1. Use big-theta notation to classify the traditional grade school algorithms for addition and multiplication. That is, if asked to add two numbers each having n-digits, how many individual additions must be performed? If asked to multiply two n-digit numbers, how many individual multiplications are required?
2. Sometimes a slight change in a problem can significantly alter the form of its solution. For example, find a simple algorithm for solving the following problem and classify it using big-theta notation:
a. Divide a group of people into two disjoint subgroups (of arbitrary size) such that the difference in the total ages of the members of the two subgroups is as large as possible.
Now change the problem so that the desired difference is as small as possible and classify your approach to the problem.