# Stack Data Structure

A stack is an Abstract Data Type (ADT), that is popularly used in most programming languages. It is named stack because it has the similar operations as the real-world stacks, for example − a pack of cards or a pile of plates, etc.

The stack follows the LIFO (Last in - First out) structure where the last element inserted would be the first element deleted.

## Stack Representation

A Stack ADT allows all data operations at one end only. At any given time, we can only access the top element of a stack.

The following diagram depicts a stack and its operations −

A stack can be implemented by means of Array, Structure, Pointer, and Linked List. Stack can either be a fixed size one or it may have a sense of dynamic resizing. Here, we are going to implement stack using arrays, which makes it a fixed size stack implementation.

## Basic Operations on Stacks

Stack operations usually are performed for initialization, usage and, de-initialization of the stack ADT.

The most fundamental operations in the stack ADT include: push(), pop(), peek(), isFull(), isEmpty(). These are all built-in operations to carry out data manipulation and to check the status of the stack.

Stack uses pointers that always point to the topmost element within the stack, hence called as the top pointer.

## Insertion: push()

The push() is an operation that inserts elements into the stack. The following is an algorithm that describes the push() operation in a simpler way.

### Algorithm

1. Checks if the stack is full.
2. If the stack is full, produces an error and exit.
3. If the stack is not full, increments top to point next
empty space.
4. Adds data element to the stack location, where top
is pointing.
5. Returns success.


### Example

Following are the implementations of this operation in various programming languages −

#include <stdio.h>
int MAXSIZE = 8;
int stack[8];
int top = -1;

/* Check if the stack is full*/
int isfull(){
if(top == MAXSIZE)
return 1;
else
return 0;
}

/* Function to insert into the stack */
int push(int data){
if(!isfull()) {
top = top + 1;
stack[top] = data;
} else {
printf("Could not insert data, Stack is full.\n");
}
}

/* Main function */
int main(){
int i;
push(44);
push(10);
push(62);
push(123);
push(15);
printf("Stack Elements: \n");

// print stack data
for(i = 0; i < 8; i++) {
printf("%d ", stack[i]);
}
return 0;
}


### Output

Stack Elements:
44 10 62 123 15 0 0 0

#include <iostream>
int MAXSIZE = 8;
int stack[8];
int top = -1;

/* Check if the stack is full*/
int isfull(){
if(top == MAXSIZE)
return 1;
else
return 0;
}

/* Function to insert into the stack */
int push(int data){
if(!isfull()) {
top = top + 1;
stack[top] = data;
} else {
printf("Could not insert data, Stack is full.\n");
}
return data;
}

/* Main function */
int main(){
int i;
push(44);
push(10);
push(62);
push(123);
push(15);
printf("Stack Elements: \n");

// print stack data
for(i = 0; i < 8; i++) {
printf("%d ", stack[i]);
}
return 0;
}


### Output

Stack Elements:
44 10 62 123 15 0 0 0

public class Demo{
final static int MAXSIZE = 8;
static int stack[] = new int[MAXSIZE];
static int top = -1;
public static int isfull(){
if(top == MAXSIZE)
return 1;
else
return 0;
}
public static int push(int data){
if(isfull() != 1) {
top = top + 1;
stack[top] = data;
} else {
System.out.print("Could not insert data, Stack is full.\n");
}
return data;
}
public static void main(String[] args){
int i;
push(44);
push(10);
push(62);
push(123);
push(15);
System.out.print("\nStack Elements: ");
// print stack data
for(i = 0; i < MAXSIZE; i++) {
System.out.print(stack[i] + " ");
}
}
}


### Output

Stack Elements: 44 10 62 123 15 0 0 0

MAXSIZE = 8
stack = [0] * MAXSIZE
top = -1
def isfull():
if(top == MAXSIZE):
return 1
else:
return 0
def push(data):
global top
if(isfull() != 1):
top = top + 1
stack[top] = data
else:
print("Could not insert data, Stack is full.")
return data
push(44)
push(10)
push(62)
push(123)
push(15)
print("Stack Elements: ")
for i in range(MAXSIZE):
print(stack[i], end = " ")


### Output

Stack Elements:
44 10 62 123 15 0 0 0


Note − In Java we have used to built-in method push() to perform this operation.

## Deletion: pop()

The pop() is a data manipulation operation which removes elements from the stack. The following pseudo code describes the pop() operation in a simpler way.

