MIS 215 Module 3

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MIS 215 Module 3 Stacks and Queues
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Where are we?
MIS215
Basic Algorithms
Introduction
List Structures
Advanced structures
Search Techniques
Intro to Java, Course
Sorting Techniques
Java lang. basics
Hashtables
Linked Lists
Binary Search
Graphs, Trees
Stacks, Queues
Arrays
Bubblesort
Fast Sorting algos (quicksort, mergesort)
Newbie
Programmers
Developers
Professionals
Designers
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Todays buzzwords

• Stack
• A data structure where items can be added to the
  top and removed from the top
• A LIFO (Last In, First Out) Structure
• Queue
• A data structure which can be used to add
  elements at one end, and remove from another
• A FIFO (First In, First Out) Structure
• Priority Queue
• A queue where highest priority items are removed
  first
• Expression Notations
• Infix standard notation ABC-D
• PostFix notation for better computability
  ABCD-
• PreFix Functional Notation -ABCD

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Stacks..

• Think of a postmans mail box...
• Before delivery, they push items on to it,
  i.e., put them on the top of the stack
• they keep going to the bottom
• During delivery, they pop items off it (cant
  reach down)
• they are the last items put on
• Other real-life scenarios?
• Is it possible you would never pop off the first
  item you pushed on?
• thats starvation

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What are some stacks?
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Stacks Concepts
Push box Q onto empty stack
A
Push box A onto stack
Pop a box from stack
Pop a box from stack
(empty)
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Stack ADT

• Properties
• items are ordered by arrival (so not sorted)
• can only access the last one stored
• commonly called Last-In-First-Out (LIFO)
• Actions
• push store an item
• pop retrieve an item
• peek see next item w/o retrieving
• size, full, empty

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Implementation of Stacks

• Implementation of stacks, like the one for any
  other data structures, includes two basic
  approaches
• Contiguous implementation
• Stack entries are stored in arrays
• Data are accessed by using indices
• linked implementation
• Stacks entries are stored in linked lists
• Data are accessed by using references

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Contiguous Stacks
Stack
Stack
Stack
bottom
bottom
Tom
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Tom
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Tom
0 1 2 3 4 5 6 7 8 9 10 11 12 13
John
John
John
Mary
Mary
Mary
Sue
Sue
Sue
Jim
Jim
Jim
Rick
Rick
Rick
top
Bob
Bob
--
Barb
Barb
--
Diana
top
Diana
top
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
After 3 pops
After 9 pushes onto an empty stack
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Queues

• You know what a queue is -- its a line you wait
  in
• Items get added to the end (rear, back, tail)
• Items come off the front (head)
• commonly called First-In-First-Out (FIFO)
• I personally prefer head/tail or front/rear
• Eventually, an item comes off, right?
• no starvation

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Queue ADT

• Properties
• items are ordered by arrival (so not sorted)
• you access the oldest one inserted
• Actions
• insert/enqueue/add
• remove/dequeue/delete
• peek, see next item w/o removing
• size, full, empty

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Implementation of Queues

• The Physical model
• A linear array with the front always in the first
  position
• Whenever front is deleted all the entries moved
  up.
• A linear array with two indices always
  increasing.
• A circular array with front and rear indices and
  one position left vacant.
• A circular array with front and rear indices and
  a Boolean variable to indicate fullness (or
  emptiness)

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Example of a Circular Array
This is only a logical circle!
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Efficiencies...

• Whats the complexity?
• Remember what we mean by complexity?
• how is the amount of work dependent upon the size
  of the input data?

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Stack and Queue Complexity
Operation Stack Queue
create/constructor O(1) O(1)
size
clear
push N/A
pop N/A
peek
Insert/enqueue N/A
remove/dequeue N/A
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Priority queues

• keep the items ordered by priority in the queue
• so, clearly, not FIFO, right?
• can an item be starved?

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Priority queue efficiency

• Typical Array Implementation
• insertion O(N)
• you gotta move things around to keep them ordered
• deletion O(1)

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Discussion Uses of Stacks and Queues

• Reversing words
• Checking for palindromes
• Matching brackets in expressions
• CPU scheduling in Operating Systems
• Later Traversal of Trees

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How would you reverse a word?

• Input structure Output erutcurts

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In-class exercise Parsing

• One simple thing that a parser needs to do is to
  check for matched brackets ( )
• Problem Write a Java program that takes in a
  program and decides if the program is valid or
  not
• How would you solve it?

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Parsing steps