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 12.3, Problem 3E
Program Plan Intro
To find the worst case and best case running times for this sorting
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A binary search tree with n keys has a minimum height of log2 n.
Choose one:
Is it true or false?
In a binary search tree, to remove a node N that has left child C1 and right child C2, we do the following:
Group of answer choices
We make C1 the left child of N’s parent and C2 the right child of N’s parent
We make C1 the right child of N’s parent and C2 the left child of N’s parent
We find the largest item L in N’s left subtree, copy the contents of L to N,
and remove L
We find the smallest item S in N’s right subtree, copy the contents of S to N, and remove N
We find the largest item L in N's right subtree, copy the contents of L to N, and remove L
Beginning with an empty binary search tree, what binary search tree is formed when you insert the following values in the order given?(Values are compared in alphabet order, e.g., A < B)
1) N, A, T, E, B, W, J
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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- In which order would one have to insert the keys 1 to n for an n ∈ N in a binary search tree,in order to minimize the number of comparisons during construction?arrow_forwardUsing a self-balancing binary search tree, binary tree sort is nevertheless slower than merge sort, taking O(n log n) time in the worst case.arrow_forwardIf we insert the entries (1,A), (2,B), (3,C), (4,D), and (5,E), in this order, into an initially empty binary search tree, what will it look like?arrow_forward
- Implement a binary search tree, create 1000 random numbers, do insertion and selection so that we have around 500 nodes in the tree. Then perform 50 trials of searching or a number in the tree. Regards the number od nodes that you have to look up and find the average number of node lookup.arrow_forwardUsing a self-balancing binary search tree, binary tree sort may complete in O(n log n) time, which is still slower than merge sort.arrow_forwardPYTHON: Design a set of computational experiments so that we can compare the search on a binary tree with a linear search.arrow_forward
- What is the best-case scenario in terms of search complexity for binary search trees? O(N-1). N is number of nodes in the tree O(log N). N is height of the tree O(log N). N is number of nodes in the tree O(N). N is number of nodes in the tree O(N+1). N is number of nodes in the treearrow_forwardconstruct a binary search tree using a set of numbers, similar to the example mentioned in the class. after constructing the BST, you need to give the pre-order traversal of the tree. Finally, you’re required to remove the root of tree. Please show me step by step how to do this!arrow_forwardCreate a SINGLE, binary search tree using the following three groups of input. For EACH of the three groups of input you add to the tree, say whether the tree is full, balanced, and/or complete. [50,25,30,24,70][72,71,26,32,22][56,60,77,54]arrow_forward
- In a binary search tree, to remove a node N that has parent P and one child C, we do the following: Group of answer choices If C is the right child of N, we make C the right child of P, and if C is the left child of N, we make C the left child of P If C is the right child of N, we make C the left child of P, and if C is the left child of N, we make C the right child of P If N is the left child of P, we make C the left child of P and if N is the right child of P, we make C the right child of P If N is the left child of P, we make C the right child of P and if N is the right child of P, we make C the left child of P none of the abovearrow_forwardDraw the binary search tree that is created if the following numbers are inserted in the tree in the given order. 8 12 2 29 17 36 13arrow_forwardIf you have a binary search tree with n nodes, what are the minimum and maximum levels in that tree? Justify your answer mathematically.arrow_forward
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