Implement dynamic deque using templates class and a circular array

The task is to implement a dynamic Deque using templates class and a circular array, having the following functionalities:  

• front(): Get the front item from the deque.
• back(): Get the last item from the deque.
• push_back(X): Push X at the end of the deque.
• push_front(X): Push X at the start of the deque.
• pop_front(): Delete an element from the start of the deque.
• pop_back(): Delete an element from the end of the deque
• empty(): Checks whether deque is empty or not
• capacity(): Current maximum number of elements deque can store
• size(): Number of elements in the deque

Below is the step by step illustration:

• Initially, the deque is empty

• Insert 1 to the back of deque

• Insert elements 2, 3 to the back of deque

• Insert 4 to the front of deque

• Insert 5 to the back of deque

• Pop 2 elements from front and 2 elements from the back of deque

• Pop 1 element from the front of deque

Approach: The idea is to double the size of the array used every time the capacity of the array gets full and copy the elements of the previous array into the new array. Follow the steps below to solve the problem:

• Initialize 4 variables say frontIndex, backIndex, sizeVar, and capacityVar, and an array say arr[] to implement the deque.
• Define a function say capacity() to find the size of the current array used and return the value of the variable, capacityVar.
• Define a function say size() to find the count of elements in the deque and return the value of the variable, sizeVar.
• Define a function say full() to find if the deque is full or not and return true if sizeVar is equal to capacityVar. Otherwise, return false.
• Define a function say empty() to find if the deque is empty or not and return true if frontIndex and backIndex are equal to -1. Otherwise, return false.
• Define a function say Front() to print the front element of the deque. If deque is not empty(), print the element of arr[frontIndex].
• Define a function say Back() to print the last element of the deque. If deque is not empty(), print the element of arr[BackIndex].
• Define a function say push_back(X) to insert an element at the end of the deque:
  • If the deque is full, then double the size of the current array and copy the elements of the previous array into the new array.
  • If deque is empty(), then assign frontIndex = backIndex = 0 and then assign X to both arr[frontIndex] and arr[backIndex] and then increment sizeVar by one.
  • Else, update backIndex as backIndex = (backIndex+1) %capacityVar and then assign X to arr[backIndex] and increment sizeVar by one.
• Define a function say push_front(X) to insert an element at the start of the deque:
  • If the deque is full, then double the size of the current array and copy the elements of the previous array into the new array.
  • If deque is empty(), then assign frontIndex = backIndex = 0 and then assign X to both arr[frontIndex] and arr[backIndex] and then increment sizeVar by one.
  • Else, update frontIndex as frontIndex = (frontIndex-1 + capacityVar)%capacityVar and then assign X to arr[frontIndex] and increment sizeVar by one.
• Define a function say pop_front() to delete an element at the front of the deque:
  • If the deque is empty, print “Underflow”.
  • Else if sizeVar is equal to 1 then assign -1 to frontIndex and backIndex both and then decrement sizeVar by one.
  • Else, Update frontIndex as frontIndex = (frontIndex+1)%capacityVar and decrement sizeVar by one.
• Define a function say pop_back() to delete an element at the front of the deque:
  • If the deque is empty, print “Underflow”.
  • Else if sizeVar is equal to 1 then assign -1 to frontIndex and backIndex both and then decrement sizeVar by one.
  • Else, Update backIndex as backIndex = (backndex-1 + capacityVar) %capacityVar and decrement sizeVar by one.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Class definition of the deque
template <class X>
class Deque {

private:
    // Stores the frontIndex
    int frontIndex;

    // Stores the backIndex
    int backIndex;

    // Stores the array
    X* arr;

    // Stores the size of deque
    int sizeVar;

    // Stores the size of array
    int capacityVar = 4;

public:
    // Deque class constructor
    Deque()
    {
        arr = new X[capacityVar];
        frontIndex = backIndex = -1;
        sizeVar = 0;
    }

    // Function methods
    bool empty();
    bool full();
    void push_back(X x);
    void push_front(X x);
    void pop_front();
    void pop_back();
    X front();
    X back();
    int capacity();
    int size();
};

// Function to find the capacity of the deque
template <class X>
int Deque<X>::capacity()
{
    return capacityVar;
}

// Function to find the number of elements
// present in deque
template <class X>
int Deque<X>::size() { return sizeVar; }

// Function to check if deque is empty or not
template <class X>
bool Deque<X>::empty()
{
    if (frontIndex == -1 && backIndex == -1)
        return true;
    else
        return false;
}

// Function to check if deque is full or not
template <class X>
bool Deque<X>::full()
{
    if (sizeVar == capacityVar)
        return true;
    else
        return false;
}

// Function to find the front element of the deque
template <class X>
X Deque<X>::front()
{
    // If deque is empty
    if (empty()) {
        cout << "Deque underflow" << endl;
        abort();
    }
    return arr[frontIndex];
}

