Introduction to Stack – Data Structure and Algorithm Tutorials

What is Stack?

A stack is a linear data structure in which the insertion of a new element and removal of an existing element takes place at the same end represented as the top of the stack.

To implement the stack, it is required to maintain the pointer to the top of the stack, which is the last element to be inserted because we can access the elements only on the top of the stack.

LIFO( Last In First Out ):

This strategy states that the element that is inserted last will come out first. You can take a pile of plates kept on top of each other as a real-life example. The plate which we put last is on the top and since we remove the plate that is at the top, we can say that the plate that was put last comes out first.

Basic Operations on Stack

In order to make manipulations in a stack, there are certain operations provided to us.

• push() to insert an element into the stack
• pop() to remove an element from the stack
• top() Returns the top element of the stack.
• isEmpty() returns true if stack is empty else false.
• size() returns the size of stack.

Stack

Push:

Adds an item to the stack. If the stack is full, then it is said to be an Overflow condition.

Algorithm for push:

begin
 if stack is full
    return
 endif
else  
 increment top
 stack[top] assign value
end else
end procedure

Pop:

Removes an item from the stack. The items are popped in the reversed order in which they are pushed. If the stack is empty, then it is said to be an Underflow condition.

Algorithm for pop:

begin
 if stack is empty
    return
 endif
else
 store value of stack[top]
 decrement top
 return value
end else
end procedure

Top:

Returns the top element of the stack.

Algorithm for Top:

begin 
  return stack[top]
end procedure

isEmpty:

Returns true if the stack is empty, else false.

Algorithm for isEmpty:

begin
 if top < 1
    return true
 else
    return false
end procedure

Understanding stack practically:

There are many real-life examples of a stack. Consider the simple example of plates stacked over one another in a canteen. The plate which is at the top is the first one to be removed, i.e. the plate which has been placed at the bottommost position remains in the stack for the longest period of time. So, it can be simply seen to follow the LIFO/FILO order.

Complexity Analysis:

• Time Complexity

Operations	Complexity
push()	O(1)
pop()	O(1)
isEmpty()	O(1)
size()	O(1)

Types of Stacks:

• Fixed Size Stack: As the name suggests, a fixed size stack has a fixed size and cannot grow or shrink dynamically. If the stack is full and an attempt is made to add an element to it, an overflow error occurs. If the stack is empty and an attempt is made to remove an element from it, an underflow error occurs.
• Dynamic Size Stack: A dynamic size stack can grow or shrink dynamically. When the stack is full, it automatically increases its size to accommodate the new element, and when the stack is empty, it decreases its size. This type of stack is implemented using a linked list, as it allows for easy resizing of the stack.

In addition to these two main types, there are several other variations of Stacks, including:

1. Infix to Postfix Stack: This type of stack is used to convert infix expressions to postfix expressions.
2. Expression Evaluation Stack: This type of stack is used to evaluate postfix expressions.
3. Recursion Stack: This type of stack is used to keep track of function calls in a computer program and to return control to the correct function when a function returns.
4. Memory Management Stack: This type of stack is used to store the values of the program counter and the values of the registers in a computer program, allowing the program to return to the previous state when a function returns.
5. Balanced Parenthesis Stack: This type of stack is used to check the balance of parentheses in an expression.
6. Undo-Redo Stack: This type of stack is used in computer programs to allow users to undo and redo actions.

Applications of the stack:

• Infix to Postfix /Prefix conversion
• Redo-undo features at many places like editors, photoshop.
• Forward and backward features in web browsers
• Used in many algorithms like Tower of Hanoi, tree traversals, stock span problems, and histogram problems.
• Backtracking is one of the algorithm designing techniques. Some examples of backtracking are the Knight-Tour problem, N-Queen problem, find your way through a maze, and game-like chess or checkers in all these problems we dive into someway if that way is not efficient we come back to the previous state and go into some another path. To get back from a current state we need to store the previous state for that purpose we need a stack.
• In Graph Algorithms like Topological Sorting and Strongly Connected Components
• In Memory management, any modern computer uses a stack as the primary management for a running purpose. Each program that is running in a computer system has its own memory allocations
• String reversal is also another application of stack. Here one by one each character gets inserted into the stack. So the first character of the string is on the bottom of the stack and the last element of a string is on the top of the stack. After Performing the pop operations on the stack we get a string in reverse order.
• Stack also helps in implementing function call in computers. The last called function is always completed first.
• Stacks are also used to implement the undo/redo operation in text editor.

