5.1 Introduction.

In this chapter we look through a number of methods often used in algorithm development. It's about general methods which often apply in many and important problems where the number of possible solutions is forbiddingly big, in a sense that it is not possible to create and/or examine all those solutions just to find the one which fulfills certain requirements.Forbiddingly large numbers are for example the exponent and fictional functions of a n quantity,such as 2n or n! in best cases,or maybe combinations of those quantities in even worst cases. Even in modern Parallel Computers the execution of 30! simple mathematical actions would require about 300 centuries of calculations!

In this chapter,all possible solutions are acceptable for a problem, but the one we look for is the best meaning that there is no other better than the one we found.Of course,the comparison is made by certain criteria.In this chapter we accept that there is a number representing every solution, for example a cost,a profit, that is difficult to calculate it,therefore we seek a solution in which this number is for example minimum.We will also consider problems,for which we do not want the best solution,but just any other acceptable one out of a forbiddingly number of potential solutions.

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