Graphs, Trees, Objects
UC Santa Cruz
CMPS 10 – Introduction to Computer Science
www.soe.ucsc.edu/classes/cmps010/Spring11
ejw@cs.ucsc.edu
8 April 2011
Class website
 http://www.soe.ucsc.edu/classes/cmps010/Spring11/
 Please write this down, and bookmark it
 Holds:
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Syllabus (including homework due dates)
Homework assignment descriptions
Description of course readings
Links to class lecture notes
 The final exam is scheduled for Tuesday, June 7, 8am-11am
 This class will have a final exam. Please plan on this.
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Tutoring available
 Learning Support Services (LSS)
 Has tutoring available for students in CMPS 10
 Students meet in small groups, led by a tutor
 Students are eligible for up to one-hour of tutoring per week per
course, and may sign-up for tutoring at
https://eop.sa.ucsc.edu/OTSS/tutorsignup/ beginning April 5th at
10:00am.
 Brett Care - bcare@ucsc.edu is the tutor for CMPS 10 that LSS has
hired
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Abstraction and Models
 Converting the real world into data:
 Create a model of the real world
 Represent that model in data
 How do you model the real world?
 Involves a process called abstraction
 Abstraction
physical world
abstraction
model
representation
data
(inside
computer)
 Prerequisite: know your problem or application
 Focus on aspects of the real world that are important to the problem
 Add those elements to your model
 Omit elements of the real world that aren’t relevant
 Implies: the same real world scenario can be modeled in many ways,
depending on the problem at hand
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Representing models as data
 Most models can be represented using:
 Basic data types
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Integers
Floating point
Boolean
Characters
Strings
 Basic data structures
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Arrays
Lists
Stacks/Queues
Trees
Graphs
 Clusters of data
 Modeling data as classes
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Modeling a music collection
 Consider your music collection
 There are many songs
 Each song belongs to an album
 OK, OK, I know there are a lot of loose singles these days, but work with me here…
 Each album has a dominant musical style (pop, rock, classical, etc.)
 Say we want to organize this musical collection
 By style, then album, then song
All music
rock/pop
The Fame
Just Dance
Poker Face
Thriller
Beat It
classical
25 Bach Favorites
Tocatta
Alegro
bluegrass
Best Loved Bluegrass
White House Blues
Train 45
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Modeling a music collection (cont’d)
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This is a hierarchical structure
 Occurs frequently: organizational charts, evolutionary tree in biology, work breakdown
structure in project management,
 databases, filesystems, programming languages
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Hierarchical structures are represented using trees
 Elements of a tree can be of any type. Tree of strings, tree of integers, tree of floats, etc.
 For the music collection, the hierarchical structure can be represented as a tree of
strings
 Music_collection is tree of string
All music
rock/pop
The Fame
Just Dance
Poker Face
Thriller
Beat It
classical
25 Bach Favorites
Tocatta
Alegro
bluegrass
Best Loved Bluegrass
White House Blues
Train 45
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Tree terminology
 There are some special terms that are used to describe trees
 The elements of a tree are called nodes
 The topmost element is called the root
 An element can have one or more child nodes
 Node “classical” is a child of node “All music”
 Node “Thriller” is a child of node “rock/pop”
 An element with no children is a leaf node
 Every node, except the root, has a parent node
 Node “rock/pop” is the parent of node “Thriller”
root node
All music
rock/pop
The Fame
Just Dance
Poker Face
Thriller
Beat It
classical
25 Bach Favorites
Tocatta
Alegro
bluegrass
Best Loved Bluegrass
White House Blues
Train 45
One of 7 leaf nodes
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Tree operations
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Trees typically support the following operations
 Insert_child(given_node, contents)
 Adds a new node with contents as a child of given_node
 Example: Insert_child(Node:The Fame, “Paparazzi”)
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Creates a new node, under “The Fame”, with contents
“Paparazzi”
The Fame
 Parent(given_node)
 Provides the parent node for given_node
 Example: Parent(Node:Poker Face) is Node:The Fame
 Leftmost_child(given_node)
Just Dance
Poker Face
Paparazzi
 Provides the leftmost child of the given_node
 Example: Leftmost_child(Node:The Fame) is “Just
Dance”
 Right_sibling(given_node)
 Provides the next sibling to the right, or null if there is
none
 Example: Right_sibling(Node:Poker Face) is
Node:Paparazzi
 Example: Right_sibling(Node:Paparazzi) is null
 Delete(given_node)
 Deletes the given node and all children
 Delete(Node:Poker Face) deletes just Poker Face
 Delete(Node:The Fame) deletes The Fame, Just Dance,
Poker Face, and Paparazzi
The Fame
Just Dance
Poker Face
Right_sibling
Paparazzi
Right_sibling
Can navigate through a tree using
leftmost_child, right_sibling, and
parent!
