A computational method is a method for solving a specific type of problem by
means of a nite set of steps operating on inputs, which are quantities given to
it before execution of the steps begins or during executing, and producing one
or more outputs, which have a specified relation to the inputs, its play an
important role in mathematics: Ancient mathematical literature contains
descriptions of algorithms for a variety of tasks.
In the modern internet world, man
feels that just by entering what he wants to search into the computers he can
get information as desired by him. He believes that, this is done by computer. A
common man seldom understands that a man made procedure called search has done
the entire job and the only support provided by the computer is the execution
speed and organized storage of information.
CHARACTERISTICS OF AN ALGORITHM
Let us try to present the scenario of a man brushing his own shoes as an
algorithm as follows:
Step 1. Take the brush
Step 2. Apply the polish
Step 3. Start brushing
Step 4. Stop
The definiteness and effectiveness
of an instruction implies the successful termination of that instruction.
However the above two may not be sufficient to guarantee the termination of the
algorithm. Therefore, while designing an algorithm care should be taken to
provide a proper termination for algorithm. Thus, every algorithm should have
the following five characteristic feature.
Therefore, an algorithm can be
defined as a sequence of definite and effective instructions, which terminates
with the production of correct output from the given input.
HOW TO DEVISE THE ALGORITHMS
The process of devising an
algorithm is both an art and a science. This is one part that cannot be
automated fully. Given a problem description, one have to think of converting
this into a series of steps, which, when executed in a given sequence solve the
problem. To do this, one has to be familiar with the problem domain and also the
computer domains. This aspect may never be taught fully and most often, given a
problem description, how a person proceeds to covert it into an algorithm
becomes a matter of his "style" - no firm rules become applicable here.
For the purpose of clarity in understanding, let us consider the following
Problem: Finding the largest value among n>=1 numbers.
Input: the value of n and n numbers
Output: the largest value
Let the value of the first be the largest value denoted by
Let R denote the number of remaining numbers. R=n-1
If R != 0 then it is implied that the list is still not
exhausted. Therefore look the next number called NEW.
Now R becomes R-1
If NEW is greater than BIG then replace BIG by the value of
Repeat steps 3 to 5 until R becomes zero.
End of algorithm
HOW TO VALIDATE THE ALGORITHMS
Once an algorithm has been
devised, it becomes necessary to show that it works. i.e it computes the correct
answer to all possible, legal inputs. One simple way is to code it into a
program. However, converting the algorithms into programs is a time consuming
process. Hence, it is essential to be reasonably sure about the effectiveness of
the algorithm before it is coded. This process, at the algorithm level, is
called "validation". Several mathematical and other empirical methods of
validation are available. Providing the validation of an algorithm is a fairly
complex process and most often a complete theoretical validation, though
desirable, may not be provided. Alternately, algorithm segments, which have been
proved else where may be used and the overall working algorithm may be
empirically validated for several test cases. Such methods, although suffice in
most cases, may often lead to the presence of unidentified bugs or side effects
HOW TO TEST THE ALGORITHMS
If there are more then one
possible way of solving a problem, then one may think of more than one algorithm
for the same problem. Hence, it is necessary to know in what domains these
algorithms are applicable. Data domain is an important aspect to be known in the
field of algorithms. Once we have more than one algorithm for a given problem,
how do we choose the best among them? The solution is to devise some data sets
and determine a performance profile for each of the algorithms. A best case data
set can be obtained by having all distinct data in the set.
A control constructs present in
the given below algorithms, A conditional statement has the following form :
If < condition> then
This pseudo code executes block1
if the condition is true otherwise block2 is executed.
2. The two types of loop
structures are counter based and conditional based and they are as follows
For variable = value1 to value2 do
Here the block is executed for all
the values of the variable from value 1 to value 2.
There are two types of conditional
looping, while type and repeat type.
While (condition) do
Here block gets executed as long
as the condition is true.
Here block is executed as long as
condition is false. It may be observed that the block is executed at least once
in repeat type.
In this article the concepts of algorithm are presented and the
properties of the algorithm are also given.