Stack Data Structure

What is a Stack?

A stack is alinear data structure where elements are stored in the LIFO (Last In First Out) principle where the last element inserted would be the first element to be deleted. 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.

Stack is considered a complex data structure because it uses other data structures for implementation, such as Arrays, Linked lists, etc.

Stack Representation

A stack 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 are usually 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 thetop pointer.

Stack 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;}

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;}

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] + " ");   }  }}

Stack Elements: 44 10 62 123 15 0 0 0

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

Stack Elements: 44 10 62 123 15 0 0 0

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

Stack Deletion: pop()

Thepop() 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;}

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;}

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 + " ");   }  }}

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

MAXSIZE = 8stack = [0] * MAXSIZEtop = -1def isempty():    if(top == -1):        return 1    else:        return 0def isfull():    if(top == MAXSIZE):        return 1    else:        return 0def 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 datadef push(data):    global top    if(isfull() != 1):        top = top + 1        stack[top] = data    else:        print("\nCould not insert data, Stack is full.")    return datapush(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 = " ")

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 from Stack: peek()

Thepeek() 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. START2. return the element at the top of the stack3. 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;}

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;}

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());  }}

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

MAXSIZE = 8;stack = [0] * MAXSIZEtop = -1def isfull():    if(top == MAXSIZE):        return 1    else:        return 0def 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 datapush(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())

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

Verifying whether the Stack is full: isFull()

TheisFull() 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. START2. 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;}

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;}

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() {      return top == -1;   }   public boolean isFull() {      return top == capacity - 1;   }   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());   }}

Stack full: true

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

Stack full: False

Verifying whether the Stack is empty: isEmpty()

TheisEmpty() 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. START2. 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;}

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;}

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); }}

Stack empty: true

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

Stack empty: True

Stack 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;}

Element at top of the stack: 15Elements: 15123621044Stack full: falseStack 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;}

Element at top of the stack: 15Elements: 15123621044Stack full: falseStack 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);   }}

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

MAXSIZE = 8stack = [0] * MAXSIZEtop = -1;def isempty():    if(top == -1):        return 1    else:        return 0def isfull():    if(top == MAXSIZE):        return 1    else:        return 0def 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 datadef push(data):    global top    if(isfull() != 1):        top = top + 1        stack[top] = data    else:        print("Could not insert data, Stack is full.")    return datapush(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]))

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

Stack Implementation in C

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