### Algorithm

1. Checks if the stack is empty.
2. If the stack is empty, produces an error and exit.
3. If the stack is not empty, accesses the data element at
which top is pointing.
4. Decreases the value of top by 1.
5. Returns success.


### Example

Following are the implementations of this operation in various programming languages −

#include <stdio.h>
int MAXSIZE = 8;
int stack[8];
int top = -1;

/* Check if the stack is empty */
int isempty(){
if(top == -1)
return 1;
else
return 0;
}

/* Check if the stack is full*/
int isfull(){
if(top == MAXSIZE)
return 1;
else
return 0;
}

/* Function to delete from the stack */
int pop(){
int data;
if(!isempty()) {
data = stack[top];
top = top - 1;
return data;
} else {
printf("Could not retrieve data, Stack is empty.\n");
}
}

/* Function to insert into the stack */
int push(int data){
if(!isfull()) {
top = top + 1;
stack[top] = data;
} else {
printf("Could not insert data, Stack is full.\n");
}
}

/* Main function */
int main(){
int i;
push(44);
push(10);
push(62);
push(123);
push(15);
printf("Stack Elements: \n");

// print stack data
for(i = 0; i < 8; i++) {
printf("%d ", stack[i]);
}
/*printf("Element at top of the stack: %d\n" ,peek());*/
printf("\nElements popped: \n");

// print stack data
while(!isempty()) {
int data = pop();
printf("%d ",data);
}
return 0;
}


### Output

Stack Elements:
44 10 62 123 15 0 0 0
Elements popped:
15 123 62 10 44

#include <iostream>
int MAXSIZE = 8;
int stack[8];
int top = -1;

/* Check if the stack is empty */
int isempty(){
if(top == -1)
return 1;
else
return 0;
}

/* Check if the stack is full*/
int isfull(){
if(top == MAXSIZE)
return 1;
else
return 0;
}

/* Function to delete from the stack */
int pop(){
int data;
if(!isempty()) {
data = stack[top];
top = top - 1;
return data;
} else {
printf("Could not retrieve data, Stack is empty.\n");
}
return data;
}

/* Function to insert into the stack */
int push(int data){
if(!isfull()) {
top = top + 1;
stack[top] = data;
} else {
printf("Could not insert data, Stack is full.\n");
}
return data;
}

/* Main function */
int main(){
int i;
push(44);
push(10);
push(62);
push(123);
push(15);
printf("Stack Elements: \n");

// print stack data
for(i = 0; i < 8; i++) {
printf("%d ", stack[i]);
}

/*printf("Element at top of the stack: %d\n" ,peek());*/
printf("\nElements popped: \n");

// print stack data
while(!isempty()) {
int data = pop();
printf("%d ",data);
}
return 0;
}


### Output

Stack Elements:
44 10 62 123 15 0 0 0
Elements popped:
15 123 62 10 44

public class Demo{
final static int MAXSIZE = 8;
public static int stack[] = new int[MAXSIZE];
public static int top = -1;
/* Check if the stack is empty */
public static int isempty(){
if(top == -1)
return 1;
else
return 0;
}
/* Check if the stack is full*/
public static int isfull(){
if(top == MAXSIZE)
return 1;
else
return 0;
}
/* Function to delete from the stack */
public static int pop(){
int data = 0;
if(isempty() != 1) {
data = stack[top];
top = top - 1;
return data;
} else {
System.out.print("Could not retrieve data, Stack is empty.");
}
return data;
}
/* Function to insert into the stack */
public static int push(int data){
if(isfull() != 1) {
top = top + 1;
stack[top] = data;
} else {
System.out.print("\nCould not insert data, Stack is full.\n");
}
return data;
}
/* Main function */
public static void main(String[] args){
push(44);
push(10);
push(62);
push(123);
push(15);
System.out.print("Stack Elements: ");
// print stack data
for(int i = 0; i < MAXSIZE; i++) {
System.out.print(stack[i] + " ");
}

/*printf("Element at top of the stack: %d\n" ,peek());*/
System.out.print("\nElements popped: ");

// print stack data
while(isempty() != 1) {
int data = pop();
System.out.print(data + " ");
}
}
}


