Reverse a stack using recursion

Difficulty Level : Medium
Last Updated : 30 Oct, 2020

Write a program to reverse a stack using recursion. You are not allowed to use loop constructs like while, for..etc, and you can only use the following ADT functions on Stack S:
isEmpty(S)
push(S)
pop(S)

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 at the bottom of the stack.
For example, let the input stack be

First 4 is inserted at the bottom.
    4 <-- top

Then 3 is inserted at the bottom
    4 <-- top    
    3

Then 2 is inserted at the bottom
    4 <-- top    
    3 
    2
     
Then 1 is inserted at the bottom
    4 <-- top    
    3 
    2
    1

So we need a function that inserts at the bottom of a stack using the above given basic stack function.
void insertAtBottom((): First pops all stack items and stores the popped item in function call stack using recursion. And when stack becomes empty, pushes new item and all items stored in call stack.
void reverse(): This function mainly uses insertAtBottom() to pop all items one by one and insert the popped items at the bottom.

C++

// C++ code to reverse a  
// stack using recursion 
#include<bits/stdc++.h> 
using namespace std; 
  
// using std::stack for  
// stack implementation 
stack<char> st; 
  
// intializing a string to store 
// result of reversed stack 
string ns; 
  
// Below is a recursive function  
// that inserts an element 
// at the bottom of a stack. 
char insert_at_bottom(char x) 
{ 
  
    if(st.size() == 0) 
    st.push(x); 
  
    else
    { 
          
        // All items are held in Function Call 
        // Stack until we reach end of the stack 
        // When the stack becomes empty, the 
        // st.size() becomes 0, the above if  
        // part is executed and the item is  
        // inserted at the bottom 
              
        char a = st.top(); 
        st.pop(); 
        insert_at_bottom(x); 
  
        // push allthe items held in  
        // Function Call Stack 
        // once the item is inserted 
        // at the bottom 
        st.push(a); 
    } 
} 
  
// Below is the function that 
// reverses the given stack using 
// insert_at_bottom() 
char reverse() 
{ 
    if(st.size()>0) 
    { 
          
        // Hold all items in Function  
        // Call Stack until we 
        // reach end of the stack  
        char x = st.top(); 
        st.pop(); 
        reverse(); 
          
        // Insert all the items held 
        // in Function Call Stack 
        // one by one from the bottom  
        // to top. Every item is 
        // inserted at the bottom  
        insert_at_bottom(x); 
    } 
} 
  
// Driver Code 
int main() 
{ 
      
    // push elements into  
    // the stack 
    st.push('1'); 
    st.push('2'); 
    st.push('3'); 
    st.push('4'); 
      
    cout<<"Original Stack"<<endl; 
      
    // print the elements  
    // of original stack 
    cout<<"1"<<" "<<"2"<<" "
        <<"3"<<" "<<"4"
        <<endl; 
      
    // function to reverse  
    // the stack 
    reverse(); 
    cout<<"Reversed Stack"
        <<endl; 
      
    // storing values of reversed  
    // stack into a string for display 
    while(!st.empty()) 
    { 
        char p=st.top(); 
        st.pop(); 
        ns+=p; 
    } 
      
    //display of reversed stack 
    cout<<ns[3]<<" "<<ns[2]<<" "
        <<ns[1]<<" "<<ns[0]<<endl; 
    return 0; 
} 
  
// This code is contributed by Gautam Singh 

C

// C program to reverse a  
// stack using recursion 
#include<stdio.h> 
#include<stdlib.h> 
#define bool int 
  
// structure of a stack node  
struct sNode 
{ 
    char data; 
    struct sNode *next; 
}; 
  
// Function Prototypes  
void push(struct sNode** top_ref,  
                   int new_data); 
int pop(struct sNode** top_ref); 
bool isEmpty(struct sNode* top); 
void print(struct sNode* top); 
  
// Below is a recursive function 
// that inserts an element 
// at the bottom of a stack. 
void insertAtBottom(struct sNode** top_ref, 
                                 int item) 
{ 
    if (isEmpty(*top_ref)) 
        push(top_ref, item); 
    else
    { 
  
        // Hold all items in Function Call 
        // Stack until we reach end of the 
        // stack. When the stack becomes 
        // empty, the isEmpty(*top_ref)becomes 
        // true, the above if part is executed 
        // and the item is inserted at the bottom  
        int temp = pop(top_ref); 
        insertAtBottom(top_ref, item); 
  
