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 18.2, Problem 1E
Program Plan Intro
To give the final result of inserting the keys F,S,Q,K,C,L,H,T,V,W,M,R,N,P,A,B,X,Y,D,Z,E in order into an empty B-tree with minimum degree2.
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Show the results of inserting the keys Q,S,F,K,H,I,F,T,V,P,M,R,N,W,A in oder to empty an B- tree with minimum degree 2. Only draw the configuration ot the tree just before some node must split and also draw the final configuration.
Show the results of inserting the keys: F, L, O, R, I, D, A, U, N, V, M, Y, C, S in order into an empty B-tree with minimal degree 2. Draw only the configurations of the tree just before some node being split, and also draw the final configuration.
Please make sure your tree configurations are drawn neatly and are easy to read and understand. See attached image for how the tree configurations should be presented
Draw a KD Tree in the space below with these points inserted in the following order: (7,2), (6,4), (9,6), (8,1), (4,9), and (2,3). Assume the first level of the KD Tree is split along the x-axis. What point (from the KD Tree ) is the nearest neighbor of the point (1,4)?
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- Answer properly Insert the following keys, in the given order, into an initially empty 2-3 tree: D, S, A, R, E, F, U, N. After drawing its equivalent LLRB tree, what is the output of a postorder traversal on the LLRB tree? A. None of the others B. A, E, D, N, U, S, R, F C. A, E, D, N, S, U, F, R D. A, E, D, N, U, S, F, R E. A, E, D, N, S, U, R, Farrow_forwardForm a B-tree with t = 4 by inserting in order nodes with the following keys: I,W,A,N,T,T,O,P,A,S,S,T,H,I,S,T,E,S,T, Draw the B-tree obtained after each improvement.arrow_forwardCreate a binary search tree as discussed in class, using the given numbers in the order they’re presented. State if the resulting tree is has the attributes of being FULL, BALANCED, or COMPLETE. 37, 20, 18, 56, 40, 42, 12, 5, 6, 77, 21, 54arrow_forward
- Exercise 4 Consider the B-tree which is a result of inserting 15,14,1,2,13,12,3,4,11,10,5,6,9, (in that order) for t = 2. (a) Draw the trees before and after adding 9. (b) Draw the final tree after adding all numbers. (c) Next draw the tree after removing 14.arrow_forwardDraw the tree that results in building a MaxHeap, top-down, by inserting keys in the order given below in an initially empty maxHeap: 4, 20, 26, 14, 10, 35, 30, 8, 12, 2, 45arrow_forwardDraw the diagrams of an AVL tree as the following items are inserted into an empty tree in the specified order: 8, 71, 90, 80, 84, 75. In your diagrams, indicate the balance factors after insertion (but before rotation), which rotations are done, and the balance factors after each step.arrow_forward
- Draw the BST constructed by inserting the values [53, 25, 11, 63, 4, 88,59, 3, 15, 82, 92, 27, 55, 14] in the order shown, into an initially empty tree. 2. Using the tree traversal algorithms and the BST from above, show theoutput sequence for a (a) Preorder traversal(b) Postorder traversal 3. Delete the node with value 25 and draw the resultant tree.(a) Use two methods to delete the node with value 25 and draw the resul-tant tree. also describe both methods that you have usedarrow_forwardGiven the keys: F, S, Q, K, C, L, H, T, V, W, M, R, N, P, A, B, X, Y, D, Z, E a) Draw the final AVL Tree by inserting the following keys above in sequence from rightmost to leftmost b) Show the final AVL Tree if you delete the elements in sequence starting from the leftmost in the order successor based on your answer in letter a: F, P, Z c) Draw the final AVL Tree after inserting the keys in sequence from the leftmost I, J, G based on your answer in letter b. d) Draw the BTree by inserting the following keys above in sequence from rightmost to leftmost e) Show the final BTree if you delete the elements in sequence starting from the leftmost in the order successor based on your answer in letter d: F, P, Z f) Draw the final BTree after inserting the keys in sequence from the leftmost I, J, G based on your answer in letter e. g) What is the height of the AVL Tree in letter c? h) What is the size of the AVL Tree in letter c? i) What are the complete leaves of…arrow_forwardThat we are given the option to put the search keys in whatever order we like and that we are aware of how frequently a BST will need to access them.Should the keys be added to the tree in a different sequence, or in order of decreasing likelihood of access? Describe your response.arrow_forward
- Is there any work that a red-black tree could execute with a time complexity of O(log n)? Pick one: To find a predecessor or a successor; to insert and delete; or to do all three togetherarrow_forwardTrace the construction of the AVL tree that results. Show the trees and the BFs for each node. Box in the final answer.99, 88, 77, 66, 55, 44, 33, 22, 11arrow_forwardDraw a KD Tree in the space below with these points inserted in the following order: (7,2), (6,4), (9,6), (8,1), (4,9), and (2,3).（just NEED the image） Assume the first level of the KD Tree is split along the x-axis. What point (from the KD Tree) is the nearest neighbor of the point (1,4)? What nodes from the KD are visited when searching for the nearest neighbor of the point (4,5)?arrow_forward
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