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Asymptotic Notation
Prepared by:- Ishita Kar
Definition:-
Asymptotic notation is a notation used to represent and compare the efficiency
of algorithms. When we use asymptotic notation to apply to the running time of an
algorithm, we need to understand which running time we mean. asymptotic notation can
apply to functions that characterize some other aspect of algorithms (the amount of space
they use, for example), or even to functions that have nothing whatsoever to do with
algorithms.
Generally we use three important notations to analyse the algorithm . These are as
follows:- Big O
Notation
O(g(n))
Big 𝜃
Notation 𝜃(g(n))
Big 𝛺
Notation
Ω(g(n))
Big O Notation
Big O Notation represents the
upper bound of the runtime of an
algorithm. In this case growth rate
of f(n) is not more than growth
rate of g(n).It means-
f(n)≤O[g(n)]
g(n)
f(n)
Time
No. of inputs
Big 𝜃 Notation
Big 𝜃 Notation represents the average
value of the runtime of an algorithm. In
this case f(n) is bound above and below
by two constant multiple of g(n).Let
c1*g(n) and c2*g(n) are two constant
multiples of g(n). So-
c1*[g(n)]≤f(n)≤c2*[g(n)]
No. of inputs
Time
c1.g(n)
c2.g(n)
f(n)
Big 𝛺 Notation
Big 𝛺 Notation represents the lower
bound of the runtime of an algorithm.
In this case growth rate of f(n) is not
less than growth rate of g(n).It means-
f(n)≥Ω[g(n)]
f(n)
g(n)
Time
No. of inputs
Any Questions?
Thank You

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Asymptotic Notation.pptx

  • 2. Definition:- Asymptotic notation is a notation used to represent and compare the efficiency of algorithms. When we use asymptotic notation to apply to the running time of an algorithm, we need to understand which running time we mean. asymptotic notation can apply to functions that characterize some other aspect of algorithms (the amount of space they use, for example), or even to functions that have nothing whatsoever to do with algorithms. Generally we use three important notations to analyse the algorithm . These are as follows:- Big O Notation O(g(n)) Big 𝜃 Notation 𝜃(g(n)) Big 𝛺 Notation Ω(g(n))
  • 3. Big O Notation Big O Notation represents the upper bound of the runtime of an algorithm. In this case growth rate of f(n) is not more than growth rate of g(n).It means- f(n)≤O[g(n)] g(n) f(n) Time No. of inputs
  • 4. Big 𝜃 Notation Big 𝜃 Notation represents the average value of the runtime of an algorithm. In this case f(n) is bound above and below by two constant multiple of g(n).Let c1*g(n) and c2*g(n) are two constant multiples of g(n). So- c1*[g(n)]≤f(n)≤c2*[g(n)] No. of inputs Time c1.g(n) c2.g(n) f(n)
  • 5. Big 𝛺 Notation Big 𝛺 Notation represents the lower bound of the runtime of an algorithm. In this case growth rate of f(n) is not less than growth rate of g(n).It means- f(n)≥Ω[g(n)] f(n) g(n) Time No. of inputs