How to Sort a Stack using Recursion

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 > -5

Input: 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++

// 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

// 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

// 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);
    }
}

Python3

# 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#

// 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

Javascript

<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

C++

#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;
}

Java

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() + " ");
        }
    }
}

Python3

# 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=" ")

C#

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();
    }
  }
}

Javascript

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

Output

Sorted numbers are: 98 92 34 31 23 3 

Time complexity: O(n^2)

Auxiliary Space: O(n)