(1)

This means creating a node takes the same amount of time regardless of list size.

Common Mistake

[X] Wrong: "Creating a node takes longer as the list grows because it has to connect to all nodes."

[OK] Correct: Creating a node only sets its own pointers; linking it to the list happens separately and usually involves just a few pointer changes.

Interview Connect

Understanding node creation time helps you explain how linked lists build up and why some operations are fast or slow.

Self-Check

"What if we added a loop to traverse the list to find the last node before adding the new node? How would the time complexity change?"

Practice

1. What is the main difference between a doubly linked list node and a singly linked list node?

easy

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

B. A doubly linked list node stores data twice.

C. A doubly linked list node can only point to the next node.

D. A doubly linked list node does not store any data.

Solution

1. Step 1: Understand node pointers in singly linked list

   A singly linked list node has only one pointer to the next node.

2. Step 2: Understand node pointers in doubly linked list

   A doubly linked list node has two pointers: one to the next node and one to the previous node.

3. Final Answer:

   A doubly linked list node has pointers to both the previous and next nodes. -> Option A

4. Quick Check:

   Doubly linked list node = two pointers [OK]

Hint: Remember: doubly linked means two directions [OK]

Common Mistakes:

• Thinking doubly linked nodes store data twice
• Confusing singly and doubly linked list pointers
• Assuming doubly linked nodes have only one pointer

2. Which of the following is the correct C struct definition for a doubly linked list node storing an integer?

easy

A. typedef struct Node { int data; struct Node* next; } Node;

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

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

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

Solution

1. Step 1: Identify required pointers in doubly linked list node

   It must have pointers to both previous and next nodes of type struct Node*.

2. Step 2: Check each option for correct pointer types and members

   typedef struct Node { int data; struct Node* prev; struct Node* next; } Node; correctly defines data, prev, and next pointers as struct Node*.

3. Final Answer:

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

4. Quick Check:

   Correct struct has prev and next pointers [OK]

Hint: Doubly linked node needs both prev and next pointers [OK]

Common Mistakes:

• Missing prev pointer in struct
• Using wrong pointer types like int* for nodes
• Defining only one pointer instead of two

3. Consider the following code snippet for a doubly linked list node initialization in C:

Node* createNode(int val) {
    Node* newNode = (Node*)malloc(sizeof(Node));
    newNode->data = val;
    newNode->prev = NULL;
    newNode->next = NULL;
    return newNode;
}

int main() {
    Node* node = createNode(10);
    printf("%d %p %p", node->data, node->prev, node->next);
    return 0;
}

What will be the output of this program?

medium

A. 10 garbage garbage

B. 10 0x0 0x0

C. 10 NULL NULL

D. Compilation error

Solution

1. Step 1: Analyze node initialization

   Node data is set to 10, prev and next pointers are set to NULL (which is 0x0 in memory).

2. Step 2: Understand printf output for pointers

   Printing pointers with %p shows their memory address; NULL prints as 0x0.

3. Final Answer:

   10 0x0 0x0 -> Option B

4. Quick Check:

   NULL pointers print as 0x0 in %p format [OK]

Hint: NULL pointers print as 0x0 with %p in C [OK]

Common Mistakes:

• Expecting 'NULL' string instead of 0x0
• Assuming garbage values for initialized pointers
• Confusing pointer print format specifiers

4. Identify the error in the following C code snippet for inserting a new node at the beginning of a doubly linked list:

void insertAtHead(Node** head, int val) {
    Node* newNode = (Node*)malloc(sizeof(Node));
    newNode->data = val;
    newNode->prev = NULL;
    newNode->next = *head;
    *head = newNode;
    if (*head != NULL) {
        (*head)->prev = newNode;
    }
}

medium

A. The condition if (*head != NULL) should be before updating *head.

B. newNode->prev should point to *head, not NULL.

C. The malloc size is incorrect.

D. No error; code is correct.

Solution

1. Step 1: Trace pointer updates

   newNode->next is set to current head, then head is updated to newNode.

2. Step 2: Check the if condition usage

   After updating *head, the condition if (*head != NULL) is always true because *head is newNode. The intention is to update old head's prev pointer.

3. Step 3: Correct order

   The if condition should check if old head (newNode->next) is not NULL before setting its prev pointer.

4. Final Answer:

   The condition if (*head != NULL) should be before updating *head. -> Option A

5. Quick Check:

   Check old head before changing pointers [OK]

Hint: Update old head's prev before changing head pointer [OK]

Common Mistakes:

• Checking *head after it points to newNode
• Setting prev pointer incorrectly
• Ignoring NULL checks before pointer updates

5. You want to design a function to delete a node from a doubly linked list given a pointer to that node. Which of the following steps is NOT required in the deletion process?

hard

A. Free the memory allocated to the node.

B. Update the next node's prev pointer to the node's prev pointer.

C. Update the previous node's next pointer to the node's next pointer.

D. Set the node's data to zero before deletion.

Solution

1. Step 1: Understand deletion in doubly linked list

   To delete a node, update the previous node's next and next node's prev pointers to bypass the node.

2. Step 2: Check necessity of setting data to zero

   Setting the node's data to zero is unnecessary because the node will be freed and memory reclaimed.

3. Step 3: Confirm freeing memory

   Freeing the node's memory is essential to avoid memory leaks.

4. Final Answer:

   Set the node's data to zero before deletion. -> Option D

5. Quick Check:

   Data reset before free is unnecessary [OK]

Hint: Free memory; no need to clear data first [OK]

Common Mistakes:

• Clearing data before freeing memory
• Forgetting to update prev or next pointers
• Not freeing the node memory