Implement two Stacks in an Array
Last Updated :
13 Jul, 2023
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.
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:
twoStacks(int n)
{
size = n;
arr = new int[n];
top1 = n / 2 + 1;
top2 = n / 2;
}
void push1(int x)
{
if (top1 > 0) {
top1--;
arr[top1] = x;
}
else {
cout << "Stack Overflow"
<< " By element : " << x << endl;
return;
}
}
void push2(int x)
{
if (top2 < size - 1) {
top2++;
arr[top2] = x;
}
else {
cout << "Stack Overflow"
<< " By element : " << x << endl;
return;
}
}
int pop1()
{
if (top1 <= size / 2) {
int x = arr[top1];
top1++;
return x;
}
else {
cout << "Stack UnderFlow";
exit(1);
}
}
int pop2()
{
if (top2 >= size / 2 + 1) {
int x = arr[top2];
top2--;
return x;
}
else {
cout << "Stack UnderFlow" << endl;
exit(1);
}
}
};
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;
twoStacks(int n)
{
size = n;
arr = new int[n];
top1 = n / 2 + 1;
top2 = n / 2;
}
void push1(int x)
{
if (top1 > 0) {
top1--;
arr[top1] = x;
}
else {
System.out.println("Stack Overflow"
+ " By element : " + x);
return;
}
}
void push2(int x)
{
if (top2 < size - 1) {
top2++;
arr[top2] = x;
}
else {
System.out.println("Stack Overflow"
+ " By element : " + x);
return;
}
}
int pop1()
{
if (top1 <= size / 2) {
int x = arr[top1];
top1++;
return x;
}
else {
System.out.print("Stack UnderFlow");
System.exit(1);
}
return 0;
}
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 {
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());
}
}
|
Python3
import math
class twoStacks:
def __init__(self, n):
self.size = n
self.arr = [None] * n
self.top1 = math.floor(n/2) + 1
self.top2 = math.floor(n/2)
def push1(self, x):
if self.top1 > 0:
self.top1 = self.top1 - 1
self.arr[self.top1] = x
else:
print("Stack Overflow by element : ", x)
def push2(self, x):
if self.top2 < self.size - 1:
self.top2 = self.top2 + 1
self.arr[self.top2] = x
else:
print("Stack Overflow by element : ", x)
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)
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)
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()))
|
C#
using System;
using System.Collections.Generic;
public class twoStacks {
public int[] arr;
public int size;
public int top1, top2;
public twoStacks(int n)
{
size = n;
arr = new int[n];
top1 = n / 2 + 1;
top2 = n / 2;
}
public void push1(int x)
{
if (top1 > 0) {
top1--;
arr[top1] = x;
}
else {
Console.Write("Stack Overflow"
+ " By element : " + x + "\n");
return;
}
}
public void push2(int x)
{
if (top2 < size - 1) {
top2++;
arr[top2] = x;
}
else {
Console.Write("Stack Overflow"
+ " By element : " + x + "\n");
return;
}
}
public int pop1()
{
if (top1 <= size / 2) {
int x = arr[top1];
top1++;
return x;
}
else {
Console.Write("Stack UnderFlow");
}
return 0;
}
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 {
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");
}
}
|
Javascript
<script>
class twoStacks
{
constructor(n)
{
this.arr = new Array(n);
this.size = n;
this.top1 = Math.floor(n / 2) + 1;
this.top2 = Math.floor(n / 2);
}
push1(x)
{
if (this.top1 > 0)
{
this.top1--;
this.arr[this.top1] = x;
}
else
{
document.write("Stack Overflow"
+ " By element : " + x +"<br>");
return;
}
}
push2(x)
{
if (this.top2 < this.size - 1)
{
this.top2++;
this.arr[this.top2] = x;
}
else
{
document.write("Stack Overflow"
+ " By element : " + x +"<br>");
return;
}
}
pop1()
{
if (this.top1 <= this.size / 2)
{
let x = this.arr[this.top1];
this.top1++;
return x;
}
else
{
document.write("Stack UnderFlow");
}
return 0;
}
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;
}
}
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>");
</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)
{
size = n;
arr = new int[n];
top1 = -1;
top2 = size;
}
void push1(int x)
{
if (top1 < top2 - 1) {
top1++;
arr[top1] = x;
}
else {
cout << "Stack Overflow";
exit(1);
}
}
void push2(int x)
{
if (top1 < top2 - 1) {
top2--;
arr[top2] = x;
}
else {
cout << "Stack Overflow";
exit(1);
}
}
int pop1()
{
if (top1 >= 0) {
int x = arr[top1];
