Internet programming Practice Questions (Q13) - Computer Application

ICAR JRF Computer Application 29 Jun 2024Shift 1

MCQ (Single Correct) +4 −1

The notation is used when the function g(n) defines a lower bound for the function f(n).

Omega Correct Big O Theta Little Oh

Asymptotic Complexity Notations:
Big-Omega ($\Omega$) Notation: Defines an asymptotic lower bound on the growth rate of an algorithm's execution time. Formally:

$$f(n) = \Omega(g(n)) \iff \exists c \gt 0, n_0 \gt 0 \text{ such that } f(n) \ge c \cdot g(n) \quad \forall n \ge n_0$$

Other Notations:
Big-O ($O$): Asymptotic upper bound ($f(n) \le c \cdot g(n)$).
Theta ($\Theta$): Asymptotically tight bound.
Little-o ($o$): Strict upper bound.
Conclusion: Omega (Option 1).

Correct option: (1) Omega

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