Homework Answers
For a simple BST (without any balancing) storing n keys and of height h,
the running time of the search operation (for a worst-case instance) is Theta(h)
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For a simple BST (without any balancing) storing n keys and of height h, the running...
fill in the blank Binary Search Tree AVL Tree Red-Black Tree complexity O(log N), O(N) in...
fill in the blank Binary Search Tree AVL Tree Red-Black Tree complexity O(log N), O(N) in the worst case O(log N) O(log N) Advantages - Increasing and decreasing order traversal is easy - Can be implemented - The complexity remains O(Log N) for a large number of input data. - Insertion and deletion operation is very efficient - The complexity remains O(Log N) for a large number of input data. Disadvantages - The complexity is O(N) in the worst case...
The INORDER traversal output of a binary tree is U,N,I,V,E,R,S,I,T,Y and the POSTORDER traversal output of the same tree is N,U,V,R,E,T,I,S,I,Y
a. The INORDER traversal output of a binary tree is U,N,I,V,E,R,S,I,T,Y and the POSTORDER traversal output of the same tree is N,U,V,R,E,T,I,S,I,Y. Construct the tree and determine the output of the PREORDER traversal output. b. One main difference between a binary search tree (BST) and an AVL (Adelson-Velski and Landis) tree is that an AVL tree has a balance condition, that is, for every node in the AVL tree, the height of the left and right subtrees differ by at most 1....
Give an algorithm with the following properties. • Worst case running time of O(n 2 log(n))....
Give an algorithm with the following properties. • Worst case running time of O(n 2 log(n)). • Average running time of Θ(n). • Best case running time of Ω(1).
When sorting n records, Merge Sort has worst-case running time O(log n) O O(n log n)...
When sorting n records, Merge Sort has worst-case running time O(log n) O O(n log n) O O(n) O(n^2)
When sorting n records, Merge sort has worst-case running time a. O(n log n) b. O(n)...
When sorting n records, Merge sort has worst-case running time a. O(n log n) b. O(n) c. O(log n) d. O(n^2)
package hw3; import java.util.LinkedList; /* *********************************************************************** * A simple BST with int keys and no values...
package hw3; import java.util.LinkedList; /* *********************************************************************** * A simple BST with int keys and no values * * Complete each function below. * Write each function as a separate recursive definition (do not use more than one helper per function). * Depth of root==0. * Height of leaf==0. * Size of empty tree==0. * Height of empty tree=-1. * * TODO: complete the functions in this file. * DO NOT change the Node class. * DO NOT change the name...
Using Sequential Search on an array of size n, the probability that the search key is...
Using Sequential Search on an array of size n, the probability that the search key is not present in the array is 1/4. The probabilities of matching the key to any of the n items in the array are all equal. What is the average case complexity function for the Sequential Search under these conditions? If we know that our system can execute one basic operation in 8 nanoseconds, what will be the estimated running times of Sequential Search under...
8. Given the BST below, show the BST that would result after inserting the key of value 180 if sp...
8. Given the BST below, show the BST that would result after inserting the key of value 180 if splaying is performed starting at the node that was inserted. 100 50 150 40 60 200 30 9. A nice property of splay trees is that each of Find, Insert and Delete takes O(logn) time. TrueFalse? 10. The keys of value N, N-1, N-2... 4, 3, 2, 1 are inserted in this order in a splay tree. What is the final...
Select each statement that is true about BTrees of order m, and height h, containing k...
Select each statement that is true about BTrees of order m, and height h, containing k keys. In the statements below, we use the phrase "expensive data operations" to denote any kind of remote data transfer required by an algorithm, including things like disk seeks and api calls. All running times are considered to be worst case. (a) h = O(logm k) (b) Searching for a key within a node is an expensive data operation. (c) We can use a...
a. Write a pseudocode for computing for any positive integer n Besides assignment and comparison, your...
a. Write a pseudocode for computing for any positive integer n Besides assignment and comparison, your algorithm may only use the four basic arithmetical operations. What is the time efficiency of your algorithm for the worst and best cases? Justify your answer. (The basic operation must be identified explicitly). Give one instance for the worst case and one instance for the best case respectively if there is any difference between the worst case and best case. Otherwise please indicate that...
When sorting n records, Merge Sort has worst-case running time O(log n) O O(n log n) O O(n) O(n^2)
8. Given the BST below, show the BST that would result after inserting the key of value 180 if splaying is performed starting at the node that was inserted. 100 50 150 40 60 200 30 9. A nice property of splay trees is that each of Find, Insert and Delete takes O(logn) time. TrueFalse? 10. The keys of value N, N-1, N-2... 4, 3, 2, 1 are inserted in this order in a splay tree. What is the final...
Select each statement that is true about BTrees of order m, and height h, containing k keys. In the statements below, we use the phrase "expensive data operations" to denote any kind of remote data transfer required by an algorithm, including things like disk seeks and api calls. All running times are considered to be worst case. (a) h = O(logm k) (b) Searching for a key within a node is an expensive data operation. (c) We can use a...
a. Write a pseudocode for computing for any positive integer n Besides assignment and comparison, your algorithm may only use the four basic arithmetical operations. What is the time efficiency of your algorithm for the worst and best cases? Justify your answer. (The basic operation must be identified explicitly). Give one instance for the worst case and one instance for the best case respectively if there is any difference between the worst case and best case. Otherwise please indicate that...
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