Why Doubly Linked List Over Singly Linked List in DSA C - Performance Analysis

Time Complexity: Why Doubly Linked List Over Singly Linked List

O(1)

Understanding Time Complexity

We want to understand how using a doubly linked list changes the time it takes to do common operations compared to a singly linked list.

Which operations become faster or slower, and why?

Scenario Under Consideration

Analyze the time complexity of inserting and deleting nodes in a doubly linked list.

// Insert a new node after a given node in doubly linked list
void insertAfter(Node* prev_node, int new_data) {
    if (prev_node == NULL) return;
    Node* new_node = (Node*)malloc(sizeof(Node));
    new_node->data = new_data;
    new_node->next = prev_node->next;
    new_node->prev = prev_node;
    if (prev_node->next != NULL) prev_node->next->prev = new_node;
    prev_node->next = new_node;
}

// Delete a given node from doubly linked list
void deleteNode(Node** head_ref, Node* del_node) {
    if (*head_ref == NULL || del_node == NULL) return;
    if (*head_ref == del_node) *head_ref = del_node->next;
    if (del_node->next != NULL) del_node->next->prev = del_node->prev;
    if (del_node->prev != NULL) del_node->prev->next = del_node->next;
    free(del_node);
}
    

This code shows how to insert and delete nodes when you have access to the node itself in a doubly linked list.

Identify Repeating Operations

Look at what repeats or dominates the work done.

• Primary operation: Adjusting pointers (prev and next) for nodes.
• How many times: Each insertion or deletion changes a fixed number of pointers, so constant time per operation.

How Execution Grows With Input

Since insertion and deletion here happen by changing a few pointers, the time does not grow with the list size.

Input Size (n)	Approx. Operations
10	5-6 pointer changes
100	5-6 pointer changes
1000	5-6 pointer changes

Pattern observation: The number of pointer changes stays the same no matter how big the list is.

Final Time Complexity

Time Complexity: O(1)

This means insertion or deletion at a known node happens in constant time, regardless of list size.

Common Mistake

[X] Wrong: "Doubly linked lists always take longer because they have more pointers to update."

[OK] Correct: Actually, having two pointers lets you delete or insert nodes faster when you have direct access, because you don't need to find the previous node by traversing.

Interview Connect

Understanding when doubly linked lists improve operation speed shows you can choose the right data structure for the task, a key skill in coding interviews.

Self-Check

"What if we only had a singly linked list and wanted to delete a node given only that node? How would the time complexity change?"

Practice

1. Why might a doubly linked list be preferred over a singly linked list?

easy

A. Because it cannot be modified after creation

B. Because it uses less memory than singly linked list

C. Because it only stores one pointer per node

D. Because it allows traversal in both forward and backward directions

Solution

1. Step 1: Understand traversal capabilities

   A singly linked list allows traversal only in one direction, from head to tail.

2. Step 2: Compare with doubly linked list

   A doubly linked list stores two pointers per node, allowing traversal forward and backward.

3. Final Answer:

   Because it allows traversal in both forward and backward directions -> Option D

4. Quick Check:

   Traversal direction = Both [OK]

Hint: Doubly linked lists have two pointers per node [OK]

Common Mistakes:

• Thinking doubly linked lists use less memory
• Confusing traversal directions
• Assuming singly linked lists allow backward traversal

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

easy

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

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

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

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

Solution

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

   A doubly linked list node must have pointers to both previous and next nodes.

2. Step 2: Check each option

   struct Node { int data; struct Node* prev; struct Node* next; }; correctly declares both prev and next pointers as struct Node pointers.

3. Final Answer:

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

4. Quick Check:

   Node pointers = prev and next [OK]

Hint: Doubly linked nodes have both prev and next pointers [OK]

Common Mistakes:

• Omitting prev pointer
• Using int instead of pointer for next/prev
• Confusing singly linked list node with doubly linked

3. What will be the output of the following code snippet that uses a doubly linked list?

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

Node* head = NULL;

// Function to add node at end
void append(int val) {
  Node* newNode = (Node*)malloc(sizeof(Node));
  newNode->data = val;
  newNode->next = NULL;
  if (head == NULL) {
    newNode->prev = NULL;
    head = newNode;
    return;
  }
  Node* temp = head;
  while (temp->next != NULL) temp = temp->next;
  temp->next = newNode;
  newNode->prev = temp;
}

// Print list forward
void printForward() {
  Node* temp = head;
  while (temp != NULL) {
    printf("%d ", temp->data);
    temp = temp->next;
  }
}

int main() {
  append(10);
  append(20);
  append(30);
  printForward();
  return 0;
}

medium

A. 10 20 30

B. 30 20 10

C. 10 20

D. Compilation error

Solution

1. Step 1: Trace append function calls

   append(10) creates first node with data 10, head points to it. append(20) adds node with 20 at end. append(30) adds node with 30 at end.

2. Step 2: Trace printForward function

   printForward starts at head and prints data while moving next. It prints 10, then 20, then 30.

3. Final Answer:

   10 20 30 -> Option A

4. Quick Check:

   List forward print = 10 20 30 [OK]

Hint: Forward print shows nodes in insertion order [OK]

Common Mistakes:

• Confusing forward and backward traversal
• Assuming printForward prints in reverse
• Missing NULL checks causing errors

4. Identify the bug in the following code snippet that tries to delete the last node of a doubly linked list:

void deleteLast() {
  if (head == NULL) return;
  Node* temp = head;
  while (temp->next != NULL) {
    temp = temp->next;
  }
  temp->prev->next = NULL;
  free(temp);
}

medium

A. No bug, code works correctly

B. Does not handle case when list has only one node

C. Incorrect pointer used for deletion

D. Memory leak due to missing free

Solution

1. Step 1: Analyze deletion logic

   The code finds last node by moving to node where next is NULL, then sets previous node's next to NULL and frees last node.

2. Step 2: Check edge case for single node list

   If list has only one node, temp->prev is NULL, so temp->prev->next causes a crash or undefined behavior.

3. Final Answer:

   Does not handle case when list has only one node -> Option B

4. Quick Check:

   Single node deletion needs special handling [OK]

Hint: Check for single node before accessing prev pointer [OK]

Common Mistakes:

• Ignoring single node edge case
• Assuming prev pointer always exists
• Not freeing memory after deletion

5. You want to implement a feature that allows moving backward through a list of recently opened files in a text editor. Which linked list type is best and why?

hard

A. Doubly linked list, because it allows moving backward and forward easily

B. Singly linked list, because it uses less memory and is simpler

C. Circular singly linked list, because it loops infinitely

D. Array, because linked lists cannot move backward

Solution

1. Step 1: Understand feature requirements

   The feature requires moving backward and forward through the list of files.

2. Step 2: Match data structure capabilities

   Singly linked lists allow only forward traversal, arrays allow random access but not efficient insertion/deletion, doubly linked lists allow easy backward and forward traversal.

3. Step 3: Evaluate options

   Doubly linked list fits best because it supports moving backward and forward efficiently.

4. Final Answer:

   Doubly linked list, because it allows moving backward and forward easily -> Option A

5. Quick Check:

   Backward traversal = Doubly linked list [OK]

Hint: Backward navigation needs doubly linked list [OK]

Common Mistakes:

• Choosing singly linked list for backward moves
• Ignoring traversal needs
• Assuming arrays handle backward traversal efficiently