Algorithm design techniques

Algorithm design is a powerful tool for viewing and clearly understanding well-posed, real-world problems. A straightforward, or brute-force, approach is available that is very simple, yet effective, for many problems. The brute-force approach is trying all possible combinations of solutions in order to solve any problem. For example, suppose a salesperson has to visit 10 cities across the country. In which order should the cities be visited in order to minimize the total distance traveled? The brute-force approach to this problem will be to calculate the total distance for all possible combinations of routes, and then select the route that provides the smallest distance.

As you might guess, the brute-force algorithm is not efficient.

It can provide useful solutions for limited input sizes, but it becomes very inefficient when the input size becomes large. Therefore, we will break the process down into two fundamental components for finding the...