Homework 1

Due September 12th:

• 1.1 Send me (mlittman@cs.duke.edu) your email address (right away).
• 1.2 Multiply using the Russian Peasant's Algorithm.
• 1.3 For Naive multiplication, carry out algorithm development Step 2.
• 1.4 Write a recursive algorithm [Step 1] for computing (where both a and b are positive integers). Prove that it is correct [Step 2]. Analyze the number of recursive calls it makes [Step 3] (it should be logarithmic). You can assume you have built-in (unit-time) multiplication and bit shifting, but not exponentiation or general division.
• CLR Problem 2-6 (pg 40).