Given a stack, the task is to sort it using recursion.
Example:
Input: elements present in stack from top to bottom -3 14 18 -5 30
Output: 30 18 14 -3 -5
Explanation: The given stack is sorted know 30 > 18 > 14 > -3 > -5Input: elements present in stack from top to bottom 1 2 3
Output: 3 2 1
Explanation: The given stack is sorted know 3 > 2 > 1
How to Sort a Stack Using Stack
The idea of the solution is to hold all values in Function Call Stack until the stack becomes empty. When the stack becomes empty, insert all held items one by one in sorted order. and then print the stack
Illustration:
Below is the illustration of above approach
- Let given stack be
-3
14 18 -5 30
- Let us illustrate sorting of stack using the above example:
First pop all the elements from the stack and store popped element in the variable ‘temp’. After popping all the elements function’s stack frame will look like this:
-3 stack frame 1 14 stack frame 2 18 stack frame 3 -5 stack frame 4 30 stack frame 5
- Now stack is empty so function insert in sorted order is called and it inserts 30 (from stack frame 5) at the bottom of the stack. Now stack looks like the below:
30
- Now next element -5 (from stack frame 4) is picked. Since -5 < 30, -5 is inserted at the bottom of the stack. Now stack becomes:
30 -5
- Next 18 (from stack frame 3) is picked. Since 18 < 30, 18 is inserted below 30. Now stack becomes:
30 18 -5
- Next 14 (from stack frame 2) is picked. Since 14 < 30 and 14 < 18, it is inserted below 18. Now stack becomes:
30 18 14 -5
- Now -3 (from stack frame 1) is picked, as -3 < 30 and -3 < 18 and -3 < 14, it is inserted below 14. Now stack becomes:
30 18 14 -3 -5
Follow the steps mentioned below to implement the idea:
- Create a stack and push all the elements in it.
- Call sortStack(), which will pop an element from the stack and pass the popped element to function sortInserted(), then it will keep calling itself until the stack is empty.
- Whenever sortInserted() is called it will insert the passed element in stack in sorted order.
- Print the stack
Below is the implementation of the above approach:
// C++ program to sort a stack using recursion #include <iostream> using namespace std;
// Stack is represented using linked list struct stack {
int data;
struct stack* next;
}; // Utility function to initialize stack void initStack( struct stack** s) { *s = NULL; }
// Utility function to check if stack is empty int isEmpty( struct stack* s)
{ if (s == NULL)
return 1;
return 0;
} // Utility function to push an item to stack void push( struct stack** s, int x)
{ struct stack* p = ( struct stack*) malloc ( sizeof (*p));
if (p == NULL) {
fprintf (stderr, "Memory allocation failed.\n" );
return ;
}
p->data = x;
p->next = *s;
*s = p;
} // Utility function to remove an item from stack int pop( struct stack** s)
{ int x;
struct stack* temp;
x = (*s)->data;
temp = *s;
(*s) = (*s)->next;
free (temp);
return x;
} // Function to find top item int top( struct stack* s) { return (s->data); }
// Recursive function to insert an item x in sorted way void sortedInsert( struct stack** s, int x)
{ // Base case: Either stack is empty or newly inserted
// item is greater than top (more than all existing)
if (isEmpty(*s) or x > top(*s)) {
push(s, x);
return ;
}
// If top is greater, remove the top item and recur
int temp = pop(s);
sortedInsert(s, x);
// Put back the top item removed earlier
push(s, temp);
} // Function to sort stack void sortStack( struct stack** s)
{ // If stack is not empty
if (!isEmpty(*s)) {
// Remove the top item
int x = pop(s);
// Sort remaining stack
sortStack(s);
// Push the top item back in sorted stack
sortedInsert(s, x);
}
} // Utility function to print contents of stack void printStack( struct stack* s)
{ while (s) {
cout << s->data << " " ;
