Queue Array Implementation

#include <bits/stdc++.h> // Includes iostream and other utilities
using namespace std;     // Uses the standard namespace

// Custom Queue implementation using a fixed-size array
class Queue {
    int *arr;    // Pointer to the dynamic array that stores queue elements
    int size;    // Maximum capacity of the queue
    int front;   // Index of the front element
    int rear;    // Index where the next element will be inserted

public:
    // Constructor: Initializes the queue
    Queue(int S) {
        size = S;          // Set the maximum size of the queue
        arr = new int[size]; // Dynamically allocate the array
        front = 0;         // Initialize front pointer to 0
        rear = 0;          // Initialize rear pointer to 0 (queue is empty when front == rear)
    }

    // Push operation: Adds an element to the rear of the queue
    void push(int val) {
        // Check for overflow: If rear has reached the end of the array
        if(rear == size) {
            cout << "Queue overflow!" << endl; // Cannot add more elements
        } else {
            arr[rear] = val; // Insert the value at the rear position
            rear++;          // Increment rear to point to the next available spot
        }
    }

    // Pop operation: Removes an element from the front of the queue
    void pop() {
        // Check for underflow: If front and rear are at the same position, queue is empty
        if(front == rear) {
            cout << "Queue underflow!" << endl; // Cannot remove from empty queue
        } else {
            front++; // Increment front to logically remove the element

            // If front catches up to rear, it means the queue has become empty
            // Reset both front and rear to 0 to reuse the array space from start
            // NOTE: This basic implementation is a linear queue and can still lead to space issues
            // once 'rear' hits 'size-1', even if 'front' has moved significantly.
            // A circular queue addresses this.
            if(front == rear) {
                front = 0;
                rear = 0;
            }
        }
    }

    // Returns the element at the front of the queue without removing it
    int frontElement() {
        // If queue is empty, return -1 (or throw an exception)
        return (front == rear) ? -1 : arr[front];
    }

    // Returns the element at the back of the queue without removing it
    int backElement() {
        // If queue is empty, return -1
        // Else, return the element just before 'rear' (as rear points to the next available slot)
        return (front == rear) ? -1 : arr[rear - 1];
    }

    // Returns the current number of elements in the queue
    int queueSize() {
        // Size is the difference between rear and front pointers
        return (rear - front);
    }

    // Checks if the queue is empty
    bool empty() {
        // Queue is empty if front and rear pointers are at the same position
        return (front == rear) ? true : false;
    }

    // Destructor to free dynamically allocated memory
    ~Queue() {
        delete[] arr;
    }
};

int main() {
    Queue q(5); // Create a queue with a maximum size of 5

    q.push(11); // Add elements
    cout << "Front element of q : " << q.frontElement() << endl; // 11
    cout << "Back element of q : " << q.backElement() << endl;   // 11

    q.push(15);
    cout << "Front element of q : " << q.frontElement() << endl; // 11
    cout << "Back element of q : " << q.backElement() << endl;   // 15

    q.push(23);
    q.push(30);
    q.push(40); // Queue is now [11, 15, 23, 30, 40], front=0, rear=5

    cout << "Size of queue : " << q.queueSize() << endl; // Size: 5

    q.push(50); // This will cause overflow, as rear == size (5 == 5)

    cout << endl << "Front before pop : " << q.frontElement() << endl; // 11
    cout << "Back before pop : " << q.backElement() << endl;   // 40

    q.pop(); // Remove 11. Queue: [_, 15, 23, 30, 40], front=1, rear=5
    cout << "Front after pop : " << q.frontElement() << endl; // 15
    cout << "Back after pop : " << q.backElement() << endl << endl; // 40

    q.pop(); // Remove 15. Queue: [_, _, 23, 30, 40], front=2, rear=5
    q.pop(); // Remove 23. Queue: [_, _, _, 30, 40], front=3, rear=5

    cout << "Size of queue : " << q.queueSize() << endl; // Size: 2 (30, 40)

    q.pop(); // Remove 30. Queue: [_,_,_,_,40], front=4, rear=5
    q.pop(); // Remove 40. Queue: [_,_,_,_,_], front=5, rear=5. Then resets to front=0, rear=0

    cout << "Size of queue : " << q.queueSize() << endl; // Size: 0 (after reset)

    // Check if empty
    if(q.empty()) {
        cout << "Queue is empty!" << endl;
    } else {
        cout << "Queue is not empty!" << endl;
    }

    q.pop(); // Try to pop from empty queue (underflow)

    return 0;
}

Concept

• Queue: A First-In, First-Out (FIFO) data structure.
• Elements are added to the rear and removed from the front.
• This is a basic array implementation, which can suffer from space wastage (fixed size) and linear time complexity for some operations if not handled carefully (e.g., if you were to shift elements on pop).
• This specific implementation has a limitation: It’s a linear queue. Once rear reaches size-1, even if elements have been popped from the front, new elements cannot be pushed. This leads to inefficient space utilization. A circular queue solves this.

Key Data Members

• int *arr: The dynamic array to store queue elements.
• int size: The maximum capacity of the queue.
• int front: Index of the element at the front of the queue.
• int rear: Index where the next element will be inserted (one position past the last element).

Operations and Logic

1. Queue(int S) (Constructor):

   • Initializes size to S.
   • Allocates memory for arr of size S.
   • Sets front = 0 and rear = 0. Initially, front == rear signifies an empty queue.

2. push(int val):

   • Overflow Check: If rear == size, the array is full. Print “Queue overflow!”.
   • Otherwise, arr[rear] stores val, then rear is incremented (rear++).

3. pop():

   • Underflow Check: If front == rear, the queue is empty. Print “Queue underflow!”.
   • Otherwise, increment front (front++). This logically removes the element from the front.
   • Reset Condition: If front == rear after incrementing front, it means the queue became empty after the pop. In this case, reset both front and rear back to 0 to reuse the array from the beginning. This is crucial for avoiding front always moving forward and hitting size-1 prematurely, though it doesn’t solve the linear queue issue of rear hitting size-1.

4. frontElement():

   • Returns arr[front] if the queue is not empty (front != rear).
   • Returns -1 (or throws an error) if the queue is empty.

5. backElement():

   • Returns arr[rear-1] if the queue is not empty (front != rear).
   • Returns -1 (or throws an error) if the queue is empty. (Note: rear-1 is used because rear points to the next available slot).

6. queueSize():

   • Returns rear - front. If front == rear, size is 0.

7. empty():

   • Returns true if front == rear, false otherwise.

Limitation of this Linear Array Implementation

• Space Wastage: Even if elements are popped from the front, rear keeps moving forward. Once rear reaches size-1, push will report “overflow” even if there’s free space at the beginning of the array. This is solved by using a Circular Queue.

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