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Graph
 The physical world contains many networks
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Towns connected by (rail)roads
Cities connected by airline flights
Pumping stations connected by water pipes
Houses and businesses connected to power stations by electrical
wires
A portion of United Airline’s Flight Route Network
content.united.com/ual/asset/UAL_NA_Map.pdf
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Graph
 A graph is a set of nodes (vertices) connected by edges (arcs)
 Often (but not always) two nodes can be connected by only one edge
 An undirected graph is one where the edges have no directionality (i.e., no
arrows)
 Can represent situations like a road, where cars can go in either direction
 A directed graph (or digraph) is one where the edges are directional (have
edges)
 Can represent situations like a water pipe network, where water typically flows in
one direction
 A node can be any type (string, integer, float, etc.)
 Edges are often labeled with data as well (string, integer, etc.)
An undirected graph with 6 nodes and 7 edges
A directed graph with 3 nodes and 3 edges
en.wikipedia.org/wiki/Graph_(mathematics)
en.wikipedia.org/wiki/Graph_(mathematics)
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Graphs in Computer Science
 Graphs are broadly useful in computer science
 Represent internal dependency structure inside software programs
 I.e., which functions/methods call which other ones?
 Represent network information
 How elements of the Internet are connected
 Represent relationships among items
 Dog is-a-kind-of mammal, dog is-a-kind-of pet, humans like pets, etc.
ConceptNet is a network of
common sense knowledge
about the world. Can be used
by software to reason about
items in the world. Open
source (freely available)
csc.media.mit.edu/conceptnet
Fragment of the Concept Net network
csc.media.mit.edu/conceptnet
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Grouping data together, treating it as one
 So far, we have focused on real world situations that can be modeled using
combinations of one single basic data type
 Temperature, which is represented using a float
 Song title, represented using a string
 More typical are situations where multiple data items are needed for a
complete representation
 Temperature
 Value: float
 Units: Fahreheit or Celsius or Kelvin
 Time: time & date (when measurement was taken)
 Song
 Title: string
 Artist: string
 Year: integer
 Ideally want to clump these together and deal with them as a whole
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Grouping data together: objects
 There are several ways of grouping data together
 Two that will be discussed in this class
 Tables in a database
 More on this when we consider databases
 Object modeling
Example of a database table
www.dwreview.com/Data_mining/DM_models.html
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Class & object modeling
 Group a series of related data items together
 Package these up into a class
 A class contains a series of related data items
 A container for data
 Each data item is either a data structure or a basic data type
 A data structure contains a series of basic data types
 A specific example of a class is called an object
 An object is an instance of a class
 Use a class box to visually
depict a class
 This is part of the unified modeling
language (UML), a common way of
visually depicting software
designs…
Class name
Data item 1: data type
Data item 2: data structure of data
type
Data item 3: data type
…
Operations
These are operations that work on the data in the class. They are
super important for object oriented programming, but we’re not
going to talk about them now…
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Class & object modeling example
 Consider again a song
 Song
 Title: string
 Artist: string
 Year: integer
 Its class box is
 Song is a class
Song
Title: String
Artist: String
Year: Integer
 It is what a lot of different
individual songs look like
 It represents the set of all songs
 Instances of song are song
objects
 Any individual, specific song will
have all of the data items filled in
 It has been “instantiated”
(an instance of it has been made)
Title: Poker Face
Artist: Lady Gaga
Year: 2008
Title: Video Killed the Radio Star
Artist: The Buggles
Year: 1979
Two instances of song – song objects
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Relationships among classes
 Is-a relationship
Clothing
 Sometimes you have situations
where there is a general class of
item, and then there are multiple
distinct subclasses
 Example
 The term “clothing” covers a wide
range of items that people wear.
 Might want to also model pants,
shirts, skirts, dresses, belts, socks,
etc.
