A stack is a linear data structure that store data in an order known as the **Last In First Out (LIFO)** order. This property is helpful in certain programming cases where the data needs to be ordered.

Stacks can be visualised like a stack of plates on a table. Only the top plate is accessible by the user at any given instant. The other plates are hidden and are not accessible by the user. The last plate that is kept on the stack is retrieved first.

## Operations in a Stack

The two primary operations in a stack are the **push** and the **pop** operations:

### Push Operation

This is used to add (or push) an element to the stack. The element always gets added to the top of the current stack items.

### Pop Operation

This is used to remove (or pop) an element from the stack. The element always gets popped off from the top of the stack.

### Peek Operation

The peek operation is used to return the first element of the stack without removing the element. It is a variation of the pop operation.

### Overflow and Underflow Conditions

A stack may have a limited space depending on the implementation. We must implement check conditions to see if we are not adding or deleting elements more than it can maximum support.

The underflow condition checks if there exists any item before popping from the stack. An empty one cannot be popped further.

if (top == -1) { // underflow condition }

The overflow condition checks if the stack is full (or more memory is available) before pushing any element. This prevents any error if more space cannot be allocated for the next item.

if (top == sizeOfStack) { // overflow condition }

### About the top pointer

To efficiently add or remove data, a special pointer is used which keeps track of the last element inserted in the structure. This pointer updates continuously and keeps a check on the **overflow and underflow** conditions.

## Creating a stack

A stack can be created using both an array or through a linked list. For simplicity, we will create one with an array.

- First, we create a one-dimensional array with fixed size (
`int stack[SIZE]`

). The SIZE value could be defined using a preprocessor. - Define a integer variable
`top`

and initialize with ‘-1’ (`int top = -1`

).

#define SIZE 10 int stack[SIZE]; int top = -1;

### Pushing to the stack

**Steps**

- Check whether stack is FULL. (
`top == SIZE-1`

) - If it is FULL, then terminate the function and throw an error.
- If it is NOT FULL, then increment top value by one (top++) and set
`stack[top]`

to`value`

(`stack[top] = value`

).

void push(int value) { if(top == SIZE-1) printf("\nOverflow. Stack is Full"); else{ top++; stack[top] = value; printf("\nInsertion was successful"); } }

### Popping from the stack

**Steps**

- Check whether stack is EMPTY. (
`top == -1`

) - If it is EMPTY, then terminate the function and throw an error.
- If it is NOT EMPTY, then delete
`stack[top]`

and decrement top value by one (`top--`

).

void pop() { if(top == -1) printf("\nUnderflow. Stack is empty"); else{ printf("\nDeleted : %d", stack[top]); top--; } }

### Accessing the top element (Peeking)

**Steps**

- Check whether stack is EMPTY (
`top == -1`

). - If it is EMPTY, then terminate the function and throw an error.
- If it is NOT EMPTY, then return
`stack[top]`

.

void peek() { if(top == -1) { printf("\n The stack is empty"); break; } else printf("%d", stack[top]); }

## Stack Complexity

### Access

An element in a stack can only be accessed by continuously removing the front element until the required element is found. This means that the time complexity is O(n).

### Search

Similar to accessing an element, searching an element will involve continuously popping an element until the required element is found. The time complexity is hence O(n).

### Insertion

Inserting an element is only possible at the top of the stack. There is no interaction needed with the rest of the elements. It is hence an O(1) operation.

### Deletion

Similar to insertion, deleting an element is only possible from the top of the stack. There is no interaction needed with the rest of the elements. It is hence an O(1) operation.

### Space Required

A stack only takes the space used to store the elements of the data type specified. This means that for storing n elements the space required is O(n).

## Applications of Stacks in Programming

**UNDO functionality in text editors**: Every change in the document is added to stack and upon a UNDO request, the last change is referred by popping it.**Parentheses checker**: The ordered manner of the stack could be used for checking the proper closing of parentheses. Every opening parentheses is pushed on to the stack and for every correct closing parentheses, it is popped off. Irregularities can then be detected if they mismatch.**Expression parsing**: Using stacks can help evaluate expressions faster using postfix or prefix notation.

## Visualizations

Stacks | VisuAlgo Stack (Array Implementation) | University of San Francisco Stack (Linked List Implementation) | University of San Francisco

## Videos

**Shorter**

- Stacks | CS50 A short and simple theoretical explanation on stacks from the popular CS50 course.
- What is a Stack Data Structure – An Introduction to Stacks | Paul Programming Good explanation from channel Paul Programming. Explains the basic functions.
- Data Structures: Stacks and Queues | HackerRank Popular book writer
**Gayle Laakmann McDowell**explains about stacks and queues in this HackerRank video. - Stacks and Queues | 0612 TV w/ NERDfirst
- Data structures: Introduction to stack | mycodeschool Good explanation from mycodeschool about stacks.

**Longer**

- CS 106B Lecture: Stacks and Queues | Stanford Full class lecture of CS 106B, Spring 2015, Stanford University.

## Continue Reading

**Stacks using Linked List**: Read about how to implement a stack using linked lists.**Expression Parsing**: Read about an application of stacks, expression parsing.