Traversals Common set of algoritms on trees are traversals A way of visiting all the nodes of a tree “Visit” is defined as performing one operation on a node a b c g d f e h i Traversals Three basic traversals Preorder Postorder Inorder Preorder Traversal

ByEmpirical Methods for AI & CS. Paul Cohen Ian P. Gent Toby Walsh cohen@cs.umass.edu ipg@dcs.st-and.ac.uk tw@cs.york.ac.uk. Introduction What are empirical methods? Why use them? Case Study Eight Basic Lessons Experiment design Data analysis

ByBinary Trees. Linear data structures. Here are some of the data structures we have studied so far: Arrays Singly-linked lists and doubly-linked lists Stacks, queues, and deques Sets These all have the property that their elements can be adequately displayed in a straight line

ByB-Trees. Motivation for B-Trees. So far we have assumed that we can store an entire data structure in main memory What if we have so much data that it won’t fit? We will have to use disk storage but when this happens our time complexity fails

ByAgenda. Introduction to Binary Trees Implementing Binary Trees Searching Binary Search Trees Tree Traversal …1. Breadth-First ….2. Depth-First Insertion Deletion by Copying Balanced Trees Heaps / Heap Sort. Lecture Outline. Heap Definition Heapifying an Array Heap Sort

ByTREES. “I wish that I could ever see a poem as lovely as a tree…”. TREES. hierarchical structures parent-child relationship. A. B. C. D E F. TREES. • The parent-child relationship exists between nodes . • A is the parent node of B and C • B,C are children of A

ByParallel algorithms for expression evaluation. Part1. Simultaneous substitution method (SimSub) Part2. A parallel pebble game. Example 1: expression evaluation. S umming the numbers 2, 1, 3, 2, 1, 3, 2, 1 we can write a sequential program x1 = 2; x2 = x1+1; x3 = x2+3; x4 = x3+2;

ByPFTFBH. Binary Search trees Fundamental Data Structure Recursive and leads to recurrence relations to analyze performance Review some concepts from Recitation/Discussion Revisit doubly-linked lists and see how Java uses both trees and lists in java.util Understanding the DNA Assignment

ByBinary Trees. Overview. Trees. Terminology. Traversal of Binary Trees. Expression Trees. Binary Search Trees. Trees. Family Trees. Organisation Structure Charts. Program Design. Structure of a chapter in a book. Parts of a Tree. Parts of a Tree. nodes. Parts of a Tree. parent node.

ByGraph Traversal. Text Weiss, § 9.6 Depth-First Search Think Stack Breadth-First Search Think Queue. Overview. Goal To systematically visit the nodes of a graph A tree is a directed, acyclic, graph (DAG) If the graph is a tree,

BySorting. Dan Barrish-Flood. The Sorting Landscape. Θ(n 2 ) sorts insertion sort; insert each element into its proper place selection sort; select the smallest element and remove it bubble sort; swap adjacent out-of-order elements Key : already discussed won’t be discussed

ByTrees. Yih-Kuen Tsay Dept. of Information Management National Taiwan University Based on [ Carrano and Henry 2013] With help from Chien Chin Chen. Data-Management Operations.

ByEmpirical Methods for AI & CS. Paul Cohen Ian P. Gent Toby Walsh cohen@cs.umass.edu ipg@dcs.st-and.ac.uk tw@cs.york.ac.uk. Introduction What are empirical methods? Why use them? Case Study Eight Basic Lessons Experiment design Data analysis

ByGraph Traversal. Text Weiss, § 9.6 Depth-First Search Think Stack Breadth-First Search Think Queue. Overview. Goal To systematically visit the nodes of a graph A tree is a directed, acyclic, graph (DAG) If the graph is a tree,

ByRepresenting Structure and Behavior. CS1316: Representing Structure and Behavior. Story. Techniques for representing data structure Arrays, linked lists, circular linked lists, trees, graphs, stacks, queues, event queues Techniques for representing behavior

ByTrees. Chapter 11. Chapter Summary. Introduction to Trees Applications of Trees ( not currently included in overheads ) Tree Traversal Spanning Trees Minimum Spanning Trees ( not currently included in overheads ). Introduction to Trees. Section 11.1. Tree Traversal. Section 11.3.

ByNew Balanced Search Trees. Siddhartha Sen Princeton University Joint work with Bernhard Haeupler and Robert E. Tarjan. Research Agenda. Elegant solutions to fundamental problems Systematically explore the design space Keep design simple, allow complexity in analysis

ByBalanced Search Trees Simplified. Siddhartha Sen , Princeton University Dagstuhl , 2010 Joint work with Bernhard Haeupler and Robert E. Tarjan. Observations. The first (good) solution to a problem may not be the best: the design space is rich

ByIntroduction to Trees. Joe Meehean. Conceptual Picture. A. B. I. C. D. E. X. Conceptual Picture. A. B. I. C. D. E. X. Terminology e ach circle is a node pointers are edges t opmost node is the root b ottom nodes are leaves no outgoing edges Every non-empty tree has

ByTopic 18 Binary Trees. "A tree may grow a thousand feet tall, but its leaves will return to its roots." -Chinese Proverb. Definitions. A tree is an abstract data type one entry point, the root Each node is either a leaf or an internal node

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