Implement two stacks in an array

Create a data structure twoStacks that represents two stacks. Implementation of twoStacks should use only one array, i.e., both stacks should use the same array for storing elements. Following functions must be supported by twoStacks.

push1(int x) –> pushes x to first stack
push2(int x) –> pushes x to second stack

pop1() –> pops an element from first stack and return the popped element
pop2() –> pops an element from second stack and return the popped element

Implementation of twoStack should be space efficient.

Method 1 (Divide the space in two halves)
A simple way to implement two stacks is to divide the array in two halves and assign the half half space to two stacks, i.e., use arr[0] to arr[n/2] for stack1, and arr[(n/2) + 1] to arr[n-1] for stack2 where arr[] is the array to be used to implement two stacks and size of array be n.



The problem with this method is inefficient use of array space. A stack push operation may result in stack overflow even if there is space available in arr[]. For example, say the array size is 6 and we push 3 elements to stack1 and do not push anything to second stack2. When we push 4th element to stack1, there will be overflow even if we have space for 3 more elements in array.

filter_none

edit
close

play_arrow

link
brightness_4
code

#include <iostream>
#include <stdlib.h>
  
using namespace std;
  
class twoStacks {
    int* arr;
    int size;
    int top1, top2;
  
public:
    // Constructor
    twoStacks(int n)
    {
        size = n;
        arr = new int[n];
        top1 = n / 2 + 1;
        top2 = n / 2;
    }
  
    // Method to push an element x to stack1
    void push1(int x)
    {
        // There is at least one empty
        // space for new element
        if (top1 > 0) {
            top1--;
            arr[top1] = x;
        }
        else {
            cout << "Stack Overflow"
                 << " By element :" << x << endl;
            return;
        }
    }
  
    // Method to push an element
    // x to stack2
    void push2(int x)
    {
  
        // There is at least one empty
        // space for new element
        if (top2 < size - 1) {
            top2++;
            arr[top2] = x;
        }
        else {
            cout << "Stack Overflow"
                 << " By element :" << x << endl;
            return;
        }
    }
  
    // Method to pop an element from first stack
    int pop1()
    {
        if (top1 <= size / 2) {
            int x = arr[top1];
            top1++;
            return x;
        }
        else {
            cout << "Stack UnderFlow";
            exit(1);
        }
    }
  
    // Method to pop an element
    // from second stack
    int pop2()
    {
        if (top2 >= size / 2 + 1) {
            int x = arr[top2];
            top2--;
            return x;
        }
        else {
            cout << "Stack UnderFlow";
            exit(1);
        }
    }
};
  
/* Driver program to test twStacks class */
int main()
{
    twoStacks ts(5);
    ts.push1(5);
    ts.push2(10);
    ts.push2(15);
    ts.push1(11);
    ts.push2(7);
    cout << "Popped element from stack1 is "
         << " : " << ts.pop1()
         << endl;
    ts.push2(40);
    cout << "\nPopped element from stack2 is "
         << ": " << ts.pop2()
         << endl;
    return 0;
}

chevron_right


Output:

Stack Overflow By element :7
Popped element from stack1 is  : 11
Stack Overflow By element :40
Popped element from stack2 is : 15

Complexity Analysis:

  • Time Complexity:

    • Push operation : O(1)
    • Pop operation : O(1)
  • Auxiliary Space: O(N).
    Use of array to implement stack so. It is not the space-optimised method as explained above.

Method 2 (A space efficient implementation)
This method efficiently utilizes the available space. It doesn’t cause an overflow if there is space available in arr[]. The idea is to start two stacks from two extreme corners of arr[]. stack1 starts from the leftmost element, the first element in stack1 is pushed at index 0. The stack2 starts from the rightmost corner, the first element in stack2 is pushed at index (n-1). Both stacks grow (or shrink) in opposite direction. To check for overflow, all we need to check is for space between top elements of both stacks. This check is highlighted in the below code.

