Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download COMP 103 Lecture 1 - School of Engineering and Computer Science
Document related concepts
no text concepts found
Transcript
COMP 103 Introduction to Trees Marcus Frean, Lindsay Groves, Peter Andreae, John Lewis, and Thomas Kuehne, VUW 2014-T2 Lecture 20 Marcus Frean School of Engineering and Computer Science, Victoria University of Wellington RECAP 2 RECAP Used linked lists to implement linear data structures Efficiency issues still remain TODAY Introduction to Trees Reading: Chapter 16 in textbook Announcements Remaining Efficiency Challenge 3 Linear Linked Structures (LinkedList, LinkedStack, …) adding but / removal operations are O(1) random access is expensive Why? reducing a search or access problem by 1 and leaving a subproblem of size n-1 is not a good divide & conquer strategy This is why a naïve QuickSort implementation can be slow (O(n2) in the worst case) Divide & Conquer 4 Challenge Guess the secret animal with as few questions as possible Strategy eliminate as many as possible in each step Mammal Egg Laying Bird Toby Tiger Lea Lion Bully Bulldog Carrie Collie Tanja Tui Reptile Kurt Kaka Tim Turtle Sally Snake Divide & Conquer 5 Linear access is slow only Toby Tiger one candidate eliminated at a time Lea Lion Bully Bulldog Carrie Collie Tanja Tui Kurt Kaka Tim Turtle Sally Snake Divide & Conquer 6 Linear access is slow only one candidate eliminated at a time Hierarchical access is fast many (proportional to total amount) eliminated at a time Mammal Feline Toby Tiger Egg Laying Canine Lea Lion Bully Bulldog Carrie Collie Bird Tanja Tui Reptile Kurt Kaka Tim Turtle Sally Snake From Linear to Hierarchical Access 7 Linear linkage structure Toby Tiger Lea Lion split into one head and the rest Bully Bulldog Carrie Collie Tanja Tui Kurt Kaka Tim Turtle Sally Snake From Linear to Hierarchical Access 8 Hierarchical linkage structure split into parts, each containing multiple elements Animal Mammal Feline Toby Tiger Egg Laying Canine Lea Lion Bully Bulldog Carrie Collie Bird Tanja Tui Reptile Kurt Kaka Tim Turtle Sally Snake From Linear to Hierarchical Access 9 Hierarchical linkage structure split into parts, each containing multiple elements Animal Mammal Feline Toby Tiger Egg Laying Canine Lea Lion Bully Bulldog Carrie Collie Bird Tanja Tui Reptile Kurt Kaka Tim Turtle Sally Snake Trees are Hierarchical Structures 10 Upside Down Trees? Animal Mammal Canine Feline Toby Tiger Egg Laying Leo Lion Bully Bulldog Carrie Collie Bird Tanja Tui Reptile Kurt Kaka Tim Turtle Sally Snake root Animal Mammal Egg Laying Canine Feline Toby Tiger branch Leo Lion Bully Bulldog Bird Carrie Collie Tanja Tui Reptile Kurt Kaka Tim Turtle Sally Snake leaves Some Terminology 11 Trees are Hierarchical Structures Trees are Hierarchical Structures 12 Same Terminology, different orientation Implementation withdespite LinkedNode++ support multiple successors, instead of just one root branch Animal leaves Mammal Canine Feline Toby Tiger Egg Laying Leo Lion Bully Bulldog Carrie Collie Bird Tanja Tui Reptile Kurt Kaka Tim Turtle Sally Snake Implementation as a Linked Structure 13 Implementation with LinkedNode++ support multiple successors, instead of just one Animal Mammal Canine Feline Toby Tiger Egg Laying Leo Lion Bully Bulldog Carrie Collie Bird Tanja Tui Reptile Kurt Kaka Tim Turtle Sally Snake Representing trees in Java 14 Generalised LinkedNode Linked List Nodes M F C Representing trees in Java 15 Generalised LinkedNode Binary Tree Nodes M F T C L Representing trees in Java 16 Generalised LinkedNode some collection type (ordered or unordered) General Tree Nodes … … … M F … … … T … … … C L … … … … … … Representing trees in Java 17 Arrays It is possible to represent trees with arrays No reference overhead! Clever assignment of nodes to array indices (we should get to this later on) More Tree Examples 18 Other Taxonomies e.g. game genres Organisational Charts CEO, Filing systems e.g., managers, employees, slaves, … the folder structure of your hard drive Computer Graphics models Octrees, for partitioning 3D space More Tree Examples 19 Other Taxonomies e.g. game genres Organisational Charts CEO, Filing systems e.g., managers, employees, slaves, … the folder structure of your hard drive Computer Graphics models Octrees, for partitioning 3D space More Tree Examples 20 Other Taxonomies e.g. game genres Organisational Charts CEO, managers, employees, slaves, … Filing systems e.g., the folder structure of your hard drive Computer Graphics models Octrees, for partitioning 3D space Decision processes … hierarchical structures naturally represented with trees (rather than using trees as an access technique) Planning 21 Tic Tac Toe search often not represented explicitly; only implicitly “created” by recursion tree for moves X X X X O X OX X X O X O X X O X O … … More Tree Terminology 22 A tree is a collection of items in a strict hierarchical structure. Each item is in a node of the tree. Children may be ordered/unordered The root is at the top. The leaves are at the bottom. Each node may have child nodes – except a leaf, which has none. Each node has one parent - except the root, which has none. An edge joins a node to its parent – may be labelled. Tree may or may not A subtree is a node plus all its descendents. store explicit parent references The depth of a node is its distance from the root. The height or depth of a tree is the depth of the lowest leaf. Level = set/list of nodes at the same depth. Branch = sequence of nodes on a path from root to a leaf. Terminology visualised 23 K O G C A I M Q E node, root, leaf, child, parent, edge, subtree, depth, height, level, branch, siblings, ancestors, descendants, cousins, …
