Characteristics of an Algorithm

While designing an algorithm as a solution to a given problem, we must take care of the following five important characteristics of an algorithm: 1. Finiteness An algorithm must terminate after a finite number of steps and further each step must be executable in finite amount of time. In order to establish a sequence of steps as an algorithm, it should be established that it terminates (in finite number of steps) on all allowed inputs. 2. Definiteness (no ambiguity)Each step of an algorithm must be precisely defined; the action to be carried...

Read More

Difference between Problems and Instances

The difference between the two concepts viz., ‘problem’ and ‘instance’, can be understood in terms of the following example. An instance of a problem is also called a question. We know that the roots of a general quadratic equation  (1) are given by the equation  (2) where a, b, c may be any real numbers except the restriction that a ≠ 0. Now, if we take a = 3, b = 4 and c = 1, we get the particular equation  (3) Using (2), the...

Read More

Euclid’s Algorithm for Finding G.C.D. of two Natural Numbers m & n

E1. {Find Remainder}. Divide m by n and let r be the (new) remainder {r have 0≤r<n} E2. {Is r zero?} If r = 0, the algorithm terminates and n is the answer. Otherwise, E3. {Interchange}. Let the new value of m be the current value of n and the new value of n be the current value of r. Go back to Step E1. The termination of the above method is guaranteed, as m and n must reduce in each iteration and r must become zero in finite number of repetitions of steps E1, E2 and E3. The great Greek mathematician Euclid sometimes between fourth and third...

Read More

Notation for expressing algorithms

This issue of notation for representations of algorithms will be discussed in some detail, later. However, mainly, some combinations of mathematical symbols, English phrases and sentences, and some sort of pseudo-high-level language notations, shall be used for the purpose. Particularly, the symbol ‘←’ is used for assignment. For example, x←y + 3, means that 3 is added to the value of the variable y and the resultant value becomes the new value of the variable x. However, the value of y remains unchanged. If in an algorithm, more than one variables...

Read More