Big-O, Big -omega, Big-Theta notation to measure the time complexity of algorithm.

1. Asymptotic Notations

2. The mathametical representation of time c
omplexity is called as Asymtotic Notation
s.
Big oh ( O)notation
Big omegap(Ω)notation
Big theta (θ) notation

3. Big oh (O) notation: It is a method repr
esenting upper bound of algorithm's running
time.
Definition:
Let f(n)& g(n) ---->two non negative function
s.
n0 & c -----> constants
n0 is some input n>n0 , c>0

4. f(n)<=c*g(n)
f(n)∈Og(n)

5. 5
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6. Example:
f(n)=2n+2 & g(n)=n2
If n=3
f(n)=2(3)+2=8
g(n)=(3)2=9
f(n)<g(n)

7. 90%
Big omega(Ω)notation
This represents lower boun
d of algorithm running time.
f(n)>=c*g(n)

9. f(n)=2n2+5 & g(n)=7n
n=0
f(n)=5 & g(n)=0
f(n)>g(n) f(n)∈Ωg(n)

10. Theta notation :(θ )
By this method tbe running time is betw
een upper bound and lower bound.
C1*g(n)<=f(n)<=c2*g(n)
Then say that
f(n)∈θg(n)

12. Example:
If f(n)=2n+8 & g(n)=7n
I e 5n<2n+8<7n n>=2

13. Hint:
1<log n<n<n2<n3........<2n
Upper bond

14. Hint:
1< log n < n< n2<n3........< 2n
Lower bound

15. Hint:
1< log n< n<n2<n3.........<2
n
Exact