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