1. Algorithms CSCI 235, Spring 2019 Lecture 3 Asymptotic Analysis

2. O notation--No faster than...
We use:
to mean:
Roughly: f(n) is at most as big as g(n)
or: f <= g 17

3. Examples
True or false?
23n2 + 17n - 12 = O(n2)
b) n3 = O(n2)

4. Strictly less than if Roughly: f(n) is way smaller than g(n)
or: f < g

5. Examples
True or false?
n2 = o(n3)
b) 2n2 + 2n + 1 = o(n2)

6. W notation--No slower than...
Roughly: f(n) is at least as big as g(n)
or: f >= g

7. Examples
True or false?
23n2 + 17n -12 = W(n2)
n3 = W(n2)

8. w notation: strictly greater thanif
Roughly: f(n) is way bigger than g(n)
or: f > g

9. Examples
True or false?
n3 = w(n2)
n! = w(2n)

10. Q notation--Just right...
Roughly: f(n) is about the same as g(n)
or: f = g 17

11. Examples
True or false?
23n2 + 17n - 12 = Q(n2)

12. Summary Say that f is: Notation Approximately Loosely
little omega g f=w(g) f is way bigger than g f>g
omega g f=W(g) f is at least as big as g f>=g
theta g f=Q(g) f is about the same as g f=g
oh g f=O(g) f is at most as big as g f<=g
little oh g f=o(g) f is way smaller than g f<g