        // Once the item is inserted  
        // at the bottom, push all 
        // the items held in Function  
        // Call Stack  
        push(top_ref, temp); 
    } 
} 
  
// Below is the function that  
// reverses the given stack using 
// insertAtBottom() 
void reverse(struct sNode** top_ref) 
{ 
    if (!isEmpty(*top_ref)) 
    { 
        // Hold all items in Function  
        // Call Stack until we 
        // reach end of the stack  
        int temp = pop(top_ref); 
        reverse(top_ref); 
  
        // Insert all the items (held in  
        // Function Call Stack) 
        // one by one from the bottom  
        // to top. Every item is 
        // inserted at the bottom  
        insertAtBottom(top_ref, temp); 
    } 
} 
  
// Driver Code 
int main() 
{ 
    struct sNode *s = NULL; 
    push(&s, 4); 
    push(&s, 3); 
    push(&s, 2); 
    push(&s, 1); 
  
    printf("\n Original Stack "); 
    print(s); 
    reverse(&s); 
    printf("\n Reversed Stack "); 
    print(s); 
    return 0; 
} 
  
// Function to check if 
// the stack is empty  
bool isEmpty(struct sNode* top) 
{ 
    return (top == NULL)? 1 : 0; 
} 
  
// Function to push an item to stack 
void push(struct sNode** top_ref,  
                    int new_data) 
{ 
      
    // allocate node 
    struct sNode* new_node = 
        (struct sNode*) malloc(sizeof(struct sNode)); 
  
    if (new_node == NULL) 
    { 
        printf("Stack overflow \n"); 
        exit(0); 
    } 
  
    // put in the data  
    new_node->data = new_data; 
  
    // link the old list  
    // off the new node  
    new_node->next = (*top_ref); 
  
    // move the head to  
    // point to the new node  
    (*top_ref) = new_node; 
} 
  
// Function to pop an item from stack 
int pop(struct sNode** top_ref) 
{ 
    char res; 
    struct sNode *top; 
  
    // If stack is empty then error  
    if (*top_ref == NULL) 
    { 
        printf("Stack overflow \n"); 
        exit(0); 
    } 
    else
    { 
        top = *top_ref; 
        res = top->data; 
        *top_ref = top->next; 
        free(top); 
        return res; 
    } 
} 
  
// Function to print a 
// linked list  
void print(struct sNode* top) 
{ 
    printf("\n"); 
    while (top != NULL) 
    { 
        printf(" %d ", top->data); 
        top = top->next; 
    } 
} 

Java

// Java code to reverse a  
// stack using recursion 
import java.util.Stack; 
  
class Test { 
      
    // using Stack class for 
    // stack implementation 
    static Stack<Character> st = new Stack<>(); 
      
    // Below is a recursive function  
    // that inserts an element 
    // at the bottom of a stack. 
    static void insert_at_bottom(char x) 
    { 
  
        if(st.isEmpty()) 
            st.push(x); 
  
        else
        { 
              
            // All items are held in Function 
            // Call Stack until we reach end 
            // of the stack. When the stack becomes 
            // empty, the st.size() becomes 0, the 
            // above if part is executed and  
            // the item is inserted at the bottom 
            char a = st.peek(); 
            st.pop(); 
            insert_at_bottom(x); 
  
            // push allthe items held  
            // in Function Call Stack 
            // once the item is inserted  
            // at the bottom 
            st.push(a); 
        } 
    } 
      
    // Below is the function that  
    // reverses the given stack using 
    // insert_at_bottom() 
    static void reverse() 
    { 
        if(st.size() > 0) 
        { 
              
            // Hold all items in Function 
            // Call Stack until we 
            // reach end of the stack  
            char x = st.peek(); 
            st.pop(); 
            reverse(); 
              
            // Insert all the items held  
            // in Function Call Stack 
            // one by one from the bottom 
            // to top. Every item is 
            // inserted at the bottom  
            insert_at_bottom(x); 
        } 
    } 
      
    // Driver Code 
    public static void main(String[] args)  
    { 
          
        // push elements into 
        // the stack 
        st.push('1'); 
        st.push('2'); 
        st.push('3'); 
        st.push('4'); 
          
        System.out.println("Original Stack"); 
          
