Question

explain big-oh, big omega and big-theta notation in asymtotic analysis

Answer 1

Big O Notation : This defines the upper bound on the running time of an algorithm. In other words, it is the Asymptotic maximum time which an algorithm would take to run.

In mathematical Notation, let f(n) and g(n) to two functions on input n, where f(n),g(n) >= 0,

Then f(n) = O(g(n)) {if f(n) <= c*g(n) for some constants c and n₀  and n > n₀ }

Big Omega Notation (Ω) : This defines the lower bound on the running time of an algorithm, In other words, it is the Asymptotic  minimum time which an algorithm would take to run.

In mathematical Notation, let f(n) and g(n) to two functions on input n, where f(n),g(n) >= 0,

                                    Then f(n) = Ω(g(n))      {if f(n) >= c*g(n) for some constants c and n₀   and n > n₀ }

Big Theta Notation (θ) : This defines the lower bound as well as the upper bound on the running time of an algorithm, In other words, it is the Asymptotic  average time which an algorithm would take to run.

In mathematical Notation, let f(n) and g(n) to two functions on input n, where f(n),g(n) >= 0,

                                    Then f(n) = θ(g(n))      {if f(n) = O(g(n)) and f(n) = Ω(g(n)) }