Question
Download Solution PDFThe running time of an algorithm is O(g(n)) if and only if
(A) its worst-case running time is O(g(n)) and its best-case running time is Ω(g(n)).(O = big O)
(B) its worst-case running time is Ω(g(n)) and its best-case running time is O(g(n)).(O = big O)
(C) O(g(n)) = Ω(g(n))(O = big O)
(D) O(g(n)) ∩ ω(g(n)) is non-empty set. (o = small o)
Choose the correct answer from the options given below:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is option 1.
Key Points
(A) its worst-case running time is O(g(n)) and its best-case running time is Ω(g(n)).(O = big O)
True,
Big-Oh(O) denotes upper bound or worst case.
Big-Omega(Ω) denotes lower bound or best case.
Big-Theta(Θ) denotes Average bound or average case.
(B) its worst-case running time is Ω(g(n)) and its best-case running time is O(g(n)).(O = big O)
False, worst case should be Big-oh and best case should be Big-Omega
(C) O(g(n)) = Ω(g(n))(O = big O)
False, Can not cover Big-Omega.
False, no such f(n) exists, i.e. the intersection is indeed the empty set.
∴ Hence the correct answer is (A) only.
Last updated on Jun 6, 2025
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