Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 21.3, Problem 1E
Program Plan Intro
To redo the exercise 21.2-2 with a disjoint-sets forest by using the rank and path compression method.
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Write a program that will undertake a range search of all elements lying within limits a, b along a dimension i of the multidimensional data set, representedas a k-d tree.
For example, given the data set {(7, 5), (4, 2), (6, 8), (1, 4), (3, 5), (2, 4), (3, 7),(9, 1), (6, 6), (5, 1)} represented as a k-d tree (k = 2), a range search of data elements lying within (a = 3, b = 7) along dimension i = 2 yields {(7, 5), (1, 4), (3, 5), (3, 7), (6, 6)}.
In a B+-tree, it always requires reorganizing the entire index file to maintain performance. True or False?
Write a program that will undertake a range search of all elements lying within limits a, b along a dimension i of the multidimensional data set, represented as a k-d tree.
For example, given the data set {(7, 5), (4, 2), (6, 8), (1, 4), (3, 5), (2, 4), (3, 7), (9, 1), (6, 6), (5, 1)} represented as a k-d tree (k = 2), a range search of data elements lying within (a = 3, b = 7) along dimension i = 2 yields {(7, 5), (1, 4), (3, 5), (3, 7), (6, 6)}
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- What would happen to insertions, deletions, and hash table searches if the linked list pointers were kept in an AVL tree? Your response must include an explanation of the running time in terms of hash table size. Is Big-Ohnotation necessary?arrow_forwardImplement a priority list using a heapordered binary tree, but instead of an array, use a triply linked structure. Each node will require three links: two to travel down the tree and one to traverse up the tree. Even if no maximum priority-queue size is known ahead of time, your implementation should ensure logarithmic running time per operation.arrow_forwardImplement a priority queue using a heapordered binary tree, but instead of an array, use a triply linked structure. Each node will require three links: two to traverse down the tree and one to traverse up the tree. Even if no maximum priority-queue size is known ahead of time, your implementation should guarantee logarithmic running time per operation.arrow_forward
- Develop an implementation of Page that represents B-tree nodes astext files on web pages, for the purposes of indexing (building a concordance for) theweb. Use a file of search terms. Take web pages to be indexed from standard input. Tokeep control, take a command-line parameter m, and set an upper limit of 10m internalnodes (check with your system administrator before running for large m). Use an mdigit number to name your internal nodes. For example, when m is 4, your nodes namesmight be BTreeNode0000, BTreeNode0001, BTreeNode0002, and so forth. Keep pairsof strings on pages. Add a close() operation to the API, to sort and write. To test yourimplementation, ook for yourself and your friends on your university’s website.arrow_forwardSuppose there are two singly linked lists both of which intersect at some point and become a single linked list. The head or start pointers of both the lists are known, but the intersecting node is unknown. Also, the number of nodes in each of the list before they intersect are unknown and both the list may have it different. List1 may have n nodes before it reaches intersection point and List2 might have m nodes before it reaches intersection point where m and n may be m = n, m > n or m < n. Give an algorithm for finding the merging point. Hints: A brute force approach would be to compare every pointer in one list with every pointer in another list. But in this case the complexity would be O(mn)arrow_forwardConsider a binary search tree (BST) whose elements are the integer values: Starting with an empty BST, show the effect of successively adding the following elements: 15, 78, 10, 5, 12, 82, 60, 68, 11 and 65. Show the effect of successively deleting 10, 78, and 15 from the resulting BST. Traverse the original BST in pre-order and post-order.arrow_forward
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