6. Union/Find operation, (a) show that the heuristic “weighting rule" for Union guarantees the height of the tree is bounded above by O(log n). Note that, in the book, the weighting rule is defined by using the "rank" of a tree. In my lecture, the weighting rule is defined by using the number of nodes. To answer this question, use the definition in the lecture (number of nodes). (b) Show that by suing the weighting rule, the bound O(log n) is achievable, i.e., there is a sequence of Unions that can produce a tree of height O(log n).
6. Union/Find operation, (a) show that the heuristic “weighting rule" for Union guarantees the height of the tree is bounded above by O(log n). Note that, in the book, the weighting rule is defined by using the "rank" of a tree. In my lecture, the weighting rule is defined by using the number of nodes. To answer this question, use the definition in the lecture (number of nodes). (b) Show that by suing the weighting rule, the bound O(log n) is achievable, i.e., there is a sequence of Unions that can produce a tree of height O(log n).
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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![6. Union/Find operation,
(a) show that the heuristic “weighting rule" for Union guarantees the height of the tree is
bounded above by O(log n). Note that, in the book, the weighting rule is defined by
using the "rank" of a tree. In my lecture, the weighting rule is defined by using the
number of nodes. To answer this question, use the definition in the lecture (number
of nodes).
(b) Show that by suing the weighting rule, the bound O(log n) is achievable, i.e., there is
a sequence of Unions that can produce a tree of height O(log n).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff0f10baf-c814-4112-826a-b133a2e73caf%2F7b9f31b3-9c1e-4265-837e-e7d81e76a9c4%2Fxdx7drj_processed.png&w=3840&q=75)
Transcribed Image Text:6. Union/Find operation,
(a) show that the heuristic “weighting rule" for Union guarantees the height of the tree is
bounded above by O(log n). Note that, in the book, the weighting rule is defined by
using the "rank" of a tree. In my lecture, the weighting rule is defined by using the
number of nodes. To answer this question, use the definition in the lecture (number
of nodes).
(b) Show that by suing the weighting rule, the bound O(log n) is achievable, i.e., there is
a sequence of Unions that can produce a tree of height O(log n).
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