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Selection Problem: Let a and b be integers with a ≤ b, and let [a, b] denote the set {a, a + 1, a + 2, . . . , b}. Suppose we are given n such sets [a1, b1], . . . , [an, bn], their multiset sum is S = {a1, a1 + 1, . . . , b1, a2, a2 + 1, . . . , b2, . . . , an, an + 1, . . . , bn}. Note that some integers can occur multiple times in the multiset sum. For example, if the intervals are [5, 25], [3, 10], [8, 12], the multiset sum is {3, 4, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, . . . , 25}. Q: Given an integer x and the sets [a1, b1], . . . , [an, bn], design an efficient algorithm that outputs the number of elements in S less than x. What is the running time of the algorithm?

Selection Problem: Let a and b be integers with a ≤ b, and let [a, b] denote the set {a, a + 1, a + 2, . . . , b}. Suppose we are given n such sets [a1, b1], . . . , [an, bn], their multiset sum is S = {a1, a1 + 1, . . . , b1, a2, a2 + 1, . . . , b2, . . . , an, an + 1, . . . , bn}. Note that some integers can occur multiple times in the multiset sum. For example, if the intervals are [5, 25], [3, 10], [8, 12], the multiset sum is {3, 4, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, . . . , 25}. Q: Given an integer x and the sets [a1, b1], . . . , [an, bn], design an efficient algorithm that outputs the number of elements in S less than x. What is the running time of the algorithm?

Computer Networking: A Top-Down Approach (7th Edition)
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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Selection Problem:

Let a and b be integers with a ≤ b, and let [a, b] denote the set {a, a + 1, a + 2, . . . , b}.

Suppose we are given n such sets [a1, b1], . . . , [an, bn], their multiset sum is S = {a1, a1 + 1, . . . , b1, a2, a2 + 1, . . . , b2, . . . , an, an + 1, . . . , bn}. Note that some integers can occur multiple times in the multiset sum. For example, if the intervals are [5, 25], [3, 10], [8, 12], the multiset sum is {3, 4, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, . . . , 25}.

Q: Given an integer x and the sets [a1, b1], . . . , [an, bn], design an efficient algorithm that outputs the number of elements in S less than x. What is the running time of the algorithm?

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