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This ﬁle contains the exercises, hints, and solutions for Chapter 1 of the book ”Introduction to the Design and Analysis of Algorithms,” 2nd edition, by A. Levitin. The problems that might be challenging for at least some students are marked by ; those that might be diﬃcult for a majority of students are marked by .

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Ada Solution ManualThis ?le contains the exercises, hints, and solutions for Chapter 1 of the book "Introduction to the Design and Analysis of Algorithms," 2nd edition, by A. Levitin. The problems that might be challenging for at least some students are marked by ; those that might be di?cult for a majority of students are marked by .Exercises 1.11. Do some research on al-Khorezmi (also al-Khwarizmi), the man from whose name the word "algorithm" is derived. In particular, you should learn what the origins of the words "algorithm" and "algebra" have in common. 2. Given that the of?cial purpose of the U.S. patent system is the promotion of the "useful arts," do you think algorithms are patentable in this country? Should they be? 3. a. Write down driving directions for going from your school to your home with the precision required by an algorithm. b. Write down a recipe for cooking your favorite dish with the precision required by an algorithm. 4. Design an algorithm for swapping two 3 digit non-zero integers n, m. Besides using arithmetic operations, your algorithm should not use any temporary variable. 5. Design an algorithm for computing gcd(m, n) using Euclid's algorithm. 6. Prove the equality gcd(m, n) = gcd(n, m mod n) for every pair of positive integers m and n. 7. What does Euclid's algorithm do for a pair of numbers in which the ?rst number is smaller than the second one? What is the largest number of times this can happen during the algorithm's execution on such

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