1. CSS446 Spring 2014 Nan Wang

2.  to study trees and binary trees  to understand how binary search trees can implement sets  to learn how red-black trees provide performance guarantees for set operations  to choose appropriate methods for tree traversal  to become familiar with the heap data structure  to use heaps for implementing priority queues and for sorting 2

3.  In computer science, a tree is a hierarchical data structure composed of nodes.  Each node has a sequence of child nodes,  and one of the nodes is the root node.  LinkedList -- linear chain of nodes  Tree – a node can have more than one child 3

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6.  A node holds ◦ a data item and ◦ a list of references to the child nodes  A tree holds a reference to the root node 6 It is different from the LinkedList node

7.  When computing tree properties, it is common to recursively visit smaller and smaller subtrees. 7 1 2 3

8.  A binary tree consists of nodes, each of which has at most two child nodes. 8

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11.  In a balanced tree, all paths from the root to the leaves have approximately the same length.  What is height of the tree?  Which one hold more nodes? 11

12.  Given the height of a tree of h, what is the number of the nodes for a complete binary tree?  Given the number of nodes in a complete binary tree, what is the height of the tree? 12

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14.  Recursive Method 14 Recursive helper Without recursive helper Method in next slides

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16.  HashSet & TreeSet  A set implementation rearrange its elements in way so that finding elements quickly. (sort elements)  Binary Search takes O(log(n))  Array takes O(n) 16

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31. 31  Start with an empty binary search tree. ◦ Insert the keys 4,12,8,16,6,18,24,2,14,3, draw the tree following each insert. ◦ From the tree above, delete the keys, 6,14,16,4 in order, draw the search tree following each deletion.

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