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Why Analysis of algorithms :

An algorithm is a step by step procedure i.e. a set of

instructions to solve the given problem. For a problem there

can be many algorithms to solve it. But how to find the best

algorithm among those?. Analysis of algorithms helps in

determining the solution for it.

What does it mean?

For example if a person wants to travel from one place

A to another place B, there can be many routes to reach from

A to B. Depending on the availability and convenience we

can choose the best route in terms of short route (if we want

to reach fast), Highway (Even though it is longer, but for

convenience) etc.

Similarly in Computer Science, there can be many

algorithms for a same problem. Analysis of algorithms helps

us in determining which of them is efficient in terms of

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space (memory) and running time by comparing the

algorithms. But how to compare algorithms ?

How to compare algorithms ?

Running time is best measure for comparing the

algorithms. It is the process of determining the processing

time increases as the size of input size (problem) increases.

Input size may vary depending on the type of problems. In

general we encounter the following types of inputs.

1) Size of array

2) No of elements in the matrix

3) Polynomial degree

4) Vertices and edges in a graph

In general, the running time of a algorithm is

expressed as a function of input size(n) i.e. f(n) and compare

these functions corresponding with their running times. This

is independent of machine time, processor, programme style

(no of statements) etc.

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Types of analysis :

To analyse the algorithm, we need to represent the

algorithm with multiple expressions: one for the case where

it takes less time and the other for the case where it takes

more time. The first case is called as Best case and the

second case is called as Worst case for that algorithm. There

are three types of analysis:

1) Best case

2) Average case

3) Worst case

For a given algorithm, we can represent the best, worst,

average cases in the form of expressions. For example

Let f(n) be the function represents the given algorithm

and n is the input size,

f(n) = n2 + n + 100 ; for worst case

f(n) = 5n + 200 ; for best case

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The expressions defines the input for which the algorithm

takes the less or average time (or memory). If both best and

worst cases, points to one expression then that expression

can be represented with average case.

f(n) = 10n + 50 ; for best and worst case

then f(n) can be represented for average case.

f(n) = 10n + 50 ; for average case