Question

Briefly describe and give an example of the following notations in algorithm analysis:

a) f(n) = O(g(n))
b) f(n) = Ω(g(n))
c) f(n) = θ(g(n))
d) None of the above is related to algorithm analysis.

Answer 1

Algorithm analysis uses notations like O, Ω, and θ to describe the running time of an algorithm.

Step-by-step explanation:

In algorithm analysis, there are several notations used to describe the running time of an algorithm:

a) f(n) = O(g(n)): This notation represents that the running time of the algorithm, denoted by f(n), is at most proportional to the running time of another function g(n). For example, if f(n) = 2n^2 + 3n + 1 and g(n) = n^2, then f(n) = O(g(n)).

b) f(n) = Ω(g(n)): This notation represents that the running time of the algorithm, denoted by f(n), is at least proportional to the running time of another function g(n). For example, if f(n) = n^2 + n and g(n) = n, then f(n) = Ω(g(n)).

c) f(n) = θ(g(n)): This notation represents that the running time of the algorithm, denoted by f(n), is both at most and at least proportional to the running time of another function g(n). For example, if f(n) = 3n^2 - 2n and g(n) = n^2, then f(n) = θ(g(n)).

d) None of the above is related to algorithm analysis.