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Design and Analysis of Algorithms by Himanshu B. Dave, Parag H. Dave

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Appendix B

Some Useful Mathematical Formulae

B.1 DEFINITIONS

f(n) = O(g(n))

iff ∃ positive c, n0 such that 0 ≤ f (n) ≤ cg(n) ∀n ≥ n0.

f(n) = Ω(g(n))

iff ∃ positive c, n0 such that f (n) ≥ cg(n) ≥ 0 ∀nn0.

f(n) = Θ(g(n))

iff f(n) = O(g(n)) and f(n) = Ω(g(n))

f(n) = o(g(n))

iff ∀ε > 0, ∃n0 such that ∣ ana∣ < ε, ∀nn0.

sup S

least b ∈ ℝ such that b ≥ s, ∀sS.

inf S

greatest b ∈ ℝ such that bssS.

Combinations: ...

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