Lecture 13, 14, 15

Graphs have vertices (nodes) connected by edges: G = (V, E)

True

A graph that contains a cycle is a tree

false

Properties of free trees:

Any two vertices in a free tree are connected by a unique path, If a single edge is removed from a free tree, it becomes disconnected; If any edge is added to a free tree, it becomes a graph with a cycle (no longer a tree)

A binary tree T is a structure defined on a finite set of nodes that either - contains no nodes, or - is composed of three disjoint sets of nodes:

A binary tree called right subtree, A root node, A binary tree called left subtree

Consider the original array 17, 8, 12, 4, 26. How many comparisons are needed to construct the BST on the original array?

10

In binary tree sort, we first construct the BST and then we perform _______ traversal to get the sorted order.

inorder

What is the worst case time complexity of the binary tree sort?

O(n^2)

What is the best case time complexity of the binary tree sort?

O(nlogn)

Binary tree sort is an in-place sorting algorithm.

False

Which of the following sorting algorithms can be considered as improvement to the binary tree sort?

Heap sort

What is the time complexity to count the number of elements in the linked list?

O(n)

Which of the following points is/are true about Linked List data structure when it is compared with array

It is easy to insert and delete elements in Linked List; Random access is not allowed in a typical implementation of Linked Lists

Which of the following sorting algorithms can be used to sort a random linked list with minimum time complexity?

Merge Sort

In the worst case, the number of comparisons needed to search a singly linked list of length n for a given element is

n

What are the time complexities of finding 8th element from beginning and 8th element from end in a singly linked list? Let n be the number of nodes in linked list, you may assume that n > 8.

O(1) and O(n)

Why do we impose restrictions like - root property is black - every leaf is black - children of red node are black - all leaves have same black

to get logarithm time complexity

What are the operations that could be performed in O(logn) time complexity by red-black tree?

insertion, deletion, finding predecessor, successor

Which of the following is an application of Red-black trees and why?

can be used in process schedulers, maps, sets

How can you save memory when storing color information in Red-Black tree?

using least significant bit of one of the pointers in the node for color information

What is the special property of red-black trees and what root should always be?

a color which is either red or black and root should always be black color only

Which of the following points is/are true about Linked List data structure when it is compared with array

The size of array has to be pre-decided, linked lists can change their size any time; Arrays have better cache locality that can make them better in terms of performance.