Implementation of Stack:

A stack can be implemented using an array or a linked list. In an array-based implementation, the push operation is implemented by incrementing the index of the top element and storing the new element at that index. The pop operation is implemented by decrementing the index of the top element and returning the value stored at that index. In a linked list-based implementation, the push operation is implemented by creating a new node with the new element and setting the next pointer of the current top node to the new node. The pop operation is implemented by setting the next pointer of the current top node to the next node and returning the value of the current top node.

Stacks are commonly used in computer science for a variety of applications, including the evaluation of expressions, function calls, and memory management. In the evaluation of expressions, a stack can be used to store operands and operators as they are processed. In function calls, a stack can be used to keep track of the order in which functions are called and to return control to the correct function when a function returns. In memory management, a stack can be used to store the values of the program counter and the values of the registers in a computer program, allowing the program to return to the previous state when a function returns.

In conclusion, a Stack is a linear data structure that operates on the LIFO principle and can be implemented using an array or a linked list. The basic operations that can be performed on a stack include push, pop, and peek, and stacks are commonly used in computer science for a variety of applications, including the evaluation of expressions, function calls, and memory management.There are two ways to implement a stack –

• Using array
• Using linked list

Implementing Stack using Arrays:

C++

/* C++ program to implement basic stack
   operations */
#include <bits/stdc++.h>

using namespace std;

#define MAX 1000

class Stack {
    int top;

public:
    int a[MAX]; // Maximum size of Stack

    Stack() { top = -1; }
    bool push(int x);
    int pop();
    int peek();
    bool isEmpty();
};

bool Stack::push(int x)
{
    if (top >= (MAX - 1)) {
        cout << "Stack Overflow";
        return false;
    }
    else {
        a[++top] = x;
        cout << x << " pushed into stack\n";
        return true;
    }
}

int Stack::pop()
{
    if (top < 0) {
        cout << "Stack Underflow";
        return 0;
    }
    else {
        int x = a[top--];
        return x;
    }
}
int Stack::peek()
{
    if (top < 0) {
        cout << "Stack is Empty";
        return 0;
    }
    else {
        int x = a[top];
        return x;
    }
}

bool Stack::isEmpty()
{
    return (top < 0);
}

// Driver program to test above functions
int main()
{
    class Stack s;
    s.push(10);
    s.push(20);
    s.push(30);
    cout << s.pop() << " Popped from stack\n";

    //print top element of stack after popping
    cout << "Top element is : " << s.peek() << endl;

    //print all elements in stack :
    cout <<"Elements present in stack : ";
    while(!s.isEmpty())
    {
        // print top element in stack
        cout << s.peek() <<" ";
        // remove top element in stack
        s.pop();
    }

    return 0;
}

C

// C program for array implementation of stack
#include <limits.h>
#include <stdio.h>
#include <stdlib.h>

// A structure to represent a stack
struct Stack {
    int top;
    unsigned capacity;
    int* array;
};

// function to create a stack of given capacity. It initializes size of
// stack as 0
struct Stack* createStack(unsigned capacity)
{
    struct Stack* stack = (struct Stack*)malloc(sizeof(struct Stack));
    stack->capacity = capacity;
    stack->top = -1;
    stack->array = (int*)malloc(stack->capacity * sizeof(int));
    return stack;
}

// Stack is full when top is equal to the last index
int isFull(struct Stack* stack)
{
    return stack->top == stack->capacity - 1;
}

// Stack is empty when top is equal to -1
int isEmpty(struct Stack* stack)
{
    return stack->top == -1;
}

// Function to add an item to stack.  It increases top by 1
void push(struct Stack* stack, int item)
{
    if (isFull(stack))
        return;
    stack->array[++stack->top] = item;
    printf("%d pushed to stack\n", item);
}

// Function to remove an item from stack.  It decreases top by 1
int pop(struct Stack* stack)
{
    if (isEmpty(stack))
        return INT_MIN;
    return stack->array[stack->top--];
}

// Function to return the top from stack without removing it
int peek(struct Stack* stack)
{
    if (isEmpty(stack))
        return INT_MIN;
    return stack->array[stack->top];
}

