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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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Let's call two numbers isomorphic if they have same number of digits and set of places having equal digits is same. We consider that all the numbers are in decimal notation and don't have leading zeroes. Consider some examples: • 12321 is isomorphic to 83538 and 45654. • 1232 is not isomorphically equal to 2342 because set of places having equal digits are {{1}, {2, 4}, {3}} and {{1, 4}, {2}, {3}} (digits are numbered from left to right using 1 based indexing). In other words, the digits order has to remain the same. • 12 isomorphic to 10,13,14, 92, but not isomorphic to 1, because their lengths are not equal and not isomorphic to 01, because leading zeroes are not allowed. Let F(X) denote the smallest integer (without leading zeroes) isomorphic to X where X is a positive integer. For example, F(12) = 10, F(213) = 102. You are given two integers N and M. Your task is to calculate F(1) % M + F(2) % M + F(3) % M + ... + F(N - 1) % M + F(N) % M.
Transcribed Image Text:Let's call two numbers isomorphic if they have same number of digits and set of places having equal digits is same. We consider that all the numbers are in decimal notation and don't have leading zeroes. Consider some examples: • 12321 is isomorphic to 83538 and 45654. • 1232 is not isomorphically equal to 2342 because set of places having equal digits are {{1}, {2, 4}, {3}} and {{1, 4}, {2}, {3}} (digits are numbered from left to right using 1 based indexing). In other words, the digits order has to remain the same. • 12 isomorphic to 10,13,14, 92, but not isomorphic to 1, because their lengths are not equal and not isomorphic to 01, because leading zeroes are not allowed. Let F(X) denote the smallest integer (without leading zeroes) isomorphic to X where X is a positive integer. For example, F(12) = 10, F(213) = 102. You are given two integers N and M. Your task is to calculate F(1) % M + F(2) % M + F(3) % M + ... + F(N - 1) % M + F(N) % M.
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