Chapter 3: Analysis Tools
Analysis.pdf
3.1 Running Time and Pseudo-Code
3.1.1 How Should Running Time be Measured?
3.1.2 Pseudo-Code
3.4 Analysis of Algorithms
3.5 Asymptotic Notation
Bog-Oh
Given functions f(n) and g(n), we say that f(n) is O(g(n)) if there are positive constants c and N
> 0 such that f(n) < c g(n) for n > N.
Big-Omega
f(n) is \Omega(g(n)) if there
is a constant c > 0 and an integer constant N > 0 such that
f(n) > c g(n) for n > N.
Big-Theta
f(n) is \Theta(g(n)) if there
are constants c'> 0 and c"> 0 and an integer constant N
> 0 such that c'g(n) < f(n) < c" g(n) for n > N.
little-oh
f(n) is o(g(n)) if, for any
constant c > 0, there is an integer constant N > 0 such that f(n)
< c g(n) for n > N.
little-omega
f(n) is \omega(g(n)) if, for
any constant c > 0, there is an integer constant N > 0
such that f(n) < cg(n) for n > N.
3.6 Asymptotic Analysis