Queue Implementation Using Array in DSA C++ - Time & Space Complexity

Time Complexity: Queue Implementation Using Array

O(1)

Understanding Time Complexity

We want to understand how the time taken by queue operations changes as the number of elements grows.

Specifically, how fast can we add or remove items in a queue implemented with an array?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

class Queue {
  int arr[100];
  int front = 0, rear = 0;
public:
  void enqueue(int x) {
    arr[rear++] = x;
  }
  int dequeue() {
    return arr[front++];
  }
};
    

This code adds elements at the rear and removes from the front of the array, simulating a queue.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Adding or removing one element by moving front or rear index.
• How many times: Each enqueue or dequeue moves the index once, no loops involved.

How Execution Grows With Input

Each operation does a fixed number of steps regardless of queue size.

Input Size (n)	Approx. Operations
10	1 per enqueue or dequeue
100	1 per enqueue or dequeue
1000	1 per enqueue or dequeue

Pattern observation: Time per operation stays the same no matter how many items are in the queue.

Final Time Complexity

Time Complexity: O(1)

This means each enqueue or dequeue operation takes the same small amount of time, no matter the queue size.

Common Mistake

[X] Wrong: "Removing an element from the front takes time proportional to the queue size because we have to shift all elements."

[OK] Correct: In this implementation, we just move the front index forward without shifting elements, so removal is quick and constant time.

Interview Connect

Understanding how queue operations work efficiently helps you explain data structure choices clearly and shows you know how to keep operations fast.

Self-Check

"What if we used a circular array to reuse space after dequeues? How would the time complexity change?"

Practice

1. What is the main purpose of using an array to implement a queue?

easy

A. To store elements in a fixed-size linear order for FIFO operations

B. To store elements randomly for quick access

C. To sort elements automatically

D. To store elements in a LIFO order

Solution

1. Step 1: Understand queue behavior

   A queue follows FIFO (First In First Out), meaning elements are processed in the order they arrive.

2. Step 2: Role of array in queue

   An array stores elements in a fixed linear order, which helps maintain the FIFO order by using front and rear indices.

3. Final Answer:

   To store elements in a fixed-size linear order for FIFO operations -> Option A

4. Quick Check:

   Queue uses array for FIFO storage = C [OK]

Hint: Queue means FIFO; array stores elements linearly [OK]

Common Mistakes:

• Confusing queue with stack (LIFO)
• Thinking array sorts elements automatically
• Assuming random access is main goal

2. Which of the following is the correct way to declare a queue array of size 5 in C++?

easy

A. array queue(5);

B. int queue[5];

C. int[5] queue;

D. queue int[5];

Solution

1. Step 1: Recall C++ array declaration syntax

   In C++, arrays are declared as: type name[size]; so int queue[5]; is correct.

2. Step 2: Check other options

   Options A, B, and C do not follow valid C++ syntax for array declaration.

3. Final Answer:

   int queue[5]; -> Option B

4. Quick Check:

   C++ array syntax = type name[size] [OK]

Hint: Remember C++ arrays: type name[size]; [OK]

Common Mistakes:

• Placing size before name
• Using wrong keywords like 'array'
• Incorrect order of type and name

3. What will be the output after performing these operations on an empty queue of size 3 implemented using array?
enqueue(10); enqueue(20); dequeue(); enqueue(30); display();
Assume enqueue adds at rear and dequeue removes from front.

medium

A. 10 -> 30 -> null

B. 10 -> 20 -> 30 -> null

C. 30 -> null

D. 20 -> 30 -> null

Solution

1. Step 1: Perform enqueue(10) and enqueue(20)

   Queue becomes: 10 -> 20 -> null

2. Step 2: Perform dequeue()

   Removes 10 from front, queue becomes: 20 -> null

3. Step 3: Perform enqueue(30)

   Add 30 at rear, queue becomes: 20 -> 30 -> null

4. Step 4: Display queue

   Output is: 20 -> 30 -> null

5. Final Answer:

   20 -> 30 -> null -> Option D

6. Quick Check:

   After dequeue and enqueue, queue = 20, 30 [OK]

Hint: Track front and rear after each operation [OK]

Common Mistakes:

• Not removing element on dequeue
• Adding new element at front instead of rear
• Confusing order of elements

4. Identify the error in this queue implementation snippet using array:

int queue[3], front = -1, rear = -1;
void enqueue(int x) {
  if (rear == 3) {
    cout << "Queue Full";
    return;
  }
  rear++;
  queue[rear] = x;
  if (front == -1) front = 0;
}

medium

A. front should be incremented in enqueue

B. rear should be initialized to 0

C. Condition should be rear == 2 to check full queue

D. No error, code is correct

Solution

1. Step 1: Understand array indexing for size 3

   Array indices are 0, 1, 2. So rear should not exceed 2.

2. Step 2: Check condition for full queue

   Condition rear == 3 is wrong because index 3 is out of bounds. It should be rear == 2.

3. Final Answer:

   Condition should be rear == 2 to check full queue -> Option C

4. Quick Check:

   Array max index = size-1 = 2 [OK]

Hint: Array max index = size - 1, check boundary carefully [OK]

Common Mistakes:

• Using size instead of size-1 for index check
• Incrementing front in enqueue
• Initializing rear incorrectly

5. Given a queue implemented using an array of size 4, initially empty, what will be the state of the queue after these operations?
enqueue(5); enqueue(10); dequeue(); enqueue(15); enqueue(20); dequeue(); enqueue(25); display();
Assume no circular queue and enqueue fails if rear reaches size-1.

hard

A. 15 -> 20 -> null

B. 10 -> 15 -> 20 -> 25 -> null

C. 15 -> 20 -> 25 -> null

D. 5 -> 10 -> 15 -> 20 -> null

Solution

1. Step 1: Perform enqueue(5), enqueue(10)

   Queue: 5 -> 10 -> null; front=0, rear=1

2. Step 2: Perform dequeue()

   Remove 5; Queue: 10 -> null; front=1, rear=1

3. Step 3: Perform enqueue(15), enqueue(20)

   Queue: 10 -> 15 -> 20 -> null; front=1, rear=3

4. Step 4: Perform dequeue()

   Remove 10; Queue: 15 -> 20 -> null; front=2, rear=3

5. Step 5: Perform enqueue(25)

   rear=3 (max index), cannot enqueue 25; operation fails, queue unchanged

6. Step 6: Display queue

   Queue elements from front=2 to rear=3: 15 -> 20 -> null

7. Final Answer:

   15 -> 20 -> null -> Option A

8. Quick Check:

   Check enqueue failure at full rear index [OK]

Hint: No circular queue means no wrap-around; watch rear limit [OK]

Common Mistakes:

• Assuming enqueue works after rear reaches max
• Not updating front after dequeue
• Confusing queue order after operations