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

#include <iostream>
#include <stdlib.h>
  
using namespace std;
  
class twoStacks {
    int* arr;
    int size;
    int top1, top2;
  
public:
    twoStacks(int n) // constructor
    {
        size = n;
        arr = new int[n];
        top1 = -1;
        top2 = size;
    }
  
    // Method to push an element x to stack1
    void push1(int x)
    {
        // There is at least one empty space for new element
        if (top1 < top2 - 1) {
            top1++;
            arr[top1] = x;
        }
        else {
            cout << "Stack Overflow";
            exit(1);
        }
    }
  
    // Method to push an element x to stack2
    void push2(int x)
    {
        // There is at least one empty
        // space for new element
        if (top1 < top2 - 1) {
            top2--;
            arr[top2] = x;
        }
        else {
            cout << "Stack Overflow";
            exit(1);
        }
    }
  
    // Method to pop an element from first stack
    int pop1()
    {
        if (top1 >= 0) {
            int x = arr[top1];
            top1--;
            return x;
        }
        else {
            cout << "Stack UnderFlow";
            exit(1);
        }
    }
  
    // Method to pop an element from second stack
    int pop2()
    {
        if (top2 < size) {
            int x = arr[top2];
            top2++;
            return x;
        }
        else {
            cout << "Stack UnderFlow";
            exit(1);
        }
    }
};
  
/* Driver program to test twStacks class */
int main()
{
    twoStacks ts(5);
    ts.push1(5);
    ts.push2(10);
    ts.push2(15);
    ts.push1(11);
    ts.push2(7);
    cout << "Popped element from stack1 is "
         << ts.pop1();
    ts.push2(40);
    cout << "\nPopped element from stack2 is "
         << ts.pop2();
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program to implement two stacks in a
// single array
class TwoStacks {
    int size;
    int top1, top2;
    int arr[];
  
    // Constructor
    TwoStacks(int n)
    {
        arr = new int[n];
        size = n;
        top1 = -1;
        top2 = size;
    }
  
    // Method to push an element x to stack1
    void push1(int x)
    {
        // There is at least one empty space for
        // new element
        if (top1 < top2 - 1) {
            top1++;
            arr[top1] = x;
        }
        else {
            System.out.println("Stack Overflow");
            System.exit(1);
        }
    }
  
    // Method to push an element x to stack2
    void push2(int x)
    {
        // There is at least one empty space for
        // new element
        if (top1 < top2 - 1) {
            top2--;
            arr[top2] = x;
        }
        else {
            System.out.println("Stack Overflow");
            System.exit(1);
        }
    }
  
    // Method to pop an element from first stack
    int pop1()
    {
        if (top1 >= 0) {
            int x = arr[top1];
            top1--;
            return x;
        }
        else {
            System.out.println("Stack Underflow");
            System.exit(1);
        }
        return 0;
    }
  
    // Method to pop an element from second stack
    int pop2()
    {
        if (top2 < size) {
            int x = arr[top2];
            top2++;
            return x;
        }
        else {
            System.out.println("Stack Underflow");
            System.exit(1);
        }
        return 0;
    }
  
    // Driver program to test twoStack class
    public static void main(String args[])
    {
        TwoStacks ts = new TwoStacks(5);
        ts.push1(5);
        ts.push2(10);
        ts.push2(15);
        ts.push1(11);
        ts.push2(7);
        System.out.println("Popped element from"
                           + " stack1 is " + ts.pop1());
        ts.push2(40);
        System.out.println("Popped element from"
                           + " stack2 is " + ts.pop2());
    }
}
// This code has been contributed by
// Amit Khandelwal(Amit Khandelwal 1).

chevron_right


Python

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python Script to Implement two stacks in a list
class twoStacks:
      
    def __init__(self, n):     # constructor
        self.size = n
        self.arr = [None] * n
        self.top1 = -1
        self.top2 = self.size
          
    # Method to push an element x to stack1
    def push1(self, x):
          
        # There is at least one empty space for new element
        if self.top1 < self.top2 - 1 :
            self.top1 = self.top1 + 1
            self.arr[self.top1] = x
  
        else:
            print("Stack Overflow ")
            exit(1)
  
    # Method to push an element x to stack2
    def push2(self, x):
  
        # There is at least one empty space for new element
        if self.top1 < self.top2 - 1:
            self.top2 = self.top2 - 1
            self.arr[self.top2] = x
  
        else :
           print("Stack Overflow ")
           exit(1)
  
    # Method to pop an element from first stack
    def pop1(self):
        if self.top1 >= 0:
            x = self.arr[self.top1]
            self.top1 = self.top1 -1
            return x
        else:
            print("Stack Underflow ")
            exit(1)
  
    # Method to pop an element from second stack
    def pop2(self):
        if self.top2 < self.size:
            x = self.arr[self.top2]
            self.top2 = self.top2 + 1
            return x
        else:
            print("Stack Underflow ")
            exit()
  
# Driver program to test twoStacks class
ts = twoStacks(5)
ts.push1(5)
ts.push2(10)
ts.push2(15)
ts.push1(11)
ts.push2(7)
  
print("Popped element from stack1 is " + str(ts.pop1()))
ts.push2(40)
print("Popped element from stack2 is " + str(ts.pop2()))
  
