1. CISC220 Fall 2009 James Atlas
Lecture 13: Binary Trees

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

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

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

5. 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

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

7. Binary Search Tree (Example)

8. 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)

9. find(7)
find(12)
find(0)
find(14)

10. 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)

11. Inserting to a Binary Search Tree

12. 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)

13. Removing from a Binary Search Tree

14. Order of operations?