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# How to Reverse a Stack using Recursion

Write a program to reverse a stack using recursion, without using any loop.

Example:

Input: elements present in stack from top to bottom 1 2 3 4
Output: 4 3 2 1

Input: elements present in stack from top to bottom 1 2 3
Output: 3 2 1

Recommended Practice

## Reverse a stack using Recursion

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.

Illustration:

Below is the illustration of the above approach

• Let given stack be

• After all calls of reverse,  4 will be passed to function insert at bottom, after that 4 will pushed to the stack when stack is empty

• Then 3 will be passed to function insert at bottom , it will check if the stack is empty or not if not then pop all the elements back and insert 3 and then push other elements back.

• Then 2 will be passed to function insert at bottom , it will check if the stack is empty or not if not then pop all the elements back and insert 2 and then push other elements back.
• Then 1 will be passed to function insert at bottom , it will check if the stack is empty or not if not then pop all the elements back and insert 1 and then push other elements back.

Follow the steps mentioned below to implement the idea:

• Create a stack and push all the elements in it.
• Call reverse(), which will pop all the elements from the stack and pass the popped element to function insert_at_bottom()
• Whenever insert_at_bottom() is called it will insert the passed element at the bottom of the stack.
• Print the stack

Below is the implementation of the above approach:

## C++

 `// C++ code to reverse a``// stack using recursion``#include ``using` `namespace` `std;` `// Below is a recursive function``// that inserts an element``// at the bottom of a stack.``void` `insert_at_bottom(stack<``int``>& st, ``int` `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` `        ``int` `a = st.top();``        ``st.pop();``        ``insert_at_bottom(st, 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()``void` `reverse(stack<``int``>& st)``{``    ``if` `(st.size() > 0) {` `        ``// Hold all items in Function``        ``// Call Stack until we``        ``// reach end of the stack``        ``int` `x = st.top();``        ``st.pop();``        ``reverse(st);` `        ``// 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(st, x);``    ``}``    ``return``;``}` `// Driver Code``int` `main()``{``    ``stack<``int``> st, st2;``    ``// push elements into``    ``// the stack``    ``for` `(``int` `i = 1; i <= 4; i++) {``        ``st.push(i);``    ``}` `    ``st2 = st;` `    ``cout << ``"Original Stack"` `<< endl;``    ``// printing the stack after reversal``    ``while` `(!st2.empty()) {``        ``cout << st2.top() << ``" "``;``        ``st2.pop();``    ``}``    ``cout<

## C

 `// C program to reverse a``// stack using recursion``#include ``#include ``#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 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 all the 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.Write(i + ``", "``); }` `        ``// function to reverse``        ``// the stack``        ``reverse();` `        ``Console.WriteLine(``"\nReversed Stack"``);``        ``foreach``(``char` `i ``in` `st) { Console.Write(i + ``", "``); }``    ``}``}` `// This code is Contributed by Arnab Kundu`

## Javascript

 ``

Output

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

Time Complexity: O(N2).
Auxiliary Space: O(N) use of Stack

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