Data Structures CSCI 132, Spring 2014 Lecture 35 Binary Trees

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

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.

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

Expression trees

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.

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); };

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

Binary search tree with pointers

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;

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

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; };