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COIS2020H Data Structures and Algorithms
Task:
Objectives
To understand and use recursion as an algorithmic tool.
To work with binary trees and their variations.
Average Binary Tree Depth
As you know from class a binary tree on N nodes may have a maximum (worst case) depth of
N-1. But what is the average depth of a binary tree on N nodes?
The height of a binary tree rooted at p is the length of the longest path from p to a leaf node.
Write a method called Height for the binary tree class that returns the height of the current binary tree.
Using the constructor of the binary tree class which builds a random binary tree on N nodes, find the average height of binary trees on N = 100, 200, 300, … 1000 nodes.
Calculate the average over 1000 trials for each N and compare it against log2N.
Output and then plot your results.
Note: Let the height of a leaf node be 0 and the height of an empty tree be -1 (which differs from our notes on AVL trees).
Grading:
Height method 10 marks
Results 5 marks
Write another method called IsAVL for the binary tree class that returns true if the current binary tree satisfies the balancing property of an AVL tree.
You may use the method Height from part a and assume that the binary tree already satisfies the property of a binary search tree.
Grading:
IsAVL method 15 marks
Testing 5 marks
Perfectly Balanced Binary Search Tree
A perfectly balanced binary search tree B is a binary search tree where the size of the left and right subtrees of each node in B differs by at most one.
Write a constructor for the binary search tree class that accepts a sorted list L and builds a perfectly balanced binary search tree.
Because constructors cannot be recursive, another method called Build must be defined to carry out the actual construction of the tree.
Grading:
Build method 15 marks
Testing 5 marks
Additional Marks
Documentation 5 marks
Submission
Submit the source code, executable code, and testing results via Blackboard. One submission per team is fine.
COIS2020H Data Structures and Algorithms
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