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 13.4, Problem 1E
Program Plan Intro
To argue that after executing RB-DELETE-FIXUP procedure, the root of the tree must be black.
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This exercise is about drawing BSTs. You are asked to:
Show the result of inserting 3, 1, 4, 6, 9, 2, 5, and 7 in an initially empty binary search tree. Then show the result of deleting the root.
Draw all binary search trees that can result from inserting permutations of 1, 2 and 3. How many types of trees are there? What are the probabilities of each type of tree’s occurring if all permutations are equally likely
Given the input {4371, 1323, 6173, 4199, 4344, 9679, 1989}, a fixed table size of 10, and a hash function H(X) = X mod 10, show the resulting
Linear probing hash table
Separate chaining hash table
Suppose that we have an estimate ahead of time of how often search keys areto be accessed in a BST, and the freedom to insert them in any order that we desire.Should the keys be inserted into the tree in increasing order, decreasing order of likely frequency of access, or some other order? Explain your answer.
Given the following key sequence (6,22,9,14,13,1,8) build the dynamic binary search tree WITHOUT BALANCING IT. How many probes (i.e., comparisons) does it take to determine that key 100 is not in the tree? (In this study case, the root is 6; the next element 22 > 6, so it goes to the right, etc).
DEPTH counting starts at 1 at the root
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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- 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_forwardDevelop a binary search tree resulting after inserting the following integer keys:-49, 127, 12, 11, 38, 77, 126, 456, 123, 6. Show the modified tree after each deletion:*Delete 6 *Delete 77 *Delete root *Delete 12arrow_forward1. Show the result of inserting 3, 1, 4, 6, 9, 2, 5, 7 into an initially empty binary search tree. a.) Given the tree in (1), show the result of deleting the rootarrow_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_forwardComputer Science Regarding to the following B-Tree Index(m=3): If we delete index key 11 and 7, what is the B-Tree Index after the deletion?arrow_forwardConsider the bottom most BST drawn on page 401 of section 3.2 of the text. Draw what the resulting tree looks like if “H” is deleted from this tree.arrow_forward
- That 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_forwardDraw the structure of a binary search treea. after these values have been inserted: 19, 34, 23, 16, 54, 89, 24, 29, 15, 61, 27.b. after two delete operations (deleting the root)arrow_forwardWhat impact will keeping linked list pointers in an AVL tree have on insertions, deletions, and hash table searches? Your answer must explain the running time in terms of the size of the hash table. Does Big-Ohnotation need to exist?arrow_forward
- Use the given AVL tree to answer each of the following questions: (a) Which is the deepest unbalanced node after inserting key 5, but before re-balancing, and what is its balance factor? (b) After the insertion, perform all the necessary rotations required to re-balance the tree, and after each rotation, state the type of rotation done and list the keys of the resulting tree in the form: After Left/Right rotation: e1, e2, e3, ...., en. (breadth-first order)arrow_forwardDraw the structure of a binary search treea. after these values have been inserted: 19, 34, 23, 16, 54, 89, 24, 29, 15, 61, 27. (show the trees after each deletion)arrow_forwardConsider the bottom most BST drawn on page 401 of the text. Draw what the resulting tree looks like if “E” is deleted from this tree.arrow_forward
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