Algorithm is a set of mathematical instructions or rules that helps to calculate a solution to a problem. Now the main thing is what a “Problem” is. You may find out any problem in any discipline. This article gives a small example which gives you a clear idea of identifying an algorithm with its proper solution.

**Sample Problem: **Find out the GCD of two numbers.

**Solution-1:**

Numbers: 24 and 20.

20 = 2 X 2 X 5

24 = 2 X 2 X 2 X 3

GCD = 2X2 = 4

Step Count = 9

**Solution-2:**

Numbers: 24 and 20.

24 % 20 = 4

20 % 4 = 0

GCD = 4

Step Count = 2

So, it can be said that the solution 2 is an optimum solution that takes minimum amount of time to produce result. A problem may have more than two solutions, but the motivation of Algorithm is to find out the optimum solution of a problem.

Hope this lecture gives a clear idea of this subject. In the next lecture we will discuss about the complexities.

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