# This code is contributed by Sunny Karira

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to implement two
// stacks in a single array
using System;
  
public class TwoStacks {
    public int size;
    public int top1, top2;
    public int[] arr;
  
    // Constructor
    public TwoStacks(int n)
    {
        arr = new int[n];
        size = n;
        top1 = -1;
        top2 = size;
    }
  
    // Method to push an element x to stack1
    public virtual void push1(int x)
    {
        // There is at least one empty
        // space for new element
        if (top1 < top2 - 1) {
            top1++;
            arr[top1] = x;
        }
        else {
            Console.WriteLine("Stack Overflow");
            Environment.Exit(1);
        }
    }
  
    // Method to push an element x to stack2
    public virtual void push2(int x)
    {
        // There is at least one empty
        // space for new element
        if (top1 < top2 - 1) {
            top2--;
            arr[top2] = x;
        }
        else {
            Console.WriteLine("Stack Overflow");
            Environment.Exit(1);
        }
    }
  
    // Method to pop an element
    // from first stack
    public virtual int pop1()
    {
        if (top1 >= 0) {
            int x = arr[top1];
            top1--;
            return x;
        }
        else {
            Console.WriteLine("Stack Underflow");
            Environment.Exit(1);
        }
        return 0;
    }
  
    // Method to pop an element
    // from second stack
    public virtual int pop2()
    {
        if (top2 < size) {
            int x = arr[top2];
            top2++;
            return x;
        }
        else {
            Console.WriteLine("Stack Underflow");
            Environment.Exit(1);
        }
        return 0;
    }
  
    // Driver Code
    public static void Main(string[] args)
    {
        TwoStacks ts = new TwoStacks(5);
        ts.push1(5);
        ts.push2(10);
        ts.push2(15);
        ts.push1(11);
        ts.push2(7);
        Console.WriteLine("Popped element from"
                          + " stack1 is " + ts.pop1());
        ts.push2(40);
        Console.WriteLine("Popped element from"
                          + " stack2 is " + ts.pop2());
    }
}
  
// This code is contributed by Shrikant13

chevron_right


PHP

filter_none

edit
close

play_arrow

link
brightness_4
code

<?php
// PHP program to implement two 
// stacks in a single array     
class twoStacks 
    private $arr
    private $size
    private $top1;
    private $top2
    function __construct($n)
    {
        $this->size = $n
        $this->arr = array(); 
        $this->top1 = -1; 
        $this->top2 = $this->size; 
    }
  
// Method to push an element x to stack1 
function push1($x
    // There is at least one empty 
    // space for new element 
    if ($this->top1 < $this->top2 - 1) 
    
        $this->top1++; 
        $this->arr[$this->top1] = $x
    
    else
    
        echo "Stack Overflow"
        exit(); 
    
  
// Method to push an element x to stack2 
function push2($x
    // There is at least one empty space
    // for new element 
    if ($this->top1 < $this->top2 - 1) 
    
        $this->top2--; 
        $this->arr[$this->top2] = $x
    
    else
    
        echo "Stack Overflow"
        exit(); 
    
  
// Method to pop an element 
// from first stack 
function pop1() 
    if ($this->top1 >= 0 ) 
    
        $x = $this->arr[$this->top1]; 
        $this->top1--; 
        return $x
    
    else
    
        echo "Stack UnderFlow"
        exit(); 
    
  
// Method to pop an element from 
// second stack 
function pop2() 
    if ($this->top2 < $this->size) 
    
        $x = $this->arr[$this->top2]; 
        $this->top2++; 
        return $x
    
    else
    
        echo "Stack UnderFlow"
        exit(); 
    
}; 
  
  
// Driver Code
$ts = new twoStacks(5); 
$ts->push1(5); 
$ts->push2(10); 
$ts->push2(15); 
$ts->push1(11); 
$ts->push2(7); 
echo "Popped element from stack1 is "
                           $ts->pop1(); 
$ts->push2(40); 
echo "\nPopped element from stack2 is "
                             $ts->pop2(); 
  
// This code is contributed by
// rathbhupendra
?>

chevron_right


Output:

Popped element from stack1 is 11
Popped element from stack2 is 40

Complexity Analysis:

  • Time Complexity:

    • Push operation : O(1)
    • Pop operation : O(1)
  • Auxiliary Space :O(N).
    Use of array to implement stack so it is a space-optimised method.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.




My Personal Notes arrow_drop_up