// Driver program to test above functions
int main()
{
    struct Stack* stack = createStack(100);

    push(stack, 10);
    push(stack, 20);
    push(stack, 30);

    printf("%d popped from stack\n", pop(stack));

    return 0;
}

Java

/* Java program to implement basic stack
operations */
class Stack {
    static final int MAX = 1000;
    int top;
    int a[] = new int[MAX]; // Maximum size of Stack

    boolean isEmpty()
    {
        return (top < 0);
    }
    Stack()
    {
        top = -1;
    }

    boolean push(int x)
    {
        if (top >= (MAX - 1)) {
            System.out.println("Stack Overflow");
            return false;
        }
        else {
            a[++top] = x;
            System.out.println(x + " pushed into stack");
            return true;
        }
    }

    int pop()
    {
        if (top < 0) {
            System.out.println("Stack Underflow");
            return 0;
        }
        else {
            int x = a[top--];
            return x;
        }
    }

    int peek()
    {
        if (top < 0) {
            System.out.println("Stack Underflow");
            return 0;
        }
        else {
            int x = a[top];
            return x;
        }
    }

    void print(){
    for(int i = top;i>-1;i--){
      System.out.print(" "+ a[i]);
    }
  }
}

// Driver code
class Main {
    public static void main(String args[])
    {
        Stack s = new Stack();
        s.push(10);
        s.push(20);
        s.push(30);
        System.out.println(s.pop() + " Popped from stack");
        System.out.println("Top element is :" + s.peek());
        System.out.print("Elements present in stack :");
        s.print();
    }
}

Python3

# Python program for implementation of stack

# import maxsize from sys module
# Used to return -infinite when stack is empty
from sys import maxsize

# Function to create a stack. It initializes size of stack as 0
def createStack():
    stack = []
    return stack

# Stack is empty when stack size is 0
def isEmpty(stack):
    return len(stack) == 0

# Function to add an item to stack. It increases size by 1
def push(stack, item):
    stack.append(item)
    print(item + " pushed to stack ")

# Function to remove an item from stack. It decreases size by 1
def pop(stack):
    if (isEmpty(stack)):
        return str(-maxsize -1) # return minus infinite

    return stack.pop()

# Function to return the top from stack without removing it
def peek(stack):
    if (isEmpty(stack)):
        return str(-maxsize -1) # return minus infinite
    return stack[len(stack) - 1]

# Driver program to test above functions
stack = createStack()
push(stack, str(10))
push(stack, str(20))
push(stack, str(30))
print(pop(stack) + " popped from stack")

C#

// C# program to implement basic stack
// operations
using System;

namespace ImplementStack {
class Stack {
    private int[] ele;
    private int top;
    private int max;
    public Stack(int size)
    {
        ele = new int[size]; // Maximum size of Stack
        top = -1;
        max = size;
    }

    public void push(int item)
    {
        if (top == max - 1) {
            Console.WriteLine("Stack Overflow");
            return;
        }
        else {
            ele[++top] = item;
        }
    }

    public int pop()
    {
        if (top == -1) {
            Console.WriteLine("Stack is Empty");
            return -1;
        }
        else {
            Console.WriteLine("{0} popped from stack ", ele[top]);
            return ele[top--];
        }
    }

    public int peek()
    {
        if (top == -1) {
            Console.WriteLine("Stack is Empty");
            return -1;
        }
        else {
            Console.WriteLine("{0} popped from stack ", ele[top]);
            return ele[top];
        }
    }

    public void printStack()
    {
        if (top == -1) {
            Console.WriteLine("Stack is Empty");
            return;
        }
        else {
            for (int i = 0; i <= top; i++) {
                Console.WriteLine("{0} pushed into stack", ele[i]);
            }
        }
    }
}

// Driver program to test above functions
class Program {
    static void Main()
    {
        Stack p = new Stack(5);

        p.push(10);
        p.push(20);
        p.push(30);
        p.printStack();
        p.pop();
    }
}
}

Javascript

<script>
/* javascript program to implement basic stack
operations
*/
 var t = -1;
      var MAX = 1000;
    var a = Array(MAX).fill(0); // Maximum size of Stack

    function isEmpty() {
        return (t < 0);
    }

    function push(x) {
        if (t >= (MAX - 1)) {
            document.write("Stack Overflow");
            return false;
        } else {
        t+=1;
            a[t] = x;

            document.write(x + " pushed into stack<br/>");
            return true;
        }
    }

    function pop() {
        if (t < 0) {
            document.write("Stack Underflow");
            return 0;
        } else {
            var x = a[t];
            t-=1;
            return x;
        }
    }

    function peek() {
        if (t < 0) {
            document.write("Stack Underflow");
            return 0;
        } else {
            var x = a[t];
            return x;
        }
    }

    function print() {
        for (i = t; i > -1; i--) {
            document.write(" " + a[i]);
        }
    }

        push(10);
        push(20);
        push(30);
        document.write(pop() + " Popped from stack");
        document.write("<br/>Top element is :" + peek());
        document.write("<br/>Elements present in stack : ");
        print();

// This code is contributed by Rajput-Ji
</script>

Output

10 pushed into stack
20 pushed into stack
30 pushed into stack
30 Popped from stack
Top element is : 20
Elements present in stack : 20 10 

Advantages of array implementation:

• Easy to implement.
• Memory is saved as pointers are not involved.

