April 2024
Intermediate to advanced
832 pages
29h 31m
English
Content preview from Design and Analysis of Algorithms
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Essential Mathematical Background 623
A.4 ASYMPTOTIC NOTATIONS
Let f : R → R and g : R → R
1. Big-Oh Notation
f is said to be big-oh of g, denoted f(x) = O(g(x)), if there are positive constants c and K such that
| f(x) | ≤ c | g(x) | ∀x ≥ K.
This means that f grows atmost as fast as g.
g is called an upper bound of f.
g is also called the order of magnitude of f.
2. Little-Oh Notation
f is said to be little-oh of g, denoted f(x) = o(g(x)), if
()
lim
()
x
fx
gx
→∞
= 0
This means that f grows slower than g.
3. Omega Notation
f is said to be omega of g, denoted f(x) = Ω (g(x)), if there are two positive constants c and K such that
c|g(x)| ...
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