2. INTRODUCTION
DATA STRUCTURES : Data structures is a particular way of storing and
organizing data in a computer so that it can be used efficiently.Data structures make it
essay for users to access and work with the data they need in appropriate ways.
ALGORITHM : An Algorithm is a procedure used for solving a problems or performing a
computation . To describe in a easy manner say to go from city “A” to city ”B” there can be many
way of accomplishing this : by flight, by bus , by train also by bicycle . Depending on the availability
and convenience we choose the one that suits us . Similarly in computer science multiple algorithm
Are available for solving the same problem .
Algorithm analysis helps us determining which of them is efficient in terms of time and space
consumed .
3. Types of analysis
To analyze the given algorithm we need to know on what input algorithm takes less time
(performing well)and on what inputs the algorithm takes long time .
That means we represent the algorithm multiple expressions one for the case where it
takes less time and other for the case where it takes more time .
There are three types of analysis .
Worst case
o Define the inputs for which the algorithm takes the long time.
o Input is the one for which the algorithm runs the slower .
Best case
o Defines the input for which the algorithm takes the lowest time .
o Input is the one for which the algorithm runs the fastest.
Average case
o Provides prediction about the running time of the algorithm .
o Asssumes that the input is random.
4. ASYMPTOTIC NOTATION
Asymptotic notation is used to describe the running time of an
algorithm how much time an algorithm takes with a given input , we
use this notation to compare the algorithms.
There are three different notation
Big O Notation.
Big theta (Θ) Notation.
Big Omega (Ω)Notation.
5. OMEGA(Ω)NOTATION
Omega notation represents the lower bound of the running time of an
algorithm. Thus, it provides the best case complexity of an algorithm.
The notation Ω(n) is the formal way to express the lower bound of an
algorithm's running time. It measures the best case time complexity or the
best amount of time an algorithm can possibly take to complete.
Ω(f(n)) ≥ { g(n) : there exists c > 0 and n0 such that g(n) ≤ c.f(n) for all n >
n0. }
6.
7. The above expression can be described
as a function f(n) belongs to the set Ω(g(n)) if
there exists a positive constant c such
that it lies above cg(n), for sufficiently
large n.
For any value of n, the minimum time
required by the algorithm is given by
Omega Ω(g(n)).
9. CONCLUSION
It was very valuable and interesting project the moral provide
a strong conclusionOmega notation represents the lower
bound of the running time of an algorithm. Thus, it provides
the best case complexity of an algorithm. The above
expression can be described as a function f(n) belongs to the
set Ω(g(n)) if there exists a positive constant c such that it
lies above cg(n) , for sufficiently large n