### Output

Stack Elements: 44 10 62 123 15 0 0 0
Elements popped: 15 123 62 10 44

MAXSIZE = 8
stack = [0] * MAXSIZE
top = -1
def isempty():
if(top == -1):
return 1
else:
return 0
def isfull():
if(top == MAXSIZE):
return 1
else:
return 0
def pop():
global top
data = 0
if(isempty() != 1):
data = stack[top]
top = top - 1
return data
else:
print("Could not retrieve data, Stack is empty.")
return data
def push(data):
global top
if(isfull() != 1):
top = top + 1
stack[top] = data
else:
print("\nCould not insert data, Stack is full.")
return data
push(44);
push(10);
push(62);
push(123);
push(15);
print("Stack Elements: ")
for i in range (MAXSIZE):
print(stack[i], end = " ")
print("\nElements popped: ")
while(isempty() != 1):
data = pop()
print(data, end = " ")


### Output

Stack Elements:
44 10 62 123 15 0 0 0
Elements popped:
15 123 62 10 44


Note − In Java we are using the built-in method pop().

## Retrieving topmost Element: peek()

The peek() is an operation retrieves the topmost element within the stack, without deleting it. This operation is used to check the status of the stack with the help of the top pointer.

### Algorithm

1. START
2. return the element at the top of the stack
3. END


### Example

Following are the implementations of this operation in various programming languages −

#include <stdio.h>
int MAXSIZE = 8;
int stack[8];
int top = -1;

/* Check if the stack is full */
int isfull(){
if(top == MAXSIZE)
return 1;
else
return 0;
}

/* Function to return the topmost element in the stack */
int peek(){
return stack[top];
}

/* Function to insert into the stack */
int push(int data){
if(!isfull()) {
top = top + 1;
stack[top] = data;
} else {
printf("Could not insert data, Stack is full.\n");
}
}

/* Main function */
int main(){
int i;
push(44);
push(10);
push(62);
push(123);
push(15);
printf("Stack Elements: \n");

// print stack data
for(i = 0; i < 8; i++) {
printf("%d ", stack[i]);
}
printf("\nElement at top of the stack: %d\n" ,peek());
return 0;
}


### Output

Stack Elements:
44 10 62 123 15 0 0 0
Element at top of the stack: 15

#include <iostream>
int MAXSIZE = 8;
int stack[8];
int top = -1;

/* Check if the stack is full */
int isfull(){
if(top == MAXSIZE)
return 1;
else
return 0;
}

/* Function to return the topmost element in the stack */
int peek(){
return stack[top];
}

/* Function to insert into the stack */
int push(int data){
if(!isfull()) {
top = top + 1;
stack[top] = data;
} else {
printf("Could not insert data, Stack is full.\n");
}
return data;
}

/* Main function */
int main(){
int i;
push(44);
push(10);
push(62);
push(123);
push(15);
printf("Stack Elements: \n");

// print stack data
for(i = 0; i < 8; i++) {
printf("%d ", stack[i]);
}
printf("\nElement at top of the stack: %d\n" ,peek());
return 0;
}


### Output

Stack Elements:
44 10 62 123 15 0 0 0
Element at top of the stack: 15

public class Demo{
final static int MAXSIZE = 8;
public static int stack[] = new int[MAXSIZE];
public static int top = -1;
/* Check if the stack is full */
public static int isfull(){
if(top == MAXSIZE)
return 1;
else
return 0;
}

/* Function to return the topmost element in the stack */
public static int peek(){
return stack[top];
}

/* Function to insert into the stack */
public static int push(int data){
if(isfull() != 1) {
top = top + 1;
stack[top] = data;
} else {
System.out.print("Could not insert data, Stack is full.");
}
return data;
}

/* Main function */
public static void main(String[] args){
push(44);
push(10);
push(62);
push(123);
push(15);
System.out.print("Stack Elements: ");

// print stack data
for(int i = 0; i < MAXSIZE; i++) {
System.out.print(stack[i] + " ");
}
System.out.print("\nElement at top of the stack: " + peek());
}
}


### Output

Stack Elements: 44 10 62 123 15 0 0 0
Element at top of the stack: 15

MAXSIZE = 8;
stack = [0] * MAXSIZE
top = -1
def isfull():
if(top == MAXSIZE):
return 1
else:
return 0
def peek():
return stack[top]
def push(data):
global top
if(isfull() != 1):
top = top + 1
stack[top] = data
else:
print("Could not insert data, Stack is full.")
return data
push(44);
push(10);
push(62);
push(123);
push(15);
print("Stack Elements: ")
for i in range(MAXSIZE):
print(stack[i], end = " ")
print("\nElement at top of the stack: ", peek())


### Output

Stack Elements:
44 10 62 123 15 0 0 0
Element at top of the stack:  15


## Verifying whether the Stack is full: isFull()

The isFull() operation checks whether the stack is full. This operation is used to check the status of the stack with the help of top pointer.