 Each of these has specific
measurements and hence would
need to be modeled differently
Brand name: string
Price: float
Color: string
Fabric: string
Pants is-a
Clothing
parent
child
child
Socks is-a
Clothing
Pants
Socks
Waist: integer
Inseam: integer
Size_min: integer
Size_max: integer
 Use a
to visually
depict the is-a relationship
 Also known as subclass
relationship
 Also: parent-child relationship
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Children inherit data fields
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The children of a subclass relationship inherit
the data fields of all parents
In the example
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Pants has
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Waist: integer
Inseam: integer
And also
Brand name: string
Price: float
Color: string
Fabric: string
Socks has
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Clothing
Size_min: integer
Size_max: integer
And also
Brand name: string
Price: float
Color: string
Fabric: string
Brand name: string
Price: float
Color: string
Fabric: string
Pants is-a
Clothing
parent
child
child
Socks is-a
Clothing
Pants
Socks
Waist: integer
Inseam: integer
Size_min: integer
Size_max: integer
Clothing only has
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Brand name: string
Price: float
Color: string
Fabric: string
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In-class exercise
 With a neighbor, make a class model of the following:
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In-class exercise: answer
 There are several ways to approach this modeling problem
 Here’s one
 Let’s assume we’re modeling vegetables for a supermarket checkout
point of sale use
 In this case, we care about:
 Description of vegetable (for the register receipt)
 Price per pound
Could also just model this as “Vegetable” – there is nothing
particularly pepper-related here
Pepper
Description: string
Price: float
Some instances:
Description: “Green pepper”
Price: 1.59
Description: “Yellow pepper”
Price: 3.19
Description: “Red pepper”
Price: 2.39
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In-class exercise: answer #2
 Here’s another modeling approach
 Let’s assume we’re modeling peppers for a cooking application
 In this case, we care about:
 Pepper type (red pepper, green pepper, etc.)
 Color (for presentation)
 Heat (is it a hot pepper?)
Another common basic data type is an enumeration. Using an
Pepper
Type: string
Color: string
Hot: boolean
enumeration, you can list all of the possible values a variable can
take. In this case, could model type as a Pepper_type
enumeration, with possible values of Red, Green,Yellow. (A
similar approach could be used for colors, using a Color_type
enumeration, with Red, Green, and Yellow values). Instead, for
this example, we use a string to hold the values “Red”,
“Green”, “Yellow”.
Some instances:
Type: “Green pepper”
Color: “Green”
Hot: false
Type: “Yellow pepper”
Color: “Yellow”
Hot: true
Description: “Red pepper”
Color: “Red”
Hot: true
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In-class exercise: answer #3
 Here’s another modeling approach
 Let’s assume we’re modeling peppers for a cooking application
 But, we also have other vegetables we’re interested in modeling
 In this case, we care about:
 What is specific about peppers that is different from other vegetables
 All vegetables have a type, and a color
Vegetable
 Only peppers have a heat
Type: string
Color: string
Some Pepper instances:
Type: “Green pepper”
Color: “Green”
Hot: false
Type: “Yellow pepper”
Color: “Yellow”
Hot: true
Some Vegetable instances:
Type: “Eggplant”
Color: “Purple”
Pepper
Hot: boolean
Type: “Carrot”
Color: “Orange”
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New exercise
 Model the following as a class
 Assume it’s for a graphic design application, so we want to model the
length, whether it is sharp, and color
Flickr: stevendepolo
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In-class exercise: answer
 Represent:
 Length as a float (since the length could be a fraction of an inch, or
centimeter)
 Color as a string
 Could also be an enumeration
 Sharp as a boolean
 True means sharp
Pencil
Length: float
Color: string
Sharp: boolean
Some instances:
Length: 5.25
Color: “pink”
Sharp: true
Length: 3.125
Color: “sky blue”
Sharp: false
Length: 4.75
Color: “yellow”
Sharp: true
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New exercise
 Model the following situation using classes
 Assume this is also for a graphic design use, so we’re interested in pencil vs
pen vs highlighter, color, sharpness, and type of tip (ball, chisel)
Flickr: calliope
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In-class exercise
 For this situation, need to use multiple classes, and inheritance
 One class to model “drawing device”
 Used for common qualities, such as color
 Subclasses for specific qualities
 Pencil: sharpness
 Pen: tip type
 Highlighter: tip type
Drawing Device
Color: string
Pencil instance:
Color: “grey”
Sharp: true
Pen instance:
Pencil
Sharp: boolean
Pen
Tip: string
Highlighter
Tip: string
Color: “red”
Tip: “ball”
Highlighter instance:
Color: “yellow”
Tip: “chisel”
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