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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Question
Chapter 12, Problem 3P
(a)
Program Plan Intro
To argue the average depth of a node in tree T is
(b)
Program Plan Intro
To argue that if a tree has n nodes then
(c)
Program Plan Intro
To show the average total path length of BST is
(d)
Program Plan Intro
To rewrite the equation
(e)
Program Plan Intro
To explain the randomized version of quicksort takes the cost of
(f)
Program Plan Intro
To describe the comparison of quicksort is equals to the comparisons need to insert the elements in BST.
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The time complexity of traversing a binary search tree that contains 'n' elements is O (n) in the worst case.The time complexity of traversing a red-black tree that contains 'n' elements is O (log2 n) in the worst case.Traversing a binary search tree, which contains integers, according to the "inorder" principle always gives us integers in sorted ascending order.If we insert a sequence of integers in an empty BST, it will always be at least as high as the tree we get if we insert the same sequence of integers in an empty red-black tree.If we insert a sequence of integers in an empty BST, it will always be twice as high as the tree we get if we insert the same sequence of integers in an empty red-black tree.Group of answer options
Only statements A, B, C and D are correct.
Only statements A, B and C are correct.
All statements are correct.
Only statements A, C, D and E are correct.
Only statements A, C and D are correct.
Illustrate that via AVL single rotation, any binary search tree T1 can betransformed into another search tree T2 (with the same items) Give an algorithm to perform this transformation using O(N log N) rotation on average
Consider 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?
Chapter 12 Solutions
Introduction to Algorithms
Ch. 12.1 - Prob. 1ECh. 12.1 - Prob. 2ECh. 12.1 - Prob. 3ECh. 12.1 - Prob. 4ECh. 12.1 - Prob. 5ECh. 12.2 - Prob. 1ECh. 12.2 - Prob. 2ECh. 12.2 - Prob. 3ECh. 12.2 - Prob. 4ECh. 12.2 - Prob. 5E
Ch. 12.2 - Prob. 6ECh. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - Prob. 9ECh. 12.3 - Prob. 1ECh. 12.3 - Prob. 2ECh. 12.3 - Prob. 3ECh. 12.3 - Prob. 4ECh. 12.3 - Prob. 5ECh. 12.3 - Prob. 6ECh. 12.4 - Prob. 1ECh. 12.4 - Prob. 2ECh. 12.4 - Prob. 3ECh. 12.4 - Prob. 4ECh. 12.4 - Prob. 5ECh. 12 - Prob. 1PCh. 12 - Prob. 2PCh. 12 - Prob. 3PCh. 12 - Prob. 4P
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- Consider the array t = [1, 2, 3, 4, 5, 8, 0 , 7, 6] of size n = 9, . a) Draw the complete tree representation for t. b) What is the index of the first leaf of the tree in Part a (in level order)? In general, give a formula for the index of the first leaf in the corresponding complete binary tree for an arbitrary array of size n. c) Redraw the tree from Part a after each call to fixheap, in Phase 1 of heapsort. Remember, the final tree obtained will be a maxheap. d) Now, starting with the final tree obtained in Part c, redraw the tree after each call to fixheap in Phase 2 of heap sort. For each tree, only include the elements from index 0 to index right (since the other elements are no longer considered part of the tree). e) For the given array t, how many calls to fixheap were made in Phase 1? How many calls to fixheap were made in Phase 2? f) In general , give a formula for the total number of calls to fixheap in Phase 1, when heapsort is given an arbitrary array of size n. Justify…arrow_forwardComputer Science Consider a left-child, right-sibling tree T containing n nodes, in which each node stores, among other information, a real number >0, called the node’s score. Find a subset S of all nodes such that the sum of the scores of nodes in S is maximized subject to the constraint that a node and its child cannot both be in S. 1. In C++, write a function to solve the max sum for the nodes with the conditions given. 2. Analyze the running timearrow_forwardFill in the blank Dijkstra's algorithm works because, on every shortest path p from a source vertex u to a target vertex v, there is a (predecessor) vertex w in p immediately before v such that removing v from p yields the shortest path from u to w. In other words, the path through the previous vertex is also the shortest path. Thus, choosing an edge from the previous vertex that brings us to v with the __ cost always yields the shortest path to v.arrow_forward
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