Question

In this exercise, we want to experiment with long-integer multiplication algorithms. 1. Write a program times $[a, b]$ for the multiplication of two long integers similar to the program plus [] in Section 7.4.1. Use the naive schoolbook method for multiplication. 2. Implement the Karatsuba method. 3. For what size of numbers is the Karatsuba method faster than the simple algorithm?

   In this exercise, we want to experiment with long-integer multiplication algorithms.
1. Write a program times $[a, b]$ for the multiplication of two long integers similar to the program plus [] in Section 7.4.1. Use the naive schoolbook method for multiplication.
2. Implement the Karatsuba method.
3. For what size of numbers is the Karatsuba method faster than the simple algorithm?

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Computer science with Mathematica: theory and practice for science, mathematics, and engineering

Computer science with Mathematica: theory and practice for science, mathematics, and engineering

Roman Maeder 1st Edition

Chapter 7, Problem 3

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Step 1

- Define a function `naive_multiplication(a, b)` where `a` and `b` are strings representing large integers. - Convert the strings `a` and `b` into lists of integers for easier manipulation. - Initialize a result list of zeros with a length equal to the sum of the Show more…

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In this exercise, we want to experiment with long-integer multiplication algorithms. 1. Write a program times $[a, b]$ for the multiplication of two long integers similar to the program plus [] in Section 7.4.1. Use the naive schoolbook method for multiplication. 2. Implement the Karatsuba method. 3. For what size of numbers is the Karatsuba method faster than the simple algorithm?

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