top1--;
return x;
}
else {
cout << "Stack UnderFlow";
exit(1);
}
}
int pop2()
{
if (top2 < size) {
int x = arr[top2];
top2++;
return x;
}
else {
cout << "Stack UnderFlow";
exit(1);
}
}
};
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
import java.io.*;
class TwoStacks {
int size;
int top1, top2;
int arr[];
TwoStacks(int n)
{
arr = new int[n];
size = n;
top1 = -1;
top2 = size;
}
void push1(int x)
{
if (top1 < top2 - 1) {
top1++;
arr[top1] = x;
}
else {
System.out.println("Stack Overflow");
System.exit(1);
}
}
void push2(int x)
{
if (top1 < top2 - 1) {
top2--;
arr[top2] = x;
}
else {
System.out.println("Stack Overflow");
System.exit(1);
}
}
int pop1()
{
if (top1 >= 0) {
int x = arr[top1];
top1--;
return x;
}
else {
System.out.println("Stack Underflow");
System.exit(1);
}
return 0;
}
int pop2()
{
if (top2 < size) {
int x = arr[top2];
top2++;
return x;
}
else {
System.out.println("Stack Underflow");
System.exit(1);
}
return 0;
}
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());
}
}
|
Python
class twoStacks:
def __init__(self, n):
self.size = n
self.arr = [None] * n
self.top1 = -1
self.top2 = self.size
def push1(self, x):
if self.top1 < self.top2 - 1:
self.top1 = self.top1 + 1
self.arr[self.top1] = x
else:
print("Stack Overflow ")
exit(1)
def push2(self, x):
if self.top1 < self.top2 - 1:
self.top2 = self.top2 - 1
self.arr[self.top2] = x
else:
print("Stack Overflow ")
exit(1)
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)
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()
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()))
|
C#
using System;
public class TwoStacks {
public int size;
public int top1, top2;
public int[] arr;
public TwoStacks(int n)
{
arr = new int[n];
size = n;
top1 = -1;
top2 = size;
}
public virtual void push1(int x)
{
if (top1 < top2 - 1) {
top1++;
arr[top1] = x;
}
else {
Console.WriteLine("Stack Overflow");
Environment.Exit(1);
}
}
public virtual void push2(int x)
{
if (top1 < top2 - 1) {
top2--;
arr[top2] = x;
}
else {
Console.WriteLine("Stack Overflow");
Environment.Exit(1);
}
}
public virtual int pop1()
{
if (top1 >= 0) {
int x = arr[top1];
top1--;
return x;
}
else {
Console.WriteLine("Stack Underflow");
Environment.Exit(1);
}
return 0;
}
public virtual int pop2()
{
if (top2 < size) {
int x = arr[top2];
top2++;
return x;
}
else {
Console.WriteLine("Stack Underflow");
Environment.Exit(1);
}
return 0;
}
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());
}
}
|
PHP
<?php
class twoStacks
{
private $arr;
private $size;
private $top1;
private $top2;
function __construct($n)
{
$this->size = $n;
$this->arr = array();
$this->top1 = -1;
$this->top2 = $this->size;
}
function push1($x)
{
if ($this->top1 < $this->top2 - 1)
{
$this->top1++;
$this->arr[$this->top1] = $x;
}
else
{
echo "Stack Overflow";
exit();
}
}
function push2($x)
{
if ($this->top1 < $this->top2 - 1)
{
$this->top2--;
$this->arr[$this->top2] = $x;
}
else
{
echo "Stack Overflow";
exit();
}
}
function pop1()
{
if ($this->top1 >= 0 )
{
$x = $this->arr[$this->top1];
$this->top1--;
return $x;
}
else
{
echo "Stack UnderFlow";
exit();
}
}
function pop2()
{
if ($this->top2 < $this->size)
{
$x = $this->arr[$this->top2];
$this->top2++;
return $x;
}
else
{
echo "Stack UnderFlow";
exit();
}
}
};
$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();
?>
|
Javascript
<script>
class TwoStacks {
constructor(n) {
this.arr = Array(n).fill(0);
this.size = n;
this.top1 = -1;
this.top2 = this.size;
}
push1(x) {
if (this.top1 < this.top2 - 1) {
this.top1++;
this.arr[this.top1] = x;
} else {
document.write("Stack Overflow");
System.exit(1);
}
}
push2(x) {
if (this.top1 < this.top2 - 1) {
this.top2--;
this.arr[this.top2] = x;
} else {
document.write("Stack Overflow");
System.exit(1);
}
}
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;
}
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;
}
}
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());
</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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