Stack Data Structure (Introduction and Program) - GeeksforGeeks

24 Apr, 2022
Stack is a linear data structure that follows a particular order in which the operations are performed. The order may be LIFO(Last In First Out) or FILO(First In Last Out).
Mainly the following four basic operations are performed in the 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
Peek or Top: Returns the top element of the stack.
Algorithm for peek:
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
How to understand a 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.
Time Complexities of operations on the stack:
push(), pop(), isEmpty() and peek() all take O(1) time. We do not run any loop in any of these operations. 
Applications of the stack:
Balancing of symbols
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: There are two ways to implement a stack: 
Using array
Using linked list
Implementing Stack using Arrays
C++
C
Java
Python3
C#
Javascript
/* 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 functionsint main(){    class Stack s;    s.push(10);    s.push(20);    s.push(30);    cout << s.pop() << " Popped from stack\n";    //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 program for array implementation of stack#include <limits.h>#include <stdio.h>#include <stdlib.h> // A structure to represent a stackstruct Stack {    int top;    unsigned capacity;    int* array;}; // function to create a stack of given capacity. It initializes size of// stack as 0struct 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 indexint isFull(struct Stack* stack){    return stack->top == stack->capacity - 1;} // Stack is empty when top is equal to -1int isEmpty(struct Stack* stack){    return stack->top == -1;} // Function to add an item to stack.  It increases top by 1void 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 1int pop(struct Stack* stack){    if (isEmpty(stack))        return INT_MIN;    return stack->array[stack->top--];} // Function to return the top from stack without removing itint peek(struct Stack* stack){    if (isEmpty(stack))        return INT_MIN;    return stack->array[stack->top];} // Driver program to test above functionsint 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 program to implement basic stackoperations */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 codeclass 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();    }}
# Python program for implementation of stack # import maxsize from sys module# Used to return -infinite when stack is emptyfrom sys import maxsize # Function to create a stack. It initializes size of stack as 0def createStack():    stack = []    return stack # Stack is empty when stack size is 0def isEmpty(stack):    return len(stack) == 0 # Function to add an item to stack. It increases size by 1def push(stack, item):    stack.append(item)    print(item + " pushed to stack ")     # Function to remove an item from stack. It decreases size by 1def pop(stack):    if (isEmpty(stack)):        return str(-maxsize -1) # return minus infinite         return stack.pop() # Function to return the top from stack without removing itdef 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# program to implement basic stack// operationsusing 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 functionsclass Program {    static void Main()    {        Stack p = new Stack(5);         p.push(10);        p.push(20);        p.push(30);        p.printStack();        p.pop();    }}}
<script>/* javascript program to implement basic stackoperations*/ 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  
Pros: Easy to implement. Memory is saved as pointers are not involved. Cons: It is not dynamic. It doesn’t grow and shrink depending on needs at runtime. Implementing Stack using Linked List:
C++
C
Java
Python3
C#
Javascript
// C++ program for linked list implementation of stack#include <bits/stdc++.h>using namespace std; // A structure to represent a stackclass 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 codeint 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 program for linked list implementation of stack#include <limits.h>#include <stdio.h>#include <stdlib.h> // A structure to represent a stackstruct 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 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());    }}
# 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 codestack = 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# Code for Linked List Implementationusing 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 */
<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 
Pros: The linked list implementation of a stack can grow and shrink according to the needs at runtime. Cons: Requires extra memory due to involvement of pointers.
https://youtu.be/vZEuSFXSMDI  We will cover the implementation of applications of the stack in separate posts.
Stack Set -2 (Infix to Postfix)  
Quiz: Stack Questions
References: http://en.wikipedia.org/wiki/Stack_%28abstract_data_type%29#Problem_Description
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