# Simple algorithm using the big theta - notation

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:

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.

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formula :- all algorithms whose graphs have a shape of parabola such as an insertion sort are classified in the class represented by (n^2) " read big-theta of n squared"

All algorithms whose graph have the shape of a logarithmic expression such as the binary search fall in the class represented by (lg n) "read big-theta of log n"

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#### Solution Preview

To divide a group of people into two disjoint subgroups such that the difference in the total ages is as large as possible, one can search for the youngest and put into one "group" and everybody else in the second. This answer would be classified as (n) because adding one more member in the group will only add one more step.

To divide this group so ...

#### Solution Summary

Simple algorithm using the big theta - notation is modeled.