OUTLINE OF ALGORITHMICS
We have already mentioned that not every problem has an algorithmic solution. The problem, which has at least one algorithmic solution (solving), is called algorithmic or computable problem. Also, we should note that there is no systematic method (i.e., algorithm) for designing algorithms even for algorithmic problems. In fact, designing an algorithm for a general algorithmic /computable problem is a difficult intellectual exercise.
It requires creativity and insight and no general rules can be formulated in this respect. As a consequence, a discipline called algorithmics has emerged that comprises large literature about tools, techniques and discussion of various issues like efficiency etc. related to the design of algorithms. In the rest of the course, we shall be explaining and practicing algorithms. Actually, algorithmics could have been an alternative name of the course. We enumerate below some well-known techniques which have been found useful in designing algorithms: