# 3.1: Stacks

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A stack is a basic data structure that can be logically thought of as a linear structure represented by a real physical stack or pile, a structure where insertion and deletion of items takes place at one end called top of the stack. The basic concept can be illustrated by thinking of your data set as a stack of plates or books where you can only take the top item of the stack in order to remove things from it. This structure is used all throughout programming.

The basic implementation of a stack is also called a LIFO (Last In First Out) to demonstrate the way it accesses data, since as we will see there are various variations of stack implementations.

There are basically three operations that can be performed on stacks. They are 1) inserting an item into a stack (push). 2) deleting an item from the stack (pop). 3) displaying the contents of the stack (peek or top).

Note:

Depending on the language and implementation the data structure may share the name with an abstract data type that support all of the data structure characteristics.

Below are some of operations a **stack data type** normally supports:

`Stack<item-type>`

Operations

**push**(`new-item`:item-type)

Adds an item onto the stack.

**top**():item-type

Returns the last item pushed onto the stack.

**pop**()

Removes the most-recently-pushed item from the stack.

**is-empty**():Boolean

True if no more items can be popped and there is no top item.

**is-full**():Boolean

True if no more items can be pushed.

**get-size**():Integer

Returns the number of elements on the stack.

All operations except `get-size()`

can be performed in \({\displaystyle O(1)}\) time. `get-size()`

runs in at worst \({\displaystyle O(N).}\)

**Linked List Implementation**

The basic linked list implementation is one of the easiest stack implementations you can do. Structurally it is a linked list.

type Stack<item_type> data list:Singly Linked List<item_type> "stack follows the LIFO (last in first out) operation" "queue follows the FIFO (first in first out) operation" constructor() list := new Singly-Linked-List() end constructor

Most operations are implemented by passing them through to the underlying linked list. When you want to **push** something onto the list, you simply add it to the front of the linked list. The previous top is then "next" from the item being added and the list's front pointer points to the new item.

method push(new_item:item_type) list.prepend(new_item) end method

To look at the **top** item, you just examine the first item in the linked list.

method top():item_type return list.get-begin().get-value() end method

When you want to **pop** something off the list, simply remove the first item from the linked list.

method pop() list.remove-first() end method

A check for emptiness is easy. Just check if the list is empty.

method is-empty():Boolean return list.is-empty() end method

A check for full is simple. Linked lists are considered to be limitless in size.

method is-full():Boolean return False end method

A check for the size is again passed through to the list.

method get-size():Integer return list.get-size() end method end type

A real Stack implementation in a published library would probably re-implement the linked list in order to squeeze the last bit of performance out of the implementation by leaving out unneeded functionality. The above implementation gives you the ideas involved, and any optimization you need can be accomplished by inlining the linked list code.

### Performance Analysis

In a linked list, accessing the first element is an \({\displaystyle O(1)}\) operation.The list contains a pointer that checks for empty/fullness as done here are also \({\displaystyle O(1)}\) (depending on what time/space tradeoff is made). Most of the time, users of a Stack do not use the `getSize()`

operation, and so a bit of space can be saved by not optimizing it.

Since all operations are at the top of the stack, the array implementation is now much, much better.

public class StackArray implements Stack { protected int top; protected Object[] data; ... }

The array implementation keeps the bottom of the stack at the beginning of the array. It grows toward the end of the array. The only problem is if you attempt to push an element when the array is full. If so

Assert.pre(!isFull(),"Stack is not full.");

will fail, raising an exception. Thus it makes more sense to implement with Vector (see StackVector) to allow unbounded growth (at cost of occasional O(n) delays).

Complexity:

All operations are O(1) with exception of occasional push and clear, which should replace all entries by null in order to let them be garbage-collected. Array implementation does not replace null entries. The Vector implementation does...