The document discusses asymptotic notation, a mathematical tool for measuring and comparing algorithm efficiency. It explains three main types of notation: big O for upper bounds (worst-case complexity), omega for lower bounds (best-case complexity), and theta for both bounds (average-case complexity). The document includes examples and definitions, alongside references for further reading.

1. PRESENTER: FIADUZ ZAMAN
STUDENT CODE: BWU/BTA/21/101
COURSE NAME: DESIGN & ANALYSIS OF
ALGORITHM
COURSE CODE: PCC-CSM402
ASYMPTOTIC NOTATION

2. ASYMPTOTIC NOTATION !

3. TABLE OF CONTENTS
More detail about Omega
Notation
OMEGA NOTATION (Ω)
03 04
01 02
Brief introduction to
Asymptotic notation
INTRODUCTION
More details of Theta Notation
THETA NOTATION (Θ)
More detail about the Big
O Notation
BIG O NOTATION

4. ASYMPTOTIC NOTATION
 EFFICIENCY MEASUREMENT: Asymptotic notation is a
mathematical tool used for measuring and comparing the
efficiency of algorithms.
 DESCRIBING GROWTH RATES: It provides a concise way to
describe how the runtime or resource usage of an algorithm
changes as the input size increases.
 ALGORITHM DESIGN: Asymptotic notation guides algorithm
design by helping to identify the most efficient approaches and
optimizations.

5. “BIG O NOTATION, O( )”
• Big-O notation represents the upper bound of the running time of an
algorithm. Thus, it gives the worst-case complexity of an algorithm.
Cg(n)
f (n)
n
F(n)=0(g(n))
n0
O(g(n)) = { f(n): there exist positive
constants c and n0
such that 0 f(n)
≤ ≤
cg(n) for all n n
≥ 0
}

6. “OMEGA NOTATION, Ω ( )”
• Omega notation represents the lower bound of the running time of
an algorithm. Thus, it provides the best case complexity of an
algorithm
cg(n)
f (n)
F(n)=Ω(g(n)) n0
Ω(g(n)) = { f(n): there exist positive
constants c and n0
such that 0 cg(n)
≤ ≤
f(n) for all n n
≥ 0
}
n

7. “THETA NOTATION, θ( )”
o Theta notation encloses the function from above and below. Since it
represents the upper and the lower bound of the running time of an
algorithm, it is used for analyzing the average-case complexity of an
algorithm.
c2g(n)
c1g(n)
f(n)
n0 f(n)=θ(g(n))
n
Θ(g(n)) = { f(n): there exist positive constants
c1
, c2
and n0
such that 0 c
≤ 1
g(n) f(n)
≤ ≤
c2
g(n) for all n n
≥ 0
}

8. “REFERENCES”
 CHATGPT
 PROGRAMIZ
https://chat.openai.com/chat
INTERNET
https://www.programiz.com/dsa/asymptotic-notations

9. THANK YOU

10. R e a c h m e a t
↓
fiaduzzaman2014@gmail.com
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