Disadvantages of array implementation:

• It is not dynamic i.e., it doesn’t grow and shrink depending on needs at runtime. [But in case of dynamic sized arrays like vector in C++, list in Python, ArrayList in Java, stacks can grow and shrink with array implementation as well].
• The total size of the stack must be defined beforehand.

Implementing Stack using Linked List:

C++

// C++ program for linked list implementation of stack
#include <bits/stdc++.h>
using namespace std;

// A structure to represent a stack
class StackNode {
public:
    int data;
    StackNode* next;
};

StackNode* newNode(int data)
{
    StackNode* stackNode = new StackNode();
    stackNode->data = data;
    stackNode->next = NULL;
    return stackNode;
}

int isEmpty(StackNode* root)
{
    return !root;
}

void push(StackNode** root, int data)
{
    StackNode* stackNode = newNode(data);
    stackNode->next = *root;
    *root = stackNode;
    cout << data << " pushed to stack\n";
}

int pop(StackNode** root)
{
    if (isEmpty(*root))
        return INT_MIN;
    StackNode* temp = *root;
    *root = (*root)->next;
    int popped = temp->data;
    free(temp);

    return popped;
}

int peek(StackNode* root)
{
    if (isEmpty(root))
        return INT_MIN;
    return root->data;
}

// Driver code
int main()
{
    StackNode* root = NULL;

    push(&root, 10);
    push(&root, 20);
    push(&root, 30);

    cout << pop(&root) << " popped from stack\n";

    cout << "Top element is " << peek(root) << endl;

    cout <<"Elements present in stack : ";
     //print all elements in stack :
    while(!isEmpty(root))
    {
        // print top element in stack
        cout << peek(root) <<" ";
        // remove top element in stack
        pop(&root);
    }

    return 0;
}

// This is code is contributed by rathbhupendra

C

// C program for linked list implementation of stack
#include <limits.h>
#include <stdio.h>
#include <stdlib.h>

// A structure to represent a stack
struct StackNode {
    int data;
    struct StackNode* next;
};

struct StackNode* newNode(int data)
{
    struct StackNode* stackNode =
      (struct StackNode*)
      malloc(sizeof(struct StackNode));
    stackNode->data = data;
    stackNode->next = NULL;
    return stackNode;
}

int isEmpty(struct StackNode* root)
{
    return !root;
}

void push(struct StackNode** root, int data)
{
    struct StackNode* stackNode = newNode(data);
    stackNode->next = *root;
    *root = stackNode;
    printf("%d pushed to stack\n", data);
}

int pop(struct StackNode** root)
{
    if (isEmpty(*root))
        return INT_MIN;
    struct StackNode* temp = *root;
    *root = (*root)->next;
    int popped = temp->data;
    free(temp);

    return popped;
}

int peek(struct StackNode* root)
{
    if (isEmpty(root))
        return INT_MIN;
    return root->data;
}

int main()
{
    struct StackNode* root = NULL;

    push(&root, 10);
    push(&root, 20);
    push(&root, 30);

    printf("%d popped from stack\n", pop(&root));

    printf("Top element is %d\n", peek(root));

    return 0;
}

Java

// Java Code for Linked List Implementation

public class StackAsLinkedList {

    StackNode root;

    static class StackNode {
        int data;
        StackNode next;

        StackNode(int data) { this.data = data; }
    }

    public boolean isEmpty()
    {
        if (root == null) {
            return true;
        }
        else
            return false;
    }

    public void push(int data)
    {
        StackNode newNode = new StackNode(data);

        if (root == null) {
            root = newNode;
        }
        else {
            StackNode temp = root;
            root = newNode;
            newNode.next = temp;
        }
        System.out.println(data + " pushed to stack");
    }

    public int pop()
    {
        int popped = Integer.MIN_VALUE;
        if (root == null) {
            System.out.println("Stack is Empty");
        }
        else {
            popped = root.data;
            root = root.next;
        }
        return popped;
    }

    public int peek()
    {
        if (root == null) {
            System.out.println("Stack is empty");
            return Integer.MIN_VALUE;
        }
        else {
            return root.data;
        }
    }

