11b.Trees1_Slides

11b.Trees1_Slides - Introduction to Trees CS 103B Stanford...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
Trees I 1 Introduction to Trees CS 103B Stanford University April 28, 2008
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Trees I 2 Outline ± Hierarchical Structures ± Tree Terminology ± Trees and Recursion ± Heaps
Background image of page 2
Trees I 3 Hierarchical Structures ± Conceptual tool for representing relationships among certain classes of items ± Relationship of the elements is one to many Family Tree
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Trees I 4 Hierarchical Structures ± Compiler uses trees for representing algebraic expressions (unambiguous order of evaluation) ± Other applications: ² File systems ² Organizational Charts
Background image of page 4
Trees I 5 Terminology ± Node or Vertex: elements of a tree ± Root: unique first node that has no predecessors but may have many successors ± Leaves : nodes that have no successors but have one unique predecessor ± Each node that is neither a root nor a leaf has a unique predecessor, called the parent node, and at least one successor, called a child node. An internal node is any node that is not a leaf (so this includes the root)
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Trees I 6 More Terminology ± Subtree ± Height ² Height = Level – 1 ± Ancestor (of node n) ± Descendent (of node n)
Background image of page 6
Trees I 7 Binary Trees ± Each node has exactly 0, 1 or 2 children (eg. expression tree) ± Recursive definition: T is a binary tree if either 1. T has no nodes, or 2. T is of the form
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Trees I 8 Binary Search Trees (BST) ± A binary tree that is "sorted" according to some particular order ± For each node n in a BST the following three properties must be satisfied : - n's value is greater than all the values in its left subtree - n's value is less than all the values in its right subtree - both T(left) and T(right) are binary trees ± Searching BST for an item is similar to a binary search
Background image of page 8
Trees I 9 Searching BST ± Find Wesley ± Contrast with linear search
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Trees I 10 Recursion ±
Background image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/01/2011 for the course CS 103B taught by Professor Sahami,m during the Winter '08 term at Stanford.

Page1 / 27

11b.Trees1_Slides - Introduction to Trees CS 103B Stanford...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online