Tree traversals Todays announcements: MT1 Feb 4, 7-9:00p WOOD 2 - - PowerPoint PPT Presentation

Tree traversals

Today’s announcements:

◮ MT1 Feb 4, 7-9:00p WOOD 2 ◮ HW2 out, due Feb 5, 11:59p

Today’s Plan

◮ Trees and their traversals

Warm up: What is the number of nodes N(h) in a perfect binary tree of height h?

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Ordered Binary Trees

C E B J G A F H I K L D ∅ ∅ ∅ ∅ ∅ ∅ ∅ ∅ ∅ ∅ ∅ ∅ ∅

An ordered binary tree is

◮ empty (∅), or ◮ root node with left and right ordered binary subtrees

Given height h binary tree,

◮ max # nodes = ◮ max # leaves = ◮ max # empty slots =

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Complete binary tree

L K J I H D E B F G C A

A complete tree of height h is

TL TR

• r

TL TR

Min/Max number of nodes in Complete(h)?

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Complete binary tree height

L K J I H D E B F G C A

Height of the complete binary tree with n nodes. H(1) = H(2) = · · · = H( ) = H( ) = · · · = H( ) =

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Ordered binary tree ADT

root ∅ dog bee emu ant cat ∅ ∅ ∅ ∅ ∅

Tree ADT

◮ insert ◮ remove ◮ traverse

template<class T> class tree { public: ... private: struct Node { T data; Node * left; Node * right; }; Node * root; ... };

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Traversals

2 9 5 20 15 10 7 30 17

inOrder( Node * x ) { If (x != null) { inorder(x->left); inorder(x->right); }} In order: 2, 5, 7, 9, 10, 15, 17, 20, 30

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Expression Evaluation

2 − ∧ / lg × 8 2 16

double eval( Node * x ) { If (x != null) { double a = eval(x->left); double b = eval(x->right); }}

Tree Copy Tree Clear

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Level (Depth) order

2 9 5 20 15 10 7 30 17

void levelOrder( ) { If( root == NULL) return; }}

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