Trees

1. Trees • Ed. 2. and 3.: Chapter 6 • Ed. 4.: Chapter 7

2. Trees • What is a tree? - Examples of trees - Tree interface and interface hierarchy • Algorithms on binary trees - Binary tree interface - Traversal on a binary tree - Binary tree implementation - Traversal on a tree • Sample case study application

3. Trees

5. Example:

6. r T u v A formal definition of trees: A tree T is a set of nodes storing elements in a parent - child relationship with the following properties: · T has a special node r , called the root of T . · Each node v of T different from r has a parent node u .

14. … …

15. Comparing Example 6.3 with Example 6.2, we can see an important difference between the ordered tree and the unordered tree. In an ordered tree, the order of the children of a node is significant while in an unordered tree, the order of the children of a node is not important.

22. The Tree Abstract Data Type

25. A Tree Interface in Java public interface Tree { public int size(); public Boolean isEmpty(); public ElementIterator elements(); public PositionIterator positions(); public void swapElements( Position v, Position w ); public Object replaceElement( Position v, Object e ); public Position root(); public Position parent( Position v ); public PositionIterator children( Position v ); public boolean isInternal( Position v ); public boolean isExternal( Position v ); public boolean isRoot( Position v ); }

26. Construction of Interface Hierarchy

30. IspectableContainer size isEmpty Elements IspectablePositionContainer positions InspectableTree root parent children isRoot isInternal isExternal PositionContainer swapElement replaceElement Tree

31. The Binary Tree Abstract Data Type

32. A Binary Tree Interface in Java