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# Notes 12 - Week 12 Trees Trees are useful Structures for...

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Week 12: Trees Trees are useful Structures for hierarchies: directory structures, organization charts, family trees, etc. Note: The last few chapters in the text are organized into four modules on trees and one module on graphs. The four modules on trees are: 1. trees in general (this weeks module) 2. binary search trees (bst) 3. heaps 4. balanced trees (especially B-trees) Chapter 25 summarizes trees in general and introduces bst, heaps and B-trees We cover the chapters in the following way: Week 12: Trees (in general) include: some of Chapter 24 Chapter 26 about tree implementations Week 13: bst some of Chapter 25 (about bst) Chapter 27 about bst implementations Week 14: heaps some of Chapter 25 (about heaps) Chapter 28 about heap implementations Week 15: B-Trees Chapter 29 and the final Week 16: Graphs Chapters 30 and 31. First some definitions: A tree is a graph without cycles. A graph is a set of nodes (vertices) and edges (lines) A parent is a node above in hierarchy A child is a node below in hierarchy A leaf is a node with no children An interior node has a parent and a child node Siblings nodes have the same parent The root is the top node The height is the number of levels in a tree. Also the number of nodes along the longest path between the root and leaf. The recursive definition of height: 1 + height of tallest subtree Alternate definition: (see page 644) first level starts at 0 instead of starting at 1 The path length of a node is the number of edges from the root Task 1: Do #1,2 and 3 on pages 643-4 Binary Trees A special case is a binary tree: a tree with at most 2 children at each node

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called the left child and the right child.
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