**What is stack?**

A stack is a container of objects that are inserted and removed according to the

**last-in-first-out (LIFO)**principle.Objects can be inserted at any time, but only the last (the most-recently inserted) object can be removed.

Inserting an item is known as “Pushing” onto the stack. “Popping” off the stack is synonymous with removing an item

Used in Operating system to implement method calls, and in evaluating Expressions.

**ADT Stack: Specification**

** Elements:** The elements are of a generic type <Type>. (In a linked implementation an element is placed in a node)

** Structure:** the elements are linearly arranged, and ordered according to the

**order of arrival**, most recently arrived element is called

__top__.

** Domain:** the number of elements in the stack is bounded therefore the domain is finite. Type of elements: Stack

** Elements:** The elements are of a generic type <Type>. (In a linked implementation an element is placed in a node)

** Structure:** the elements are linearly arranged, and ordered according to the

**order of arrival**, most recently arrived element is called

__top__.

** Domain:** the number of elements in the stack is bounded therefore the domain is finite. Type of elements: Stack

** Operations**:

All operations operate on a stack S.

1.**Method** push (Type e)

**requires:** Stack S is not full.

**input:** Type e.

**results:** Element e is added to the stack as its most recently added elements.

**output:** none.

2.**Method** pop (Type e)

**requires**: Stack S is not empty.

**input**: none

**results**: the most recently arrived element in S is removed and its value assigned to e.

**output**: Type e.

3.**Method** empty (boolean flag)

**input**: none

**results**: If Stack S is empty then flag is true, otherwise false.

**output**: flag

4.**Method** Full (boolean flag).

**requires**:

**input**: none

**results**: If S is full then Full is true, otherwise Full is false.

**output**: flag.

**Stack Interface**

```
public interface Stack<T>{
public T pop( );
public void push(T e);
public boolean empty( );
public boolean full( );
}
```

**ADT Stack (Linked-List)**

Below the structure of stack implementation

**Linked-List: Element**

**public class **Node<T> {
**public **T data;
**public **Node<T> next;
**public **Node () {
data = **null**;
next = **null**;
}
**public **Node (T val) {
data = val;
next = **null**;
}
// Setters/Getters?
}

**Linked-List: Implementation**

**public class **LinkedStack<T> implements Stack<T> {
**private** Node<T> top;
/* Creates a new instance of LinkStack */
**public **LinkedStack() {
top = **null**;
}

**Linked-List Array Representation**

**public class **ArrayStack<T> implements Stack<L> {
**private int **maxsize;
**private int** top;
**private **T[] nodes;
/** Creates a new instance of ArrayStack */
**public **ArrayStack(**int** n) {
maxsize = n;
top = -1;
nodes = (T[]) **new** Object[n];
}

**public boolean** empty(){
**return** top == -1;
}
**public boolean** full(){
**return** top == maxsize - 1;
}

**public void **push(T e){
nodes[++top] = e;
}
**public **T pop(){
**return **nodes[top--];
}
}

**Applications of Stacks**

Some applications of stacks are:

Balancing symbols.

Computing or evaluating postfix expressions.

Converting expressions from infix to postfix.

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