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Consider a rectangle whose side lengths are two consecutive Fibonacci numbers. (Of course, neither of them is 0.) Such a rectangle could be, for example, 3 by 5, or 8 by 13, or 21 by 34, etc. (a) Give a recursive algorithm to dissect such a rectangle into squares such that no more than two of the resulting squares are the same size. (For example, if you had two 3 by 3 squares, you could have at most one 4 by 4 square.) Here's a specification for your algorithm: // Input: Two consecutive Fibonacci numbers f0, f1, representing an f0 by f1 rectangle, such that f0 <= f1. (Neither f0 nor f1 will be 0.) // Output: A list of integers representing side lengths of squares, such that the input rectangle can be dissected into squares of those sizes. No more than two of the squares can be the same size.

Consider a rectangle whose side lengths are two consecutive Fibonacci numbers. (Of course, neither of them is 0.) Such a rectangle could be, for example, 3 by 5, or 8 by 13, or 21 by 34, etc. (a) Give a recursive algorithm to dissect such a rectangle into squares such that no more than two of the resulting squares are the same size. (For example, if you had two 3 by 3 squares, you could have at most one 4 by 4 square.) Here's a specification for your algorithm: // Input: Two consecutive Fibonacci numbers f0, f1, representing an f0 by f1 rectangle, such that f0 <= f1. (Neither f0 nor f1 will be 0.) // Output: A list of integers representing side lengths of squares, such that the input rectangle can be dissected into squares of those sizes. No more than two of the squares can be the same size.

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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2. Consider a rectangle whose side lengths are two consecutive Fibonacci numbers. (Of course, neither of them is 0.) Such a rectangle could be, for example, 3 by 5, or 8 by 13, or 21 by 34, etc. (a) Give a recursive algorithm to dissect such a rectangle into squares such that no more than two of the resulting squares are the same size. (For example, if you had two 3 by 3 squares, you could have at most one 4 by 4 square.) Here's a specification for your algorithm: // Input: Two consecutive Fibonacci numbers f0, f1, representing an f0 by f1 rectangle, such that f0 <= f1. (Neither f0 nor f1 will be 0.) // Output: A list of integers representing side lengths of squares, such that the input rectangle can be dissected into squares of those sizes. No more than two of the squares can be the same size. Please be sure to give an English description of the algorithm along with pseu- docode, explaining the main points of its design, and a concise inductive argument for its correctness (i.e., say what makes the base case correct, what makes the re- cursive cases correct, and how you know the algorithm terminates). T
Transcribed Image Text:2. Consider a rectangle whose side lengths are two consecutive Fibonacci numbers. (Of course, neither of them is 0.) Such a rectangle could be, for example, 3 by 5, or 8 by 13, or 21 by 34, etc. (a) Give a recursive algorithm to dissect such a rectangle into squares such that no more than two of the resulting squares are the same size. (For example, if you had two 3 by 3 squares, you could have at most one 4 by 4 square.) Here's a specification for your algorithm: // Input: Two consecutive Fibonacci numbers f0, f1, representing an f0 by f1 rectangle, such that f0 <= f1. (Neither f0 nor f1 will be 0.) // Output: A list of integers representing side lengths of squares, such that the input rectangle can be dissected into squares of those sizes. No more than two of the squares can be the same size. Please be sure to give an English description of the algorithm along with pseu- docode, explaining the main points of its design, and a concise inductive argument for its correctness (i.e., say what makes the base case correct, what makes the re- cursive cases correct, and how you know the algorithm terminates). T
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