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 20.3, Problem 4E
Program Plan Intro
To explain the modification in vEB trees so it check an element is present or not in constant time.
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What happens if you call VEB-TREE-INSERT with an element that is already inthe vEB tree? What happens if you call VEB-TREE-DELETE with an element thatis not in the vEB tree? Explain why the procedures exhibit the behavior that theydo. Show how to modify vEB trees and their operations so that we can check inconstant time whether an element is present.
You are implementing a binary search tree class from scratch, which, in additionto insert, find, and delete, has a method getRandomNode() which returns a random node from the tree. All nodes should be equally likely to be chosen. Design and implement an algorithm for getRandomNode, and explain how you would implement the rest of the methods
What happens if you use an element that is already in the vEB tree to call VEB-TREE-INSERT? What happens if you use an element that isn't in the vEB tree to call VEB-TREE-DELETE? Explain why the procedures behave the way they do. Show how to change vEB trees and their operations such that we may verify whether an element is there in constant time.
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- You are implementing a binary search tree class from scratch, which, in additionto insert, find, and delete, has a method getRandomNode() which returns a random nodefrom the tree. All nodes should be equally likely to be chosen. Design and implement an algorithm for getRandomNode, and explain how you would implement the rest of the methods.arrow_forwardYou are implementing a binary tree class from scratch which, in addition to insert, find, and delete, has a method getRandomNode() which returns a random node from the tree. All nodes should be equally likely to be chosen. Design and implement an algorithm for getRandomNode, and explain how you would implement the rest of the methods.arrow_forwardYou are creating a binary tree class from scratch, and one of its methods, getRandomNode(), returns a random node from the tree in addition to the standard insert, find, and delete operations. There should be an equal chance of selecting each node. Explain how you would develop the other methods after designing and implementing an algorithm for getRandomNode.arrow_forward
- Q2. You are asked to write a method that takes a binary search tree (BST) as a parameter and returns the AVL tree obtained by rearranging the BST. The method should convert the BST into an AVL tree by using rotation operations. Explain your function in detail and give theoretical run time complexity analysis of that method in the report.arrow_forwardExamine a traversal of a binary tree. Let's say that visiting a node means to display the data in the node. What are the result of each of the following traversals of the tree included? It is preorder, postorder, inorder or level order?arrow_forwardr. Is it possible to write a nonrecursive version of keys() that uses spaceproportional to the tree height (independent of the number of keys in the range)?arrow_forward
- You are creating a binary search tree class from scratch that contains a function getRandomNode() that returns a random node from the tree in addition to insert, find, and remove. All nodes should have an equal chance of being picked. Create an algorithm for getRandomNode and describe how you would construct the remaining methods.arrow_forwardWrite a test program that randomly generates 500,000 numbers and inserts them into a BST, reshuffles the 500,000 numbers and performs a search, and reshuffles the numbers again before deleting them from the tree. Do the same thing using an AVL tree. Make sure to have the program compare the running times for completing all of these tasks for these two different trees.arrow_forwardAdd support in LinkedBinaryTree for a method, pruneSubtree(p), that removes the entire subtree rooted at position p, making sure to maintain an accurate count of the size of the tree. What is the running time of your implementation? write code as pythonarrow_forward
- Question: Explain the deletion operation and its rules in the red-black tree. Please use your own words.arrow_forwardThere is now a search key object to handle search keys that are not unique. What might this mean for how tall the B+ tree gets?arrow_forwardA new property was added to the search key to address non-unique search keys. What impact may this modification have on the height of the B+-tree?arrow_forward
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