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# Reverse a Stack

#### Algorithms Data Structures Stack

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The objective of this article at OPENGENUS is to explore various approaches that can be used to reverse the given stack (stack is a linear data structure where insertion and deletion are made at the same end).

Various approaches to reverse a stack:

• Approach 1: Naive approach
• Approach 2: Reverse a Stack recursively
Both approaches take O(N) time and O(N) space complexity.

## Approach 1

1)Naive Approach: The naive approach is to keep on removing the top element from the given stack and pushing it to a new stack until the given stack becomes empty.

Algorithm

• Step 1: Remove the `top element` from the given stack.
• Step 2: Push the removed element to a new stack.
• Step 3: if the given stack is `empty`, then return the new stack.
• Step 4: if the given stack is not empty then repeat step 1 and step 2 until the stack becomes empty.

Complexity:

• The Time complexity of this approach is O(n) because we access each element of stack exactly once.
• The Space complexity of this approach is also O(n) because we need an extra stack of size n (no of elements in the given stack) to store the elements of the given stack.

Example

Let us condier that the given stack has elements from 1 to 6 and 6 is the topmost element

when the stack is displayed from top the stack looks like

`````` 6 5 4 3 2 1
``````

Now let us take a new empty stack and push the last element from given stack to new stack

After step 1 the stack looks like

`````` given stack -> 5 4 3 2 1
new stack -> 6
``````

lets repeat the same procedure until given stack becomes empty

after step 2 the stack looks like

``````given stack -> 4 3 2 1
new stack -> 5 6
``````

after step 3 the stack looks like

``````given stack -> 3 2 1
new stack -> 4 5 6
``````

after step 4 the stack looks like

``````given stack -> 2 1
new stack -> 3 4 5 6
``````

after step 5 the stack looks like

``````given stack -> 1
new stack -> 2 3 4 5 6
``````

after step 4 the stack looks like

``````given stack ->
new stack -> 1 2 3 4 5 6
``````

when given stack becomes empty, the new stack is the reversed stack of given stack.

• C
• C++
• Java

### C

``````
#include <stdio.h>
#include <stdbool.h>

typedef struct Stack
{
int a[1000000];
int top;
} Stack;

void push (int x, Stack * b)
{
(*b).top=(*b).top+1;
(*b).a[(*b).top] = x;
}

int pop (Stack * b)
{
if ((*b).top != -1)
{
int temp=(*b).a[(*b).top];
(*b).top=(*b).top - 1;
return temp;
}
}

bool isempty (Stack *b)
{
if ((*b).top == -1)
{
return true;
}
return false;
}

void display (Stack *b)
{
for (int i = (*b).top; i >= 0; i--)
{
printf("%d ",(*b).a[i]);
}
}

int main ()
{
//creating stack which has to be reversed
Stack given_stack;//creating a stack
given_stack.top = -1;//assigning top value -1
push (1, &given_stack);
push (2, &given_stack);
push (3, &given_stack);
push (4, &given_stack);
push (5, &given_stack);
push (6, &given_stack);

//displaying the given stack
//Elements which are added recently is displayed first
printf("The given stack from top element is :\n");
display (&given_stack);
printf("\n");

/*creating a stack which will store the values of reversed given_stack*/
Stack reversed_stack;
reversed_stack.top=-1;
while (!isempty (&given_stack))
{
int x = pop (&given_stack);//removing the top element from given stack
push (x,&reversed_stack);//pushing the removed element to new stack.
}

//displaying the reversed stack
//Elements which are added recently is displayed first
printf("The reversed stack from top element is :\n");
display (&reversed_stack);
}
``````

### C++

``````
#include <iostream>
using namespace std;

//defining stack class
class Stack{
int a[1000000];
int top=-1;

public:
void push(int x){
a[++top]=x;
}

int pop(){
if(top!=-1){
return a[top--];
}
}

bool isempty(){
if(top==-1){
return true;
}
return false;
}

void display(){
for(int i=top;i>=0;i--){
cout<<a[i]<<" ";
}
}
};

int main(){
//creating stack which has to be reversed
Stack given_stack;//creating a stack
given_stack.push(1);
given_stack.push(2);
given_stack.push(3);
given_stack.push(4);
given_stack.push(5);
given_stack.push(6);

//displaying the given stack
//Elements which are added recently is displayed first
cout<<"The given stack from top element is :\n";
given_stack.display();
cout<<endl;

/*creating a stack which will store the values of reversed given_stack*/
Stack reversed_stack;
while(!given_stack.isempty()){
int x=given_stack.pop();//removing the top element from given stack
reversed_stack.push(x);//pushing the removed element to new stack.
}

//displaying the reversed stack
//Elements which are added recently is displayed first
cout<<"The reversed stack from top element is :\n";
reversed_stack.display();
}
``````

### Java

``````
//defining stack class
class Stack{
int a[]=new int[1000000];
int top=-1;

public void push(int x){
a[++top]=x;
}

public int pop(){
if(top!=-1){
return a[top--];
}
return -1;
}

public boolean isempty(){
if(top==-1){
return true;
}
return false;
}

public void display(){
for(int i=top;i>=0;i--){
System.out.print(a[i]+" ");
}
}
};

public class Main{
public static void main(String args[]){
//creating stack which has to be reversed
Stack given_stack=new Stack();//creating a stack
given_stack.push(1);
given_stack.push(2);
given_stack.push(3);
given_stack.push(4);
given_stack.push(5);
given_stack.push(6);

//displaying the given stack
//Elements which are added recently is displayed first
System.out.println("The given stack from top element is :\n");
given_stack.display();
System.out.println("");

/*creating a stack which will store the values of reversed given_stack*/
Stack reversed_stack=new Stack();
while(!given_stack.isempty()){
int x=given_stack.pop();//removing the top element from given stack
reversed_stack.push(x);//pushing the removed element to new stack.
}

//displaying the reversed stack
//Elements which are added recently is displayed first
System.out.println("The reversed stack from top element is :\n");
reversed_stack.display();
}
};
``````

### Output

``````The given stack from top element is :
6 5 4 3 2 1
The reversed stack from top element is :
1 2 3 4 5 6
``````

## Approach 2

2)Reverse a stack using recursion: In this approach we are going to use the concept of recursion to reverse the given stack. In this approach We will remove elements present in the stack using `pop()` and store them in a function call, When the stack becomes empty we add the stored element in the function call to the bottom of the stack.