s = s->next;
}
cout << "\n" ;
} // Driver code int main( void )
{ struct stack* top;
initStack(&top);
push(&top, 30);
push(&top, -5);
push(&top, 18);
push(&top, 14);
push(&top, -3);
cout << "Stack elements before sorting:\n" ;
printStack(top);
sortStack(&top);
cout << "\n" ;
cout << "Stack elements after sorting:\n" ;
printStack(top);
return 0;
} // This code is contributed by SHUBHAMSINGH10 |
// C program to sort a stack using recursion #include <stdio.h> #include <stdlib.h> // Stack is represented using linked list struct stack {
int data;
struct stack* next;
}; // Utility function to initialize stack void initStack( struct stack** s) { *s = NULL; }
// Utility function to check if stack is empty int isEmpty( struct stack* s)
{ if (s == NULL)
return 1;
return 0;
} // Utility function to push an item to stack void push( struct stack** s, int x)
{ struct stack* p = ( struct stack*) malloc ( sizeof (*p));
if (p == NULL) {
fprintf (stderr, "Memory allocation failed.\n" );
return ;
}
p->data = x;
p->next = *s;
*s = p;
} // Utility function to remove an item from stack int pop( struct stack** s)
{ int x;
struct stack* temp;
x = (*s)->data;
temp = *s;
(*s) = (*s)->next;
free (temp);
return x;
} // Function to find top item int top( struct stack* s) { return (s->data); }
// Recursive function to insert an item x in sorted way void sortedInsert( struct stack** s, int x)
{ // Base case: Either stack is empty or newly inserted
// item is greater than top (more than all existing)
if (isEmpty(*s) || x > top(*s)) {
push(s, x);
return ;
}
// If top is greater, remove the top item and recur
int temp = pop(s);
sortedInsert(s, x);
// Put back the top item removed earlier
push(s, temp);
} // Function to sort stack void sortStack( struct stack** s)
{ // If stack is not empty
if (!isEmpty(*s)) {
// Remove the top item
int x = pop(s);
// Sort remaining stack
sortStack(s);
// Push the top item back in sorted stack
sortedInsert(s, x);
}
} // Utility function to print contents of stack void printStack( struct stack* s)
{ while (s) {
printf ( "%d " , s->data);
s = s->next;
}
printf ( "\n" );
} // Driver code int main( void )
{ struct stack* top;
initStack(&top);
push(&top, 30);
push(&top, -5);
push(&top, 18);
push(&top, 14);
push(&top, -3);
printf ( "Stack elements before sorting:\n" );
printStack(top);
sortStack(&top);
printf ( "\n\n" );
printf ( "Stack elements after sorting:\n" );
printStack(top);
return 0;
} |
// Java program to sort a Stack using recursion // Note that here predefined Stack class is used // for stack operation import java.util.ListIterator;
import java.util.Stack;
class Test {
// Recursive Method to insert an item x in sorted way
static void sortedInsert(Stack<Integer> s, int x)
{
// Base case: Either stack is empty or newly
// inserted item is greater than top (more than all
// existing)
if (s.isEmpty() || x > s.peek()) {
s.push(x);
return ;
}
// If top is greater, remove the top item and recur
int temp = s.pop();
sortedInsert(s, x);
// Put back the top item removed earlier
s.push(temp);
}
// Method to sort stack
static void sortStack(Stack<Integer> s)
{
// If stack is not empty
if (!s.isEmpty()) {
// Remove the top item
int x = s.pop();
// Sort remaining stack
sortStack(s);
// Push the top item back in sorted stack
sortedInsert(s, x);
}
}
// Utility Method to print contents of stack
static void printStack(Stack<Integer> s)
{
ListIterator<Integer> lt = s.listIterator();
// forwarding
while (lt.hasNext())
lt.next();
// printing from top to bottom
while (lt.hasPrevious())
System.out.print(lt.previous() + " " );
}
// Driver code
public static void main(String[] args)
{
Stack<Integer> s = new Stack<>();
s.push( 30 );
s.push(- 5 );
s.push( 18 );
s.push( 14 );
s.push(- 3 );
System.out.println(
"Stack elements before sorting: " );
