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Implement two Stacks in an Array

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  • Difficulty Level : Easy
  • Last Updated : 18 Nov, 2022
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Create a data structure twoStacks that represent 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.

Complete Interview Preparation - GFG

Implement two stacks in an array by Dividing the space into two halves:

The idea to implement two stacks is to divide the array into two halves and assign two halves 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. 

Follow the steps below to solve the problem:

  • To implement push1():
    • First, check whether the top1 is greater than 0 
      • If it is then add an element at the top1 index and decrement top1 by 1
      • Else return Stack Overflow
  • To implement push2():
    • First, check whether top2 is less than n – 1
      • If it is then add an element at the top2 index and increment the top2 by 1
      • Else return Stack Overflow
  • To implement pop1():
    • First, check whether the top1 is less than or equal to n / 2
      • If it is then increment the top1 by 1 and return that element.
      • Else return Stack Underflow
  • To implement pop2():
    • First, check whether the top2 is greater than or equal to (n + 1) / 2
      • If it is then decrement the top2 by 1 and return that element.
      • Else return Stack Underflow

Below is the implementation of the above approach.

C++




#include <bits/stdc++.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" << endl;
            exit(1);
        }
    }
};
 
/* Driver program to test twoStacks 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 << "Popped element from stack2 is "
         << ": " << ts.pop2() << endl;
    return 0;
}


Java




import java.util.*;
 
class twoStacks {
    int[] arr;
    int size;
    int top1, top2;
 
    // 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 {
            System.out.println("Stack Overflow"
                             + " By element : " + x);
            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 {
            System.out.println("Stack Overflow"
                             + " By element : " + x);
            return;
        }
    }
 
    // Method to pop an element from first stack
    int pop1()
    {
        if (top1 <= size / 2) {
            int x = arr[top1];
            top1++;
            return x;
        }
        else {
            System.out.print("Stack UnderFlow");
            System.exit(1);
        }
        return 0;
    }
 
    // Method to pop an element
    // from second stack
    int pop2()
    {
        if (top2 >= size / 2 + 1) {
            int x = arr[top2];
            top2--;
            return x;
        }
        else {
            System.out.print("Stack UnderFlow");
            System.exit(1);
        }
        return 1;
    }
};
class GFG {
 
    /* Driver program to test twoStacks 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 is contributed by aashish1995


Python3




# Python Script to Implement two stacks in a list
import math
 
 
class twoStacks:
 
    def __init__(self, n):     # constructor
        self.size = n
        self.arr = [None] * n
        self.top1 = math.floor(n/2) + 1
        self.top2 = math.floor(n/2)
 
    # 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 > 0:
            self.top1 = self.top1 - 1
            self.arr[self.top1] = x
        else:
            print("Stack Overflow by element : ", x)
 
    # Method to push an element x to stack2
 
    def push2(self, x):
 
        # There is at least one empty space for new element
        if self.top2 < self.size - 1:
            self.top2 = self.top2 + 1
            self.arr[self.top2] = x
        else:
            print("Stack Overflow by element : ", x)
 
    # Method to pop an element from first stack
 
    def pop1(self):
        if self.top1 <= self.size/2:
            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 >= math.floor(self.size/2) + 1:
            x = self.arr[self.top2]
            self.top2 = self.top2 - 1
            return x
        else:
            print("Stack Underflow")
            exit(1)
 
 
# Driver program to test twoStacks class
if __name__ == '__main__':
    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 Gautam goel


C#




using System;
using System.Collections.Generic;
 
public class twoStacks {
    public int[] arr;
    public int size;
    public int top1, top2;
 
    // Constructor
    public twoStacks(int n)
    {
        size = n;
        arr = new int[n];
        top1 = n / 2 + 1;
        top2 = n / 2;
    }
 
    // Method to push an element x to stack1
    public void push1(int x)
    {
 
        // There is at least one empty
        // space for new element
        if (top1 > 0) {
            top1--;
            arr[top1] = x;
        }
        else {
            Console.Write("Stack Overflow"
                          + " By element : " + x + "\n");
            return;
        }
    }
 
    // Method to push an element
    // x to stack2
    public void push2(int x)
    {
 
        // There is at least one empty
        // space for new element
        if (top2 < size - 1) {
            top2++;
            arr[top2] = x;
        }
        else {
            Console.Write("Stack Overflow"
                          + " By element : " + x + "\n");
            return;
        }
    }
 
    // Method to pop an element from first stack
    public int pop1()
    {
        if (top1 <= size / 2) {
            int x = arr[top1];
            top1++;
            return x;
        }
        else {
            Console.Write("Stack UnderFlow");
        }
        return 0;
    }
 
    // Method to pop an element
    // from second stack
    public int pop2()
    {
        if (top2 >= size / 2 + 1) {
            int x = arr[top2];
            top2--;
            return x;
        }
        else {
            Console.Write("Stack UnderFlow");
        }
        return 1;
    }
};
 
public class GFG {
 
    /* Driver program to test twoStacks 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);
        Console.Write("Popped element from stack1 is "
                      + ": " + ts.pop1() + "\n");
        ts.push2(40);
        Console.Write("Popped element from stack2 is "
                      + ": " + ts.pop2() + "\n");
    }
}
 
