# Introduction to Stack – Data Structure and Algorithm Tutorials

• Difficulty Level : Easy
• Last Updated : 14 Sep, 2022

## Stack

It is a linear data structure that follows a particular order in which the operations are performed.

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 is 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

## Types of Stacks:

• Register Stack: This type of stack is also a memory element present in the memory unit and can handle a small amount of data only. The height of the register stack is always limited as the size of the register stack is very small compared to the memory.
• Memory Stack: This type of stack can handle a large amount of memory data. The height of the memory stack is flexible as it occupies a large amount of memory data.

## 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.

## Implementation of Stack:

There are two ways to implement a stack

• Using array
• Using linked list

## C++

 `/* C++ program to implement basic stack``   ``operations */``#include `` ` `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 poping``    ``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 ``#include ``#include `` ` `// 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

 ``

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.
• It doesn’t grow and shrink depending on needs at runtime.

## C++

 `// C++ program for linked list implementation of stack``#include ``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 ``#include ``#include `` ` `// 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

 ``

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 ```

• 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.
• Stacks are more secure and reliable as they do not get corrupted easily.
• Stack cleans up the objects automatically.