printStack(s);
sortStack(s);
System.out.println(
" \n\nStack elements after sorting:" );
printStack(s);
}
} |
# Python program to sort a stack using recursion # Recursive method to insert element in sorted way def sortedInsert(s, element):
# Base case: Either stack is empty or newly inserted
# item is greater than top (more than all existing)
if len (s) = = 0 or element > s[ - 1 ]:
s.append(element)
return
else :
# Remove the top item and recur
temp = s.pop()
sortedInsert(s, element)
# Put back the top item removed earlier
s.append(temp)
# Method to sort stack def sortStack(s):
# If stack is not empty
if len (s) ! = 0 :
# Remove the top item
temp = s.pop()
# Sort remaining stack
sortStack(s)
# Push the top item back in sorted stack
sortedInsert(s, temp)
# Printing contents of stack def printStack(s):
for i in s[:: - 1 ]:
print (i, end = " " )
print ()
# Driver Code if __name__ = = '__main__' :
s = []
s.append( 30 )
s.append( - 5 )
s.append( 18 )
s.append( 14 )
s.append( - 3 )
print ( "Stack elements before sorting: " )
printStack(s)
sortStack(s)
print ( "\nStack elements after sorting: " )
printStack(s)
# This code is contributed by Muskan Kalra. |
// C# program to sort a Stack using recursion // Note that here predefined Stack class is used // for stack operation using System;
using System.Collections;
public class GFG {
// Recursive Method to insert an item x in sorted way
static void sortedInsert(Stack s, int x)
{
// Base case: Either stack is empty or
// newly inserted item is greater than top
// (more than all existing)
if (s.Count == 0 || x > ( int )s.Peek()) {
s.Push(x);
return ;
}
// If top is greater, remove
// the top item and recur
int temp = ( int )s.Peek();
s.Pop();
sortedInsert(s, x);
// Put back the top item removed earlier
s.Push(temp);
}
// Method to sort stack
static void sortStack(Stack s)
{
// If stack is not empty
if (s.Count > 0) {
// Remove the top item
int x = ( int )s.Peek();
s.Pop();
// Sort remaining stack
sortStack(s);
// Push the top item back in sorted stack
sortedInsert(s, x);
}
}
// Utility Method to print contents of stack
static void printStack(Stack s)
{
foreach ( int c in s) { Console.Write(c + " " ); }
}
// Driver code
public static void Main(String[] args)
{
Stack s = new Stack();
s.Push(30);
s.Push(-5);
s.Push(18);
s.Push(14);
s.Push(-3);
Console.WriteLine(
"Stack elements before sorting: " );
printStack(s);
sortStack(s);
Console.WriteLine(
" \n\nStack elements after sorting:" );
printStack(s);
}
} // This code is Contributed by Arnab Kundu |
<script> // JavaScript program to sort a Stack using recursion // Note that here predefined Stack class is used // for stack operation // Recursive Method to insert an item x in sorted way function sortedInsert(s,x)
{ // Base case: Either stack is empty or newly
// inserted item is greater than top (more than all
// existing)
if (s.length==0 || x > s[s.length-1])
{
s.push(x);
return ;
}
// If top is greater, remove the top item and recur
let temp = s.pop();
sortedInsert(s, x);
// Put back the top item removed earlier
s.push(temp);
} // Method to sort stack function sortStack(s)
{ // If stack is not empty
if (s.length!=0)
{
// Remove the top item
let x = s.pop();
// Sort remaining stack
sortStack(s);
// Push the top item back in sorted stack
sortedInsert(s, x);
}
} // Utility Method to print contents of stack function printStack(s)
{ for (let i=s.length-1;i>=0;i--)
{
document.write(s[i]+ " " );
}
document.write( "<br>" )
} // Driver code
let s=[]; s.push(30); s.push(-5); s.push(18); s.push(14); s.push(-3); document.write( "Stack elements before sorting: <br>" );
printStack(s); sortStack(s); document.write( " <br><br>Stack elements after sorting:<br>" );
printStack(s); // This code is contributed by avanitrachhadiya2155 </script> |
Time Complexity: O(N2).
