1. Data Structures CSCI 132, Spring 2014 Lecture 35 Binary Trees

2. Binary Trees
Definition: 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

3. 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.

4. Tree traversal examples
preorder: 1 2 3
inorder: 2 1 3
postorder: 2 3 1 1 2 3 1
We will work this one out in class. 2 3 4 5

5. Expression trees

6. 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.

7. 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); };

8. Binary_tree class template <class Entry> class Binary_tree {
public:
// Add methods here.
protected:
// Add auxiliary function prototypes here.
Binary_node<Entry> *root; };

9. Binary search tree with pointers

10. Implementation of constructor and empty( ) functions
template <class Entry>
Binary_tree<Entry> :: Binary_tree( ) {
root = NULL; }
bool Binary_tree<Entry> :: empty( ) const
return root == NULL;

11. In order traversal template <class Entry>
void Binary_tree<Entry> :: inorder(void (*visit)(Entry &)) {
recursive_inorder(root, visit); }
void Binary_tree<Entry> :: recursive_inorder(Binary_node<Entry> *sub_root,
void (*visit)(Entry &))
//We'll work this out in class

12. Binary_tree specification
template <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; };