Tài liệu Feaculty of Computer Science and Engineering Department of Computer Scienc Tutorial 4 Questions pptx

AVL Tree Required Questions Question 1.. For each of the following key sequences determining the AVL tree obtained when the keys are inserted one-by-one in the order given into an in

DATA STRUCTURES & ALGORITHMS

Tutorial 4 Questions AVL Tree and Heap

Part 1 AVL Tree

Required Questions

Question 1

For each of the following key sequences determining the AVL tree obtained when the keys are inserted one-by-one in the order given into an initially empty tree:

a) 1, 2, 3, 4, 5, 6, 7

b) 4, 2, 1, 3, 6, 5, 7

c) 1, 6, 7, 2, 4, 3, 5

d) 45, 9, 2, 17, 84, 92, 71, 18, 30, 62, 55, 20, 27

Question 2

For each of the AVL trees obtained in Question 1 determine the tree obtained when the root is withdrawn

Question 3

Write a global function in pseudo code to generate an AVL tree from an input list by insert elements in the list into an initial empty AVL Refer to Question 1 for an example

algorithm generateAVLfromList (val list <List>)

This algorithm generate a AVL from the input list

Pre

Post the AVL is built by inserting elements in the list into an initial

empty tree one-by-one from the beginning of the list

Return the AVL

end generateAVLfromList

Question 4

Devise an algorithm to test whether a given binary search tree is AVL balanced

algorithm testAVL (val tree <BSTTree>)

Pre

Post

Return true if tree is an AVL, otherwise return false

end testAVL

Advanced Questions

Question 5

Devise an algorithm to merge the contents of two binary search trees into one What is the running time of

Question 6

Suggest a data structure that supports the following operation and given time complexities:

Init Init the DS with n real numbers (unordered) O(nlogn) Insert(x) Insert x to the DS O(logn) findMin Return the value of the minimal element O(logn) findMax Return the value of the maximal element O(logn) findMed Return the value of the median element O(1) DelMin Remove the minimal element O(logn) DelMax Remove the maximal element O(logn) DelMed Remove the median element O(logn)

Part 2 Heap

Required Questions

Question 7

Show the heap (tree) you will have after inserting the following values:

a) 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

b) 8, 4, 3, 6, 11, 9, 10, 10, 9

c) 3, 1, 4, 1, 5, 9, 2, 6, 5, 4

d) 2, 7, 1, 8, 2, 8, 1, 8, 2

e) 45, 9, 2, 17, 84, 92, 71, 18, 30, 62, 55, 20, 27

Question 8

Show the heap (tree) you will have after removing (from 1-3 times) the root element of the tree generated

in the all cases of the previous question

Advanced Questions

Question 9

The following class definition will be used for the problem that follow:

public class BinaryTree <E extends Comparable<E>> {

private class Node {

E data;

Node left, right;

}

Node root;

Write a recursive method called isCompleteBinaryTree() that returns true if the binary tree represents a complete binary tree (one that satisfies the shape property for heaps)

Notice that the tree might not be a complete tree