// This code is contributed by umadevi9616


Javascript




<script>
 
class twoStacks
{
    // Constructor
    constructor(n)
    {
        this.arr = new Array(n);
        this.size = n;
        this.top1 = Math.floor(n / 2) + 1;
        this.top2 = Math.floor(n / 2);       
    }
 
// Method to push an element x to stack1
push1(x)
{
    // There is at least one empty
    // space for new element
    if (this.top1 > 0)
    {
      this.top1--;
      this.arr[this.top1] = x;
    }
    else
    {
      document.write("Stack Overflow"
                       + " By element : " +  x +"<br>");
      return;
    }
}
 
// Method to push an element
  // x to stack2
push2(x)
{
    // There is at least one empty
    // space for new element
    if (this.top2 < this.size - 1)
    {
      this.top2++;
      this.arr[this.top2] = x;
    }
    else
    {
      document.write("Stack Overflow"
                       + " By element : " +  x +"<br>");
      return;
    }
}
 
// Method to pop an element from first stack
pop1()
{
    if (this.top1 <= this.size / 2)
    {
      let x = this.arr[this.top1];
      this.top1++;
      return x;
    }
    else
    {
      document.write("Stack UnderFlow");
       
    }
    return 0;
}
 
// Method to pop an element
  // from second stack
pop2()
{
    if (this.top2 >= Math.floor(this.size / 2) + 1)
    {
      let x = this.arr[this.top2];
      this.top2--;
      return x;
    }
    else
    {
      document.write("Stack UnderFlow");
       
    }
    return 1;
  }
 
}
 
/* Driver program to test twoStacks class */
let ts = new twoStacks(5);
ts.push1(5);
ts.push2(10);
ts.push2(15);
ts.push1(11);
ts.push2(7);
document.write("Popped element from stack1 is "
                 + " : " +  ts.pop1() +"<br>");
ts.push2(40);
document.write("Popped element from stack2 is "
                 + ": " +  ts.pop2()
                 +"<br>");
 
// This code is contributed by avanitrachhadiya2155
</script>


Output

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

Time Complexity: 

  • Both Push operation: O(1)
  • Both Pop operation: O(1)

Auxiliary Space: O(N), Use of array to implement stack.

Problem in the above implementation:

The problem in the above implementation is that as we reserve half of the array for a stack and another half for the another stack. So, let if 1st half is full means first stack already have n/2 numbers of elements and 2nd half is not full means it doesn’t have n/2 numbers of elements. So, if we look into the array, there are free spaces inside array(eg. in the next half) but we cannot push elements for stack 1(because first half is reserved for stack 1 and it’s already full). It means this implementation show stack overflow although the array is not full. The solution for this answer is the below implementation.

Implement two stacks in an array by Starting from endpoints:

The idea is to start two stacks from two extreme corners of arr[]. 

Follow the steps below to solve the problem:

  • Stack1 starts from the leftmost corner of the array, the first element in stack1 is pushed at index 0 of the array. 
  • Stack2 starts from the rightmost corner of the array, the first element in stack2 is pushed at index (n-1) of the array. 
  • Both stacks grow (or shrink) in opposite directions. 
  • To check for overflow, all we need to check is for availability of space between top elements of both stacks.
  • To check for underflow, all we need to check is if the value of the top of the both stacks  is between 0 to (n-1) or not.

Below is the implementation of above approach:

C++




#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 twoStacks 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;
}


Java




// Java program to implement two stacks in a
// single array
 
import java.io.*;
 
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).


Python




# 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


C#




// 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


PHP




<?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
?>


Javascript




<script>
// javascript program to implement two stacks in a
// single array
class TwoStacks {
    // Constructor
    constructor(n) {
        this.arr = Array(n).fill(0);
        this.size = n;
        this.top1 = -1;
        this.top2 = this.size;
    }
  
 
    // Method to push an element x to stack1
    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 {
            document.write("Stack Overflow");
            System.exit(1);
        }
    }
 
    // Method to push an element x to stack2
     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 {
            document.write("Stack Overflow");
            System.exit(1);
        }
    }
 
    // Method to pop an element from first stack
     pop1() {
        if (this.top1 >= 0) {
            var x = this.arr[this.top1];
            this.top1--;
            return x;
        } else {
            document.write("Stack Underflow");
            System.exit(1);
        }
        return 0;
    }
 
    // Method to pop an element from second stack
     pop2() {
        if (this.top2 < this.size) {
            var x = this.arr[this.top2];
            this.top2++;
            return x;
        } else {
            document.write("Stack Underflow");
            System.exit(1);
        }
        return 0;
    }
 
    // Driver program to test twoStack class
    }
        var ts = new TwoStacks(5);
        ts.push1(5);
        ts.push2(10);
        ts.push2(15);
        ts.push1(11);
        ts.push2(7);
        document.write("Popped element from" + " stack1 is " + ts.pop1());
        ts.push2(40);
        document.write("<br/>Popped element from" + " stack2 is " + ts.pop2());
 
// This code contributed by Rajput-Ji
</script>


Output

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

Time Complexity: 

  • Both Push operation: O(1)
  • Both Pop operation: O(1)

Auxiliary Space: O(N), Use of the array to implement stack.


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