    // Driver code
    public static void main(String[] args)
    {

        StackAsLinkedList sll = new StackAsLinkedList();

        sll.push(10);
        sll.push(20);
        sll.push(30);

        System.out.println(sll.pop()
                           + " popped from stack");

        System.out.println("Top element is " + sll.peek());
    }
}

Python3

# Python program for linked list implementation of stack

# Class to represent a node


class StackNode:

    # Constructor to initialize a node
    def __init__(self, data):
        self.data = data
        self.next = None


class Stack:

    # Constructor to initialize the root of linked list
    def __init__(self):
        self.root = None

    def isEmpty(self):
        return True if self.root is None else False

    def push(self, data):
        newNode = StackNode(data)
        newNode.next = self.root
        self.root = newNode
        print ("% d pushed to stack" % (data))

    def pop(self):
        if (self.isEmpty()):
            return float("-inf")
        temp = self.root
        self.root = self.root.next
        popped = temp.data
        return popped

    def peek(self):
        if self.isEmpty():
            return float("-inf")
        return self.root.data


# Driver code
stack = Stack()
stack.push(10)
stack.push(20)
stack.push(30)

print ("% d popped from stack" % (stack.pop()))
print ("Top element is % d " % (stack.peek()))

# This code is contributed by Nikhil Kumar Singh(nickzuck_007)

C#

// C# Code for Linked List Implementation
using System;

public class StackAsLinkedList {

    StackNode root;

    public class StackNode {
        public int data;
        public StackNode next;

        public StackNode(int data) { this.data = data; }
    }

    public bool isEmpty()
    {
        if (root == null) {
            return true;
        }
        else
            return false;
    }

    public void push(int data)
    {
        StackNode newNode = new StackNode(data);

        if (root == null) {
            root = newNode;
        }
        else {
            StackNode temp = root;
            root = newNode;
            newNode.next = temp;
        }
        Console.WriteLine(data + " pushed to stack");
    }

    public int pop()
    {
        int popped = int.MinValue;
        if (root == null) {
            Console.WriteLine("Stack is Empty");
        }
        else {
            popped = root.data;
            root = root.next;
        }
        return popped;
    }

    public int peek()
    {
        if (root == null) {
            Console.WriteLine("Stack is empty");
            return int.MinValue;
        }
        else {
            return root.data;
        }
    }

    // Driver code
    public static void Main(String[] args)
    {

        StackAsLinkedList sll = new StackAsLinkedList();

        sll.push(10);
        sll.push(20);
        sll.push(30);

        Console.WriteLine(sll.pop() + " popped from stack");

        Console.WriteLine("Top element is " + sll.peek());
    }
}

/* This code contributed by PrinciRaj1992 */

Javascript

<script>
// javascript Code for Linked List Implementation

var root;

     class StackNode {

        constructor(data) {
            this.data = data;
            this.next = null;
        }
    }

     function isEmpty() {
        if (root == null) {
            return true;
        } else
            return false;
    }

     function push(data) {
        var newNode = new StackNode(data);

        if (root == null) {
            root = newNode;
        } else {
            var temp = root;
            root = newNode;
            newNode.next = temp;
        }
        document.write(data + " pushed to stack<br/>");
    }

     function pop() {
        var popped = Number.MIN_VALUE;
        if (root == null) {
            document.write("Stack is Empty");
        } else {
            popped = root.data;
            root = root.next;
        }
        return popped;
    }

     function peek() {
        if (root == null) {
            document.write("Stack is empty");
            return Number.MIN_VALUE;
        } else {
            return root.data;
        }
    }

    // Driver code
        push(10);
        push(20);
        push(30);

        document.write(pop() + " popped from stack<br/>");

        document.write("Top element is " + peek());

// This code is contributed by Rajput-Ji
</script>

Output

10 pushed to stack
20 pushed to stack
30 pushed to stack
30 popped from stack
Top element is 20
Elements present in stack : 20 10 

Advantages of Linked List implementation:

• The linked list implementation of a stack can grow and shrink according to the needs at runtime.
• It is used in many virtual machines like JVM.

Disadvantages of Linked List implementation:

• Requires extra memory due to the involvement of pointers.
• Random accessing is not possible in stack.