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 13.1, Problem 1E
Program Plan Intro
To draw the red black tree with different heights 2, 3 and 4 from the complete binary tree of height 3 on the keys
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The pre-order of a binary search tree 11, 5, 4, 6, 12, 13
Then the post-order of it is
a.
4, 6, 5, 13, 12, 11
b.
11, 5, 4, 6, 12, 13
c.
11, 5, 12, 4, 6, 13
d.
4, 5, 6, 11, 12, 13
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
Draw the binary search tree that would result if the given elements were added to an empty binary search tree in the given order. Use paint to draw.
a. Lisa, Bart, marge, maggie, flanders, smithers, miljouse
b. 12,34,1,5,-5,6,19,45,2,-7,47
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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Similar questions
- 1. 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_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_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_forward
- 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.arrow_forwardConsider the sequence of keys (5,16,22,45,2,10,18,30,50,12,1, 77, 66, 55). Draw the result of inserting entries with these keys (in the given order) into an initially empty red-black tree.arrow_forwardConsider 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_forward
- Problem 1. Insert the following set of keys {1, 7, 6, 8, 0, 5, 2, 12, 3, 18} in an empty red-black tree in the order they are listed.arrow_forwardFor the given complete binary tree (given in an array): 1 2 3 4 5 6 7 8 9 10 11 J B K A O T U X R Q D Convert it into a max heap and provide your answer by dragging and dropping the given alphabets on correct positions in array.arrow_forwardConsider an input: 7, 5, 12, 9, 10, 6, 3, 15, 13, 4, 17, 1, 8 Create a Binary Search Tree (Read the input from left to right) Write in-order traversal of the tree Delete node 12 and redraw the treearrow_forward
- Draw the structure of a binary search tree a. 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) *show the trees after each deletionarrow_forward2. We are given a complete binary tree with height h and n nodes. The link between a node and its left child is labeled as 0 and the link between a node and its right child is labeled as 1. A path from the root to each external node at the last level can be labeled by an h-tuple (X1, X2, ..., xh) of 1s and Os that lie on its links. See the following example: 0 0 1 1 0 0 1 0 (0,0,0) (0,1,1)arrow_forwardConsider an input: 5, 3, 10, 7, 8, 4, 1, 13, 11, 2, 15, 16 Create a Binary Search Tree (Read the input from left to right) Write in-order traversal of the tree Delete node 10 and redraw the tree B2. a. Find a closed form for the generating function for the given sequence 4, 16, 64, 256, … B2. b. Find the coefficient of x^9 in the power series of this function f(x)=1/(1-2x)^2 B2. c. What is the probability that a bit string of length 8 has exactly four 1’s?arrow_forward
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