Write a pseudocode for this version of Euclid’s algorithm. Euclid’s algorithm, as presented in Euclid’s treatise, uses subtractions rather than integer divisions. What is the largest number of divisions made by Euclid’s algorithm among all inputs 1 ≤ m, n ≤ 10? 9. What is the smallest number of divisions made by Euclid’s algorithm among all inputs 1 ≤ m, n ≤ 10? b. What does Euclid’s algorithm do for a pair of numbers in which the first number is smaller than the second one? What is the largest number of times this can happen during the algorithm’s execution on such an input? 8. Prove the equality gcd( m, n ) = gcd( n, m mod n ) for every pair of positive integers m and n. Estimate how many times faster it will be to find gcd (31415, 14142) by Euclid’s algorithm compared with the algorithm based on checking consecutive integers from min down to gcd( m, n ). Find gcd (31415, 14142) by applying Euclid’s algorithm. Be- sides assignment and comparison, your algorithm may only use the four basic arithmetical operations.
Design an algorithm for computing √ n for any positive integer n. Write down a recipe for cooking your favorite dish with the precision required by an algorithm. Write down driving directions for going from your school to your home with the precision required by an algorithm. patent system is the promo- tion of the “useful arts,” do you think algorithms are patentable in this country? Should they be? 3. Given that the official purpose of the U.S. In particular, you should learn what the origins of the words “algorithm” and “algebra” have in common. Do some research on al-Khorezmi (also al-Khwarizmi), the man from whose name the word “algorithm” is derived. 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. 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.
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