Enqueue Using Linked List in DSA C - Time & Space Complexity

Time Complexity: Enqueue Using Linked List

O(1)

Understanding Time Complexity

We want to understand how the time to add an item to a linked list queue grows as the queue gets bigger.

How does the enqueue operation's time change when the queue size increases?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

#include <stdlib.h>

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

void enqueue(struct Node** front, struct Node** rear, int value) {
    struct Node* newNode = malloc(sizeof(struct Node));
    newNode->data = value;
    newNode->next = NULL;
    if (*rear == NULL) {
        *front = *rear = newNode;
        return;
    }
    (*rear)->next = newNode;
    *rear = newNode;
}
    

This code adds a new element to the end of a linked list queue, updating front and rear pointers.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Creating a new node and linking it at the end.
• How many times: This happens once per enqueue call, no loops or recursion inside.

How Execution Grows With Input

Each enqueue adds one node by directly linking at the rear pointer without searching.

Input Size (n)	Approx. Operations
10	About 1 main linking operation
100	About 1 main linking operation
1000	About 1 main linking operation

Pattern observation: The time stays roughly the same no matter how big the queue is.

Final Time Complexity

Time Complexity: O(1)

This means adding an item takes the same short time regardless of queue size.

Common Mistake

[X] Wrong: "Enqueue takes longer as the queue grows because we must find the end each time."

[OK] Correct: We keep a rear pointer, so we add directly without searching, keeping time constant.

Interview Connect

Knowing how to keep enqueue fast by using a rear pointer shows you understand efficient queue design, a key skill in many coding tasks.

Self-Check

"What if we did not keep a rear pointer and had to find the end each time? How would the time complexity change?"

Practice

1. What does the enqueue operation do in a queue implemented using a linked list?

easy

A. Deletes the entire queue

B. Adds an element at the end (rear) of the queue

C. Checks if the queue is empty

D. Removes an element from the front of the queue

Solution

1. Step 1: Understand enqueue operation

   Enqueue means adding a new element to the queue.

2. Step 2: Identify position of insertion in linked list queue

   In a linked list queue, new elements are added at the rear (end) to maintain order.

3. Final Answer:

   Adds an element at the end (rear) of the queue -> Option B

4. Quick Check:

   Enqueue = Add at rear [OK]

Hint: Enqueue always adds at the rear in a queue [OK]

Common Mistakes:

• Confusing enqueue with dequeue operation
• Thinking enqueue adds at the front
• Mixing queue with stack operations

2. Which of the following is the correct syntax to create a new node for enqueue in C linked list?

easy

A. newNode = malloc(sizeof(Node));

B. struct Node newNode = (struct Node*)malloc(sizeof(struct Node));

C. Node newNode = malloc(sizeof(Node));

D. struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));

Solution

1. Step 1: Allocate memory for new node

   In C, use malloc with sizeof(struct Node) to allocate memory.

2. Step 2: Correct pointer declaration and casting

   Declare pointer as struct Node* and cast malloc result to (struct Node*).

3. Final Answer:

   struct Node* newNode = (struct Node*)malloc(sizeof(struct Node)); -> Option D

4. Quick Check:

   Correct malloc syntax = struct Node* newNode = (struct Node*)malloc(sizeof(struct Node)); [OK]

Hint: Always cast malloc to (struct Node*) in C [OK]

Common Mistakes:

• Missing struct keyword in declaration
• Not casting malloc result
• Using wrong variable types

3. What will be the state of the queue after executing the following code?

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

struct Node* front = NULL;
struct Node* rear = NULL;

// Enqueue 10
struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));
newNode->data = 10;
newNode->next = NULL;
if (rear == NULL) {
  front = rear = newNode;
} else {
  rear->next = newNode;
  rear = newNode;
}

// Enqueue 20
newNode = (struct Node*)malloc(sizeof(struct Node));
newNode->data = 20;
newNode->next = NULL;
rear->next = newNode;
rear = newNode;

medium

A. 10 -> NULL

B. 20 -> 10 -> NULL

C. 10 -> 20 -> NULL

D. 20 -> NULL

Solution

1. Step 1: Enqueue 10 when queue is empty

   Both front and rear point to new node with data 10.

2. Step 2: Enqueue 20 when queue has one element

   rear->next points to new node with data 20, rear moves to this node.

3. Final Answer:

   10 -> 20 -> NULL -> Option C

4. Quick Check:

   Order of enqueue = 10 then 20 [OK]

Hint: New nodes link at rear, order stays FIFO [OK]

Common Mistakes:

• Reversing order of nodes
• Not updating rear pointer
• Forgetting to set next to NULL

4. Identify the error in the following enqueue function for a linked list queue:

void enqueue(int value) {
  struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));
  newNode->data = value;
  newNode->next = NULL;
  if (front == NULL) {
    front = newNode;
  } else {
    rear->next = newNode;
    rear = newNode;
  }
}

medium

A. rear pointer is not updated when queue is empty

B. newNode->next should point to front

C. malloc size is incorrect

D. front pointer is updated incorrectly

Solution

1. Step 1: Check rear pointer update when queue is empty

   When front is NULL, only front = newNode is executed, rear remains uninitialized.

2. Step 2: No rear update in if branch

   The else block sets rear = newNode, but it is skipped when queue is empty.

3. Final Answer:

   rear pointer is not updated when queue is empty -> Option A

4. Quick Check:

   rear must be set when queue is empty [OK]

Hint: Always update rear when queue was empty [OK]

Common Mistakes:

• Not setting rear when queue is empty
• Incorrect next pointer assignment
• Wrong malloc size or casting

5. Given a linked list queue with elements 5 -> 15 -> 25 -> NULL, what will be the queue after enqueueing 35 and then 45? Show the final linked list state.

hard

A. 5 -> 15 -> 25 -> 35 -> 45 -> NULL

B. 45 -> 35 -> 25 -> 15 -> 5 -> NULL

C. 5 -> 15 -> 25 -> NULL

D. 35 -> 45 -> 5 -> 15 -> 25 -> NULL

Solution

1. Step 1: Understand enqueue adds at rear

   Enqueue adds new nodes at the end of the queue to maintain order.

2. Step 2: Add 35 and then 45 at the rear

   After adding 35, queue becomes 5 -> 15 -> 25 -> 35 -> NULL. Then adding 45 results in 5 -> 15 -> 25 -> 35 -> 45 -> NULL.

3. Final Answer:

   5 -> 15 -> 25 -> 35 -> 45 -> NULL -> Option A

4. Quick Check:

   Enqueue order preserved at rear [OK]

Hint: Enqueue appends at rear, order stays same [OK]

Common Mistakes:

• Adding new nodes at front instead of rear
• Reversing the order of elements
• Not updating rear pointer after enqueue