        System.out.println(st); 
          
        // function to reverse  
        // the stack 
        reverse(); 
          
        System.out.println("Reversed Stack"); 
          
        System.out.println(st); 
    } 
} 

Python3

# Python program to reverse a  
# stack using recursion 
  
# Below is a recursive function  
# that inserts an element 
# at the bottom of a stack. 
def insertAtBottom(stack, item): 
    if isEmpty(stack): 
        push(stack, item) 
    else: 
        temp = pop(stack) 
        insertAtBottom(stack, item) 
        push(stack, temp) 
  
# Below is the function that  
# reverses the given stack 
# using insertAtBottom() 
def reverse(stack): 
    if not isEmpty(stack): 
        temp = pop(stack) 
        reverse(stack) 
        insertAtBottom(stack, temp) 
  
# Below is a complete running  
# program for testing above 
# functions. 
  
# Function to create a stack.  
# It initializes size of stack 
# as 0 
def createStack(): 
    stack = [] 
    return stack 
  
# Function to check if  
# the stack is empty 
def isEmpty( stack ): 
    return len(stack) == 0
  
# Function to push an  
# item to stack 
def push( stack, item ): 
    stack.append( item ) 
  
# Function to pop an  
# item from stack 
def pop( stack ): 
  
    # If stack is empty 
    # then error 
    if(isEmpty( stack )): 
        print("Stack Underflow ") 
        exit(1) 
  
    return stack.pop() 
  
# Function to print the stack 
def prints(stack): 
    for i in range(len(stack)-1, -1, -1): 
        print(stack[i], end = ' ') 
    print() 
  
# Driver Code 
  
stack = createStack() 
push( stack, str(4) ) 
push( stack, str(3) ) 
push( stack, str(2) ) 
push( stack, str(1) ) 
print("Original Stack ") 
prints(stack) 
  
reverse(stack) 
  
print("Reversed Stack ") 
prints(stack) 
  
# This code is contributed by Sunny Karira 

C#

// C# code to reverse a  
// stack using recursion 
using System; 
using System.Collections; 
  
public class GFG  
{  
  
    // using Stack class for  
    // stack implementation  
    static Stack st = new Stack();  
      
    // Below is a recursive function  
    // that inserts an element  
    // at the bottom of a stack.  
    static void insert_at_bottom(char x)  
    {  
  
        if(st.Count==0)  
            st.Push(x);  
  
        else
        {  
              
            // All items are held in Function  
            // Call Stack until we reach end  
            // of the stack. When the stack becomes  
            // empty, the st.size() becomes 0, the  
            // above if part is executed and  
            // the item is inserted at the bottom  
            char a = (char)st.Peek();  
            st.Pop();  
            insert_at_bottom(x);  
  
            // push allthe items held  
            // in Function Call Stack  
            // once the item is inserted  
            // at the bottom  
            st.Push(a);  
        }  
    }  
      
    // Below is the function that  
    // reverses the given stack using  
    // insert_at_bottom()  
    static void reverse()  
    {  
        if(st.Count > 0)  
        {  
              
            // Hold all items in Function  
            // Call Stack until we  
            // reach end of the stack  
            char x = (char)st.Peek();  
            st.Pop();  
            reverse();  
              
            // Insert all the items held  
            // in Function Call Stack  
            // one by one from the bottom  
            // to top. Every item is  
            // inserted at the bottom  
            insert_at_bottom(x);  
        }  
    }  
      
    // Driver Code  
    public static void Main(String []args)  
    {  
          
        // push elements into  
        // the stack  
        st.Push('1');  
        st.Push('2');  
        st.Push('3');  
        st.Push('4');  
          
        Console.WriteLine("Original Stack");  
          
        foreach (char i in st) 
        { 
            Console.WriteLine(i); 
        } 
          
        // function to reverse  
        // the stack  
        reverse();  
          
        Console.WriteLine("Reversed Stack");  
        foreach (char i in st) 
        { 
            Console.WriteLine(i); 
        } 
    }  
  
}  
  
// This code is Contibuted by Arnab Kundu 

Output:

 Original Stack 
 1  2  3  4 
 Reversed Stack 
 4  3  2  1

Time Complexity: This approach takes the worst time complexity of O(n^2),

Please write comments if you find any bug in above code/algorithm, or find other ways to solve the same problem.

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