Implement two Stacks in an Array
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
- First, check whether the top1 is greater than 0
- 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
- First, check whether top2 is less than n – 1
- 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
- First, check whether the top1 is less than or equal to n / 2
- 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
- First, check whether the top2 is greater than or equal to (n + 1) / 2
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> |
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> |
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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