### Algorithm

1. START
2. If the size of the stack is equal to the top position of the stack,
the stack is full. Return 1.
3. Otherwise, return 0.
4. END


### Example

Following are the implementations of this operation in various programming languages −

#include <stdio.h>
int MAXSIZE = 8;
int stack[8];
int top = -1;

/* Check if the stack is full */
int isfull(){
if(top == MAXSIZE)
return 1;
else
return 0;
}

/* Main function */
int main(){
printf("Stack full: %s\n" , isfull()?"true":"false");
return 0;
}


### Output

Stack full: false

#include <iostream>
int MAXSIZE = 8;
int stack[8];
int top = -1;

/* Check if the stack is full */
int isfull(){
if(top == MAXSIZE)
return 1;
else
return 0;
}

/* Main function */
int main(){
printf("Stack full: %s\n" , isfull()?"true":"false");
return 0;
}


### Output

Stack full: false

import java.io.*;
public class StackExample {
private int arr[];
private int top;
private int capacity;
StackExample(int size) {
arr = new int[size];
capacity = size;
top = -1;
}
public boolean isEmpty() {
}
public boolean isFull() {
}
public void push(int key) {
if (isFull()) {
System.out.println("Stack is Full\n");
return;
}
arr[++top] = key;
}
public static void main (String[] args) {
StackExample stk = new StackExample(5);
stk.push(1); // inserting 1 in the stack
stk.push(2);
stk.push(3);
stk.push(4);
stk.push(5);
System.out.println("Stack full: " + stk.isFull());
}
}


### Output

Stack full: true

#python code for stack(IsFull)
MAXSIZE = 8
stack = [None] * MAXSIZE
top = -1
#Check if the stack is empty
def isfull():
if top == MAXSIZE - 1:
return True
else:
return False
#main function
print("Stack full:", isfull())


### Output

Stack full: False


## Verifying whether the Stack is empty: isEmpty()

The isEmpty() operation verifies whether the stack is empty. This operation is used to check the status of the stack with the help of top pointer.

### Algorithm

1. START
2. If the top value is -1, the stack is empty. Return 1.
3. Otherwise, return 0.
4. END


### Example

Following are the implementations of this operation in various programming languages −

#include <stdio.h>
int MAXSIZE = 8;
int stack[8];
int top = -1;

/* Check if the stack is empty */
int isempty() {
if(top == -1)
return 1;
else
return 0;
}

/* Main function */
int main() {
printf("Stack empty: %s\n" , isempty()?"true":"false");
return 0;
}


### Output

Stack empty: true

#include <iostream>
int MAXSIZE = 8;
int stack[8];
int top = -1;

/* Check if the stack is empty */
int isempty(){
if(top == -1)
return 1;
else
return 0;
}

/* Main function */
int main(){
printf("Stack empty: %s\n" , isempty()?"true":"false");
return 0;
}


### Output

Stack empty: true

public class Demo{
final static int MAXSIZE = 8;
static int stack[] = new int[MAXSIZE];
static int top = -1;

/* Check if the stack is empty */
public static int isempty(){
if(top == -1)
return 1;
else
return 0;
}

/* Main function */
public static void main(String[] args){
boolean res = isempty() == 1 ? true : false;
System.out.print("Stack empty: " + res);
}
}


### Output

Stack empty: true

#python code for stack(IsFull)
MAXSIZE = 8
stack = [None] * MAXSIZE
top = -1
#Check if the stack is empty
def isempty():
if top == -1:
return True
else:
return False
#main function
print("Stack empty:", isempty())


### Output

Stack empty: True


## Complete implementation

Following are the complete implementations of Stack in various programming languages −

#include <stdio.h>
int MAXSIZE = 8;
int stack[8];
int top = -1;
/* Check if the stack is empty */
int isempty(){
if(top == -1)
return 1;
else
return 0;
}
/* Check if the stack is full */
int isfull(){
if(top == MAXSIZE)
return 1;
else
return 0;
}

/* Function to return the topmost element in the stack */
int peek(){
return stack[top];
}

/* Function to delete from the stack */
int pop(){
int data;
if(!isempty()) {
data = stack[top];
top = top - 1;
return data;
} else {
printf("Could not retrieve data, Stack is empty.\n");
}
}

