New Summit College(B.Sc.CSIT)
Principles of Analyzing algorithms and Problems
An algorithm is a finite set of computational instructions, each instruction can be executed in finite
time, to perform computation or problem solving by giving some value, or set of values as input to
produce some value, or set of values as output. Algorithms are not dependent on a particular
machine, programming language or compilers i.e. algorithms run in same manner everywhere. So
the algorithm is a mathematical object where the algorithms are assumed to be run under machine
with unlimited capacity.
Examples of problems
• You are given two numbers, how do you find the Greatest Common Divisor.
• Given an array of numbers, how do you sort them?
We need algorithms to understand the basic concepts of the Computer Science, programming.
Where the computations are done and to understand the input output relation of the problem we
must be able to understand the steps involved in getting output(s) from the given input(s).
You need designing concepts of the algorithms because if you only study the algorithms then you
are bound to those algorithms and selection among the available algorithms. However if you have
knowledge about design then you can attempt to improve the performance using different design
The analysis of the algorithms gives a good insight of the algorithms under study. Analysis of
algorithms tries to answer few questions like; is the algorithm correct? i.e. the
Algorithm generates the required result or not?, does the algorithm terminate for all the inputs
under problem domain? The other issues of analysis are efficiency, optimality, etc. So knowing the
different aspects of different algorithms on the similar problem domain we can choose the better
algorithm for our need. This can be done by knowing the resources needed for the algorithm for its
execution. Two most important resources are the time and the space. Both of the resources are
measures in terms of complexity for time instead of absolute time we consider growth
Input(s)/output(s): There must be some inputs from the standard set of inputs and an
algorithm’s execution must produce outputs(s).
Definiteness: Each step must be clear and unambiguous.
Finiteness: Algorithms must terminate after finite time or steps.
Correctness: Correct set of output values must be produced from the each set of inputs.
Effectiveness: Each step must be carried out in finite time.
Here we deal with correctness and finiteness.
By Bhupendra Saud
This RAM model is the base model for our study of design and analysis of algorithms to have
design and analysis in machine independent scenario. In this model each basic operations (+, -)
takes 1 step, loops and subroutines are not basic operations. Each memory reference is 1 step. We
measure run time of algorithm by counting the steps.
Random Access Machine Model