// Function to find the last element of the deque
template <class X>
X Deque<X>::back()
{
    // If deque is empty
    if (empty()) {
        cout << "Deque underflow" << endl;
        abort();
    }
    return arr[backIndex];
}

// Function to insert the element
// to the back of the deque
template <class X>
void Deque<X>::push_back(X x)
{
    if (full()) {

        // If the deque is full, then
        // double the capacity
        capacityVar = capacityVar * 2;

        // Initialize new array of
        // double size
        X* temp = new X[capacityVar];

        // Copy the elements of the
        // previous array
        int i = frontIndex;
        int j = 0;
        while (i != backIndex) {
            temp[j] = arr[i];
            i = (i + 1) % sizeVar;
            j++;
        }
        temp[j] = arr[i];

        frontIndex = 0;
        backIndex = sizeVar - 1;

        // Deallocate the memory
        // of previous array
        delete[] arr;
        arr = temp;
    }

    // If size is zero
    if (empty()) {
        frontIndex = backIndex = 0;
        arr[backIndex] = x;
        sizeVar++;
        return;
    }

    // Increment back index cyclically
    backIndex = (backIndex + 1) % capacityVar;
    arr[backIndex] = x;
    sizeVar++;
    return;
}

// Function to insert the element
// to the front of the deque
template <class X>
void Deque<X>::push_front(X x)
{
    if (full()) {

        // If the deque is full, then
        // double the capacity
        capacityVar = capacityVar * 2;

        // Initialize new array of
        // double size
        X* temp = new X[capacityVar];

        // Copy the elements of the
        // previous array
        int i = frontIndex;
        int j = 0;
        while (i != backIndex) {
            temp[j] = arr[i];
            i = (i + 1) % sizeVar;
            j++;
        }
        temp[j] = arr[i];

        frontIndex = 0;
        backIndex = sizeVar - 1;

        // Deallocate the memory
        // of previous array
        delete[] arr;
        arr = temp;
    }

    // If size is zero
    if (empty()) {
        frontIndex = backIndex = 0;
        arr[backIndex] = x;
        sizeVar++;
        return;
    }

    // Decrement front index cyclically
    frontIndex
        = (frontIndex - 1 + capacityVar) % capacityVar;
    arr[frontIndex] = x;
    sizeVar++;
    return;
}

// Function to delete the element
// from the front of the deque
template <class X>
void Deque<X>::pop_front()
{
    // If deque is empty
    if (empty()) {
        cout << "Deque underflow" << endl;
        abort();
    }

    // If there is only one character
    if (frontIndex == backIndex) {

        // Mark deque as empty
        // and decrement sizeVar
        frontIndex = backIndex = -1;
        sizeVar--;
        return;
    }

    // Increment frontIndex cyclically
    frontIndex = (frontIndex + 1) % capacityVar;
    sizeVar--;
    return;
}

// Function to delete the element
// from the back of the deque
template <class X>
void Deque<X>::pop_back()
{
    // If deque is empty
    if (empty()) {
        cout << "Deque underflow" << endl;
        abort();
    }

    // If there is only one character
    if (frontIndex == backIndex) {

        // Mark deque as empty
        // and decrement sizeVar
        frontIndex = backIndex = -1;
        sizeVar--;
        return;
    }

    // Decrement backIndex cyclically
    backIndex = (backIndex - 1 + capacityVar) % capacityVar;
    sizeVar--;
    return;
}

// Driver Code
int main()
{
    // Deque initialization
    Deque<int> q;

    // Iterate range [1, 100],
    // push even numbers at the back
    // and push odd numbers at the front
    for (int i = 1; i < 10; i++)
        if (i % 2 == 0)
            q.push_back(i);
        else
            q.push_front(i);

    // Print the current capacity
    cout << "Current capacity " << q.capacity() << endl;

    // Print the current size
    cout << "Current size " << q.size() << endl;

    // Print front elements of deque
    cout << "Front element " << q.front() << endl;

    // Print last element of the deque
    cout << "Rear element " << q.back() << endl;

    cout << endl;

    cout << "Pop an element from front" << endl;

    // Pop an element from the front of deque
    q.pop_front();

    cout << "Pop an element from back" << endl;

    // Pop an element from the back of deque
    q.pop_back();

    cout << endl;

    // Print the current capacity
    cout << "Current capacity " << q.capacity() << endl;

    // Print current size
    cout << "Current size " << q.size() << endl;

    // Print front elements of deque
    cout << "Front element " << q.front() << endl;

    // Print last element of the deque
    cout << "Rear element " << q.back() << endl;

    return 0;
}

Output

Current capacity 16
Current size 9
Front element 9
Rear element 8

Pop an element from front
Pop an element from back

Current capacity 16
Current size 7
Front element 7
Rear element 6

Time Complexity: O(N)
Auxiliary Space: O(N)