Auxiliary Space: O(N) use of Stack
Another Method Using STL stack, collection in Java
#include <stack> #include <iostream> using namespace std;
// Function to sort a stack using recursion void sortStack(stack< int > &s) {
// If the stack is empty, return
if (s.empty())
return ;
// Remove the top element of the stack
int x = s.top();
s.pop();
// Sort the remaining elements in the stack using recursion
sortStack(s);
// Create two auxiliary stacks
stack< int > tempStack;
// Move all elements that are greater than x from the main stack to the tempStack
while (!s.empty() && s.top() > x) {
tempStack.push(s.top());
s.pop();
}
// Push x back into the main stack
s.push(x);
// Move all elements from tempStack back to the main stack
while (!tempStack.empty()) {
s.push(tempStack.top());
tempStack.pop();
}
} int main() {
// Create a stack
stack< int > s;
// Push elements into the stack
s.push(34);
s.push(3);
s.push(31);
s.push(98);
s.push(92);
s.push(23);
// Sort the stack
sortStack(s);
// Print the sorted elements
cout << "Sorted numbers are: " ;
while (!s.empty()) {
cout << s.top() << " " ;
s.pop();
}
return 0;
} |
import java.util.Stack;
public class Main {
public static void sortStack(Stack<Integer> s)
{
// If the stack is empty, return
if (s.empty())
return ;
// Remove the top element of the stack
int x = s.pop();
// Sort the remaining elements in the stack using
// recursion
sortStack(s);
// Create two auxiliary stacks
Stack<Integer> tempStack = new Stack<>();
// Move all elements that are greater than x from
// the main stack to the tempStack
while (!s.empty() && s.peek() > x) {
tempStack.push(s.pop());
}
// Push x back into the main stack
s.push(x);
// Move all elements from tempStack back to the main
// stack
while (!tempStack.empty()) {
s.push(tempStack.pop());
}
}
public static void main(String[] args)
{
// Create a stack
Stack<Integer> s = new Stack<>();
// Push elements into the stack
s.push( 34 );
s.push( 3 );
s.push( 31 );
s.push( 98 );
s.push( 92 );
s.push( 23 );
// Sort the stack
sortStack(s);
// Print the sorted elements
System.out.print( "Sorted numbers are: " );
while (!s.empty()) {
System.out.print(s.pop() + " " );
}
}
} |
# Function to sort a stack using recursion def sortStack(s):
# If the stack is empty, return
if not s:
return
# Remove the top element of the stack
x = s.pop()
# Sort the remaining elements in the stack using recursion
sortStack(s)
# Create two auxiliary stacks
tempStack = []
# Move all elements that are greater than x from the main stack to the tempStack
while s and s[ - 1 ] > x:
tempStack.append(s.pop())
# Push x back into the main stack
s.append(x)
# Move all elements from tempStack back to the main stack
while tempStack:
s.append(tempStack.pop())
# Create a stack s = []
# Push elements into the stack s.append( 34 )
s.append( 3 )
s.append( 31 )
s.append( 98 )
s.append( 92 )
s.append( 23 )
# Sort the stack sortStack(s) # Print the sorted elements print ( "Sorted numbers are: " , end = "")
while s:
print (s.pop(), end = " " )
|
using System;
using System.Collections.Generic;
public class Program
{ // Function to sort a stack using recursion
public static void SortStack(Stack< int > s)
{
// If the stack is empty, return
if (s.Count == 0)
return ;
// Remove the top element of the stack
int x = s.Peek();
s.Pop();
// Sort the remaining elements in the stack using recursion
SortStack(s);
// Create two auxiliary stacks
Stack< int > tempStack = new Stack< int >();
// Move all elements that are greater than x from the main stack to the tempStack
while (s.Count > 0 && s.Peek() > x) {
tempStack.Push(s.Peek());
s.Pop();
}
// Push x back into the main stack
s.Push(x);
// Move all elements from tempStack back to the main stack
while (tempStack.Count > 0) {
s.Push(tempStack.Peek());
tempStack.Pop();
}
}
public static void Main()
{
// Create a stack
Stack< int > s = new Stack< int >();
// Push elements into the stack
s.Push(34);
s.Push(3);
s.Push(31);
s.Push(98);
s.Push(92);
s.Push(23);
// Sort the stack
SortStack(s);
// Print the sorted elements
Console.Write( "Sorted numbers are: " );
while (s.Count > 0) {
Console.Write(s.Peek() + " " );
s.Pop();
}
}
} |
function sortStack(s) {
// If the stack is empty or has only one element, return
if (s.length <= 1) {
return ;
}
// Remove the top element of the stack
let x = s.pop();
// Sort the remaining elements in the stack using recursion
sortStack(s);
// Create two auxiliary stacks
let tempStack = [];
// Move all elements that are greater than x from the main stack to the tempStack
while (s.length !== 0 && s[s.length - 1] > x) {
tempStack.push(s.pop());
}
// Push x back into the main stack
s.push(x);
// Move all elements from tempStack back to the main stack
while (tempStack.length !== 0) {
s.push(tempStack.pop());
}
} // Create a stack let s = []; // Push elements into the stack s.push(34); s.push(3); s.push(31); s.push(98); s.push(92); s.push(23); // Sort the stack sortStack(s); // Print the sorted elements let result = "Sorted numbers are: " ;
while (s.length !== 0) {
result += s.pop() + " " ;
} console.log(result.trim()); // This code is contributed by divyansh2212 |
Sorted numbers are: 98 92 34 31 23 3
Time complexity: O(n^2)
Auxiliary Space: O(n)