Algorithm

• Step 1: Remove the top element from the stack using `pop()`.
• Step 2: Insert the removed element to the function call.
• Step 3: If stack is not empty repeat step 1 and step 2 until stack becomes empty.
• Step 4: Insert the elements to the bottom of the stack while moving back in the recursion tree.

Complexity:

• The Time complexity of this approach is O(n2) because for each element in the stack we are performing insert at bottom which takes O(n) operations.
• The Space complexity of this approach is also O(n) because we store n (no of elements in the given stack) elements in the function call.

• C
• C++
• Java

### C

``````
#include <stdio.h>
#include <stdbool.h>

typedef struct Stack
{
int a[1000000];
int top;
} Stack;

void push (int x, Stack * b)
{
(*b).top=(*b).top+1;
(*b).a[(*b).top] = x;
}

int pop (Stack * b)
{
if ((*b).top != -1)
{
int temp=(*b).a[(*b).top];
(*b).top=(*b).top - 1;
return temp;
}
}

bool isempty (Stack *b)
{
if ((*b).top == -1)
{
return true;
}
return false;
}

void insert_at_bottom(int x,Stack *b)
{
if((*b).top== -1)
push(x,b);
else
{
int cur_ele = pop(b);//remove top element from stack
insert_at_bottom(x,b);
push(cur_ele,b);
}
}

void reverse_stack(Stack *b)
{
if((*b).top!=-1)//while stack is not empty
{
char x = pop(b);
reverse_stack(b);
insert_at_bottom(x,b);
}
}

void display (Stack *b)
{
for (int i = (*b).top; i >= 0; i--)
{
printf("%d ",(*b).a[i]);
}
}

int main ()
{
//creating stack which has to be reversed
Stack given_stack;//creating a stack
given_stack.top = -1;//assigning top value -1
push (1, &given_stack);
push (2, &given_stack);
push (3, &given_stack);
push (4, &given_stack);
push (5, &given_stack);
push (6, &given_stack);

//displaying the given stack
//Elements which are added recently is displayed first
printf("The given stack from top element is :\n");
display (&given_stack);
printf("\n");

reverse_stack(&given_stack);
printf("The reversed stack from top element is :\n");
display(&given_stack);
}
``````

### C++

``````
#include <iostream>
using namespace std;

//defining stack class
class Stack{
int a[1000000];
int top=-1;

public:
void push(int x){
a[++top]=x;
}

int pop(){
if(top!=-1){
return a[top--];
}
}

bool isempty(){
if(top==-1){
return true;
}
return false;
}

void insert_at_bottom(int x)
{
if(top== -1)
push(x);
else
{
int cur_ele = pop();//remove top element from stack
insert_at_bottom(x);
push(cur_ele);
}
}

void reverse_stack()
{
if(top!=-1)//while stack is not empty
{
char x = pop();
reverse_stack();
insert_at_bottom(x);
}
}

void display(){
for(int i=top;i>=0;i--){
cout<<a[i]<<" ";
}
}
};

int main(){
//creating stack which has to be reversed
Stack given_stack;//creating a stack
given_stack.push(1);
given_stack.push(2);
given_stack.push(3);
given_stack.push(4);
given_stack.push(5);
given_stack.push(6);

//displaying the given stack
//Elements which are added recently is displayed first
cout<<"The given stack from top element is :\n";
given_stack.display();
cout<<endl;

given_stack.reverse_stack();
cout<<"The reversed stack from top element is :"<<endl;
given_stack.display();
}
``````

### Java

``````
//defining stack class
class Stack{
int a[]=new int[1000000];
int top=-1;

public void push(int x){
a[++top]=x;
}

public int pop(){
if(top!=-1){
return a[top--];
}
return -1;
}

public boolean isempty(){
if(top==-1){
return true;
}
return false;
}

public void insert_at_bottom(int x)
{
if(top== -1)
push(x);
else
{
int cur_ele = pop();//remove top element from stack
insert_at_bottom(x);
push(cur_ele);
}
}

public void reverse_stack()
{
if(top!=-1)//while stack is not empty
{
int x = pop();
reverse_stack();
insert_at_bottom(x);
}
}

public void display(){
for(int i=top;i>=0;i--){
System.out.print(a[i]+" ");
}
}
};

public class Main{
public static void main(String args[]){
//creating stack which has to be reversed
Stack given_stack=new Stack();//creating a stack
given_stack.push(1);
given_stack.push(2);
given_stack.push(3);
given_stack.push(4);
given_stack.push(5);
given_stack.push(6);

//displaying the given stack
//Elements which are added recently is displayed first
System.out.println("The given stack from top element is :\n");
given_stack.display();
System.out.println("");

given_stack.reverse_stack();
System.out.println("The reversed stack from top element is :\n");
given_stack.display();
System.out.println("");
}
};
``````

### Output

``````The given stack from top element is :
6 5 4 3 2 1
The reversed stack from top element is :
1 2 3 4 5 6
``````
Reverse a Stack