Trees

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Trees
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Example Tree
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Formal Definition (from Googles definetree)

• In graph theory, a directed acyclic graph (DAG)
  in which the root node has no parent and every
  other node has exactly one parent.www.mindspring.
  com/scarlson/tc/glossary.htm
• In computer science, a tree is a widely-used
  computer data structure that emulates a tree
  structure with a set of linked nodes. Each node
  has zero or more child nodes, which are below it
  in the tree (in computer science, unlike in
  nature, trees grow down, not up). A node that has
  a child is called the child's parent node. A
  child has at most one parent a node without a
  parent is called the root node (or root). Nodes
  with no children are called leaf nodes.
  en.wikipedia.org/wiki/Tree_(computing)

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Tree Terminology
Root A
Leaf D, E, G, J, K, L
Non-leaf A, B, C, F, H
Subtree ( of F ) F, G, H, J, K, L
Natural Order A, B, D, E, C, F, G, H, J , K, L
Level (of F) 2

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Uses of Trees

• Paragraph Numbering in a Document
• Family (aSexual reproduction!)
• File system e.g. Unix, Dos
• Classification e.g. Linaus, Dewey
• Hierarchical Database e.g. IBMs MIS, LDAP
• Web site structure
• Hierarchical Menu
• Organisational Hierarchy
• Class Hierarchy in Java
• Assembly / Part hierarchy
• Document Object Model
• XML
• B-tree for efficient indexing

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Legal Numberingin a document
In natural order with A as root   1          B 1.1       D 1.2        E 2.          C 2.1        F 2.1.1     G 2.1.2     H 2.1.2.1  J 2.1.2.2  K 2.1.2.3  L
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Family TerminologyFor object F
Parent (at most 1) C
Children G, H
Siblings (none)
Descendents G, H, J, K, L
Ancestors C, A
Node and Descendents F, G, H, J, K, L
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File system

• File system in Unix or Windows
• C\Program Files\eXist\webapp\admin\admin.xql
• Actually this is a Forest of trees, each drive
  a separate Tree

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Folder Hierarchy
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Navigation in File System(from F)
Root /
Current directory (context) .
Child G G (or ./G)
Parent ..
Sibling (none)
Cousin ../../B/E
Absolute Path /A/C/F
Leaf name File
Node name Directory or Folder
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Taxonomy

• Animal Kingdom
• Home Kingdom Animalia Phylum Arthropoda
  Class Insecta Order Lepidoptera Suborder
  Macrolepidoptera Family Nymphalidae Species
  Vanessa atalanta
• Knowledge
• Dewey Decimal Classification
• Finding Butterflies

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Type (A Kind of) Hierarchyrelative to F
supertype C
subtype G, H
G and H would inherit all the attributes and
methods of F and define additional attributes and
methods of their own.  A type hierarchy allows
sharing of definitions. see Normalisation Easi
ly confused with an Object Hierarchy or
Whole/Part hierarchy.
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Object Hierarchy

• An object hierarchy supports one or more of a
  number of kinds of relationship.
• Containment 
• One object is contained within, is a part of, 
  a parent object.  A containment relationship is
  used to move, copy or delete a whole subtree.
• Scoping 
• Names of objects must be unique within some
  scope. Often these scopes are hierarchical.  The
  name of a child is unique within the scope of the
  parent. 
• Delegation 
• A child object delegates responsibility for a
  property to its parent, and so on up the
  hierarchy until an object defines the property. 
• Aggregation 
• A parent object has properties determined by the
  properties of its children.  For example, the
  value of the cost in a non-leaf would be
  defined as the sum of cost values over all
  children, with actual cost values defined at the
  leaves. Min, max, average are other aggregate
  relationships.
• Distribution 
• A parent property is distributed over the
  children for example a budget value defined in
  the parent is distributed over the children.

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HTML Document (Object Tree)
lthtmlgt ltheadgt lttitlegtSample
Documentlt/titlegt lt/headgt ltbodygt
lth1gtAn HTML Documentlt/h1gt ltpgtThis is
a ltigtsimplelt/igt document. lt/pgt lt/bodygt
lt/htmlgt
From Flanagan,D. (2002) JavaScript The Definitive
Guide , OReilly on-line
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DOM Class Tree
From Flanagan,D. (2002) JavaScript The Definitive
Guide , OReilly on-line
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  XPATH DOM
Declarative Procedural (navigational)
Root /  document
Context Node Current Directory (self) .
Local Name n  
Child 1 last() n.childNodes n.firstChild n.lastChild
Parent .. f.parentNode
Sibling ../g ../ f.nextSibling f.previousSibling
Attribute f/_at_att f.getAttribute(att) 
Locate node by ID //_at_id'f1' documents.getElementByID('f1') 
Locate nodes by Tag //img document.getElementsByTagName('img')
Number of nodes in sequence s.length s.length
Select by predicate _at_size 10 and . 'fred'
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Exercise

• XPath Vizualiser

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Exercises(based on hoax.xml)

• Write XPath expressions to locate the following
• The recipe title
• All recipe ingredients
• The amount of brown sugar
• The last instruction
• Write DOM code to access the same data