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Data Structures

CSCI 132, Spring 2014Lecture 35Binary Trees

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Binary TreesDefinition: A binary tree is either empty or it consists of a root together with two binary trees called the left subtree and the right subtree.

Examples:Two node trees

Three node trees

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Traversing Binary Trees

To traverse a tree, we move through the tree and visit each node one at a time. This can be done in various orders:

preorder: VLR--Visit a node, then visit the left subtree, then visit the right subtree.

inorder: LVR--Visit the left subtree, then visit the node, then visit the right subtree.

postorder: LRV--Visit the left subtree, then visit the right subtree, then visit the node.

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Tree traversal examples

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2 3

preorder: 1 2 3inorder: 2 1 3postorder: 2 3 1

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2

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4 5

We will work this one out in class.

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Expression trees

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Comparison trees for binary search

Binary search of the following list:Amy Ann Dot Eva Guy Jan Jim Jon Kay Kim Ron Roy Tim Tom

Note that inorder traversal gives the list in alphabetical order.

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Binary_node struct

template <class Entry>struct Binary_node { // data members: Entry data; Binary_node<Entry> *left; Binary_node<Entry> *right; // constructors: Binary_node( ); Binary_node(const Entry &x);};

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Binary_tree class

template <class Entry>class Binary_tree {public:

// Add methods here.protected:

// Add auxiliary function prototypes here.Binary_node<Entry> *root;

};

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Binary search tree with pointers

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Implementation of constructor and empty( ) functions

template <class Entry>Binary_tree<Entry> :: Binary_tree( ){

root = NULL;}

template <class Entry>bool Binary_tree<Entry> :: empty( ) const{

return root == NULL;}

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In order traversal

template <class Entry>void Binary_tree<Entry> :: inorder(void (*visit)(Entry &)) {

recursive_inorder(root, visit);}

template <class Entry>void Binary_tree<Entry> :: recursive_inorder(Binary_node<Entry> *sub_root,

void (*visit)(Entry &)) {

//We'll work this out in class}

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Binary_tree specificationtemplate <class Entry>class Binary_tree {public:

Binary_tree( );bool empty( ) const;void preorder(void (*visit)(Entry &));void inorder(void (*visit)(Entry &));void postorder(void (*visit)(Entry &));int size( ) const;void clear( );int height( ) const;void insert(const Entry &);Binary_tree (const Binary_tree<Entry> &original);Binary_tree & operator = (const Binary_tree<Entry> &original);~Binary_tree( );

protected:// Add auxiliary function prototypes here.Binary_node<Entry> *root;

};