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 13.3, Problem 3E
Program Plan Intro
To verify that the indicated transformation preserves the property 5.
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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
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.
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)?
Chapter 13 Solutions
Introduction to Algorithms
Ch. 13.1 - Prob. 1ECh. 13.1 - Prob. 2ECh. 13.1 - Prob. 3ECh. 13.1 - Prob. 4ECh. 13.1 - Prob. 5ECh. 13.1 - Prob. 6ECh. 13.1 - Prob. 7ECh. 13.2 - Prob. 1ECh. 13.2 - Prob. 2ECh. 13.2 - Prob. 3E
Ch. 13.2 - Prob. 4ECh. 13.2 - Prob. 5ECh. 13.3 - Prob. 1ECh. 13.3 - Prob. 2ECh. 13.3 - Prob. 3ECh. 13.3 - Prob. 4ECh. 13.3 - Prob. 5ECh. 13.3 - Prob. 6ECh. 13.4 - Prob. 1ECh. 13.4 - Prob. 2ECh. 13.4 - Prob. 3ECh. 13.4 - Prob. 4ECh. 13.4 - Prob. 5ECh. 13.4 - Prob. 6ECh. 13.4 - Prob. 7ECh. 13 - Prob. 1PCh. 13 - Prob. 2PCh. 13 - Prob. 3PCh. 13 - Prob. 4P
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- Consider a B-Tree with order as 3. Which of the following will be the correct B-tree for the given key value sequence? 12, 13, 7, 16, 19, 20, 25, 3, 6arrow_forwardDraw 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_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 emptytree. 2. Using the tree traversal algorithms and the BST from (1) above, show theoutput sequence for a (a) Preorder traversal(b) Postorder traversal3. 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. (b) Briefly describe both methods that you have used.arrow_forward
- Consider a B Tree used as an index that has THREE levels including the root node. If a newkey is inserted in this index, then what shall be the maximum number of nodes? Explain youranswer with an example.arrow_forwardConsider the values 19, 10, 4, 30, 55, 24, 9, 13, 11 and 22: Draw the 2-3-4 tree that results from inserting these values in that order into an initially empty 2-3-4 tree. Show your workings.arrow_forwardExercise 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_forward
- If index entries were placed in sorted order, what would the occupancy of each leaf node of a B+-tree be? Justify your reasoning.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_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
- Consider a rooted n node binary tree represented using pointers. The best upper bound on the time required to determine the number of subtrees having exactly 4 nodes is O(na logbn). Then the value of a + 10b is.arrow_forwardDraw a K-d tree for the following points inserted in this order (assume the root is an even level and that we use x coordiantes for the odd levels, y coordiantes for even levels): (10, 10) (5, 5) (8, 4) (12, 18) (15, 8)arrow_forwardTrace the construction of an AVL tree using the insertion sequence:BOX IN YOUR FINAL AVL ANSWER50, 25, 10, 5, 7, 3, 30, 20, 8, 15arrow_forward
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