CISC220 Fall 2009 James Atlas Lecture 13: Binary Trees

Objectives for Today Understand Trees/Terminology Understand binary search trees Construct and use binary search trees Reading - K+W Chap 8

Tree Terminology root, leaf parent, child, sibling subtree external, internal node ancestor, descendant depth, height

Binary Trees Each node has 0, 1, or 2 children

Binary Search Trees Binary search trees Elements in left subtree < element in subtree root Elements in right subtree > element in subtree root Both the left and right subtrees are binary search trees

Binary Search Tree (Example) Is this a binary search tree?

Binary Search Tree (Example)

Searching a BST Search algorithm: if the tree is empty, return NULL if target equals to root node, return that data if target < root node, return search(left subtree) otherwise return search(right subtree)

find(7) find(12) find(0) find(14)

Inserting to a Binary Search Tree if root is NULL replace empty tree with new data leaf; else if item < root->data return insert(left subtree, item) else return insert(right subtree, item) http://www.cs.jhu.edu/~goodrich/dsa/trees/btree.html

Inserting to a Binary Search Tree

Removing from a Binary Search Tree Item not present: do nothing Item present in leaf: remove leaf (change to null) Item in non-leaf with one child: Replace current node with that child Item in non-leaf with two children? Find largest item in the left subtree Recursively remove it Use it as the parent of the two subtrees (Could use smallest item in right subtree)

Removing from a Binary Search Tree

Order of operations?