/* Function to insert into the stack */
int push(int data){
if(!isfull()) {
top = top + 1;
stack[top] = data;
} else {
printf("Could not insert data, Stack is full.\n");
}
}
/* Main function */
int main(){
push(44);
push(10);
push(62);
push(123);
push(15);
printf("Element at top of the stack: %d\n" ,peek());
printf("Elements: \n");
// print stack data
while(!isempty()) {
int data = pop();
printf("%d\n",data);
}
printf("Stack full: %s\n" , isfull()?"true":"false");
printf("Stack empty: %s\n" , isempty()?"true":"false");
return 0;
}


### Output

Element at top of the stack: 15
Elements:
15123
62
10
44
Stack full: false
Stack empty: true

#include <iostream>
using namespace std;
int MAXSIZE = 8;
int stack[8];
int top = -1;
/* Check if the stack is empty */
int isempty(){
if(top == -1)
return 1;
else
return 0;
}
/* Check if the stack is full */
int isfull(){
if(top == MAXSIZE)
return 1;
else
return 0;
}
/* Function to return the topmost element in the stack */
int peek(){
return stack[top];
}
/* Function to delete from the stack */
int pop(){
int data;
if(!isempty()) {
data = stack[top];
top = top - 1;
return data;
} else
cout << "Could not retrieve data, Stack is empty." << endl;
}
/* Function to insert into the stack */
int push(int data){
if(!isfull()) {
top = top + 1;
stack[top] = data;
} else
cout << "Could not insert data, Stack is full." << endl;
}
/* Main function */
int main(){
push(44);
push(10);
push(62);
push(123);
push(15);
cout << "Element at top of the stack: " << peek() << endl;
printf("Elements: \n");
// print stack data
while(!isempty()) {
int data = pop();
cout << data <<endl;
}
printf("Stack full: %s\n" , isfull()?"true":"false");
printf("Stack empty: %s\n" , isempty()?"true":"false");
return 0;
}


### Output

Element at top of the stack: 15
Elements:
15
123
62
10
44
Stack full: false
Stack empty: true

public class Demo{
final static int MAXSIZE = 8;
public static int stack[] = new int[MAXSIZE];
public static int top = -1;
/* Check if the stack is empty */
public static int isempty(){
if(top == -1)
return 1;
else
return 0;
}
/* Check if the stack is full */
public static int isfull(){
if(top == MAXSIZE)
return 1;
else
return 0;
}
/* Function to return the topmost element in the stack */
public static int peek(){
return stack[top];
}
/* Function to delete from the stack */
public static int pop(){
int data = 0;
if(isempty() != 1) {
data = stack[top];
top = top - 1;
return data;
} else
System.out.print("Could not retrieve data, Stack is empty.");
return data;
}
/* Function to insert into the stack */
public static int push(int data){
if(isfull() != 1) {
top = top + 1;
stack[top] = data;
} else
System.out.print("Could not insert data, Stack is full.");
return data;
}
/* Main function */
public static void main(String[] args){
push(44);
push(10);
push(62);
push(123);
push(15);
System.out.print("Element at top of the stack: " + peek());
System.out.print("\nElements: ");
// print stack data
while(isempty() != 1) {
int data = pop();
System.out.print(data + " ");
}
boolean res1 = isfull() == 1 ? true : false;
boolean res2 = isempty() == 1 ? true : false;
System.out.print("\nStack full: " + res1);
System.out.print("\nStack empty: " + res2);
}
}


### Output

Element at top of the stack: 15
Elements: 15 123 62 10 44
Stack full: false
Stack empty: true

MAXSIZE = 8
stack = [0] * MAXSIZE
top = -1;
def isempty():
if(top == -1):
return 1
else:
return 0
def isfull():
if(top == MAXSIZE):
return 1
else:
return 0
def peek():
return stack[top]
def pop():
global data, top
if(isempty() != 1):
data = stack[top];
top = top - 1;
return data
else:
print("Could not retrieve data, Stack is empty.")
return data
def push(data):
global top
if(isfull() != 1):
top = top + 1
stack[top] = data
else:
print("Could not insert data, Stack is full.")
return data
push(44)
push(10)
push(62)
push(123)
push(15)
print("Element at top of the stack: ", peek())
print("Elements: ")
while(isempty() != 1):
data = pop();
print(data, end = " ")
print("\nStack full: ",bool({True: 1, False: 0} [isfull() == 1]))
print("Stack empty: ",bool({True: 1, False: 0} [isempty() == 1]))


### Output

Element at top of the stack:  15
Elements:
15 123 62 10 44
Stack full:  False
Stack empty:  True