Lecture 13, 14, 15

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Graphs have vertices (nodes) connected by edges: G = (V, E)
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True
A graph that contains a cycle is a tree
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false
Properties of free trees:
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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:
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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?
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10
In binary tree sort, we first construct the BST and then we perform _______ traversal to get the sorted order.
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inorder
What is the worst case time complexity of the binary tree sort?
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O(n^2)
What is the best case time complexity of the binary tree sort?
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O(nlogn)
Binary tree sort is an in-place sorting algorithm.
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False
Which of the following sorting algorithms can be considered as improvement to the binary tree sort?
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Heap sort
What is the time complexity to count the number of elements in the linked list?
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O(n)
Which of the following points is/are true about Linked List data structure when it is compared with array
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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?
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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
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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.
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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
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to get logarithm time complexity
What are the operations that could be performed in O(logn) time complexity by red-black tree?
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insertion, deletion, finding predecessor, successor
Which of the following is an application of Red-black trees and why?
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can be used in process schedulers, maps, sets
How can you save memory when storing color information in Red-Black tree?
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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?
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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
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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.

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