CS2005 Week 8 Lectures Maps & Binary Trees

Aims Describe and specify the Map Data Type CS2005 Aims Describe and specify the Map Data Type Describe java.util.HashMap and java.util.TreeMap Describe the Binary Tree Data Structure Define basic Binary Tree terminology Describe ways of traversing a Binary Tree Java implementation of a Binary Tree

Learning Outcomes describe and use a Map ADT CS2005 Learning Outcomes describe and use a Map ADT describe the structure of a Binary Tree implement a simple Binary Tree in Java write Java code to perform simple operations using Binary Trees recall main points of Watt & Brown chs 10 & 11

Map equivalent to table CS2005 Map equivalent to table

CS2005 Map equivalent to set

Map ADT Essential Operations create:  Map CS2005 Map ADT Essential Operations create:  Map put: Key  Value  Map  Map containsKey: Key  Map  Boolean get: Key  Map  Value remove: Key  Map  Map isEmpty: Map  Boolean

Java.util classes TreeMap HashMap complexity O(log n) CS2005 Java.util classes TreeMap complexity O(log n) iterator over set of keys is sorted HashMap complexity O(1) iterator over set of keys ‘random’

CS2005 Binary Tree Structure Terminology: node, branch, root node, leaf node, parent, child, ancestor, descendant, subtree, null tree, depth

Balanced Binary Trees M = abs(Size(left stree) - Size(right stree)) CS2005 Balanced Binary Trees M = abs(Size(left stree) - Size(right stree)) Tree balanced if M <= 1 for itself and all its subtrees Measure if ill-balance largest value of M for tree and all subtrees Degree of ill-balance 0 (for trees of size 0 or 1) (Measure if ill-balance)/(size-1) otherwise

Tree Traversals Breadth First Depth First visit root node CS2005 Tree Traversals Breadth First visit root node then all nodes depth 1 then all nodes depth 2, etc Depth First visit all nodes in one subtree before another same rule applies to all subtrees

Breadth First Traversal CS2005 Breadth First Traversal If tree empty then return Make empty queue Q Append root node to Q Loop until Q is empty remove node from Q process node append child nodes to Q Return

Depth First Traversal (pre- order) CS2005 Depth First Traversal (pre- order) If tree empty then return Make empty stack S Push root node on S Loop until S is empty pop node from S process node push child nodes on S Return

Depth First Traversal (recursive) CS2005 Depth First Traversal (recursive) If tree is empty then return Process the root node Recursively traverse left subtree Recursively traverse right subtree Return Order of middle steps can be changed

Java Implementation Public class BTNode { protected Object element; CS2005 Java Implementation Public class BTNode { protected Object element; protected BTNode left, right; protected BTNode(Object elem, BTNode lt, BTNode rt) { element = elem; left = lt; right = rt; }

CS2005 Sample Code Html document Binary tree code test program

Example - equals method CS2005 Example - equals method public static boolean equals(CharTree t1, CharTree t2) { if (t1==t2) return true; if (t1==null || t2==null) return false; return ((t1.element == t2.element) && (CharTree.equals(t1.left,t2.left)) && (CharTree.equals(t1.right,t2.right))); }