If an algorithm has a time complexity of Θ(n2), which of the following is TRUEGroup of answer choicesits running time is Ω(n^3)its running time is Ω(n log n)its running time is Ω(n)its running time is Ω(n^2)
Question
If an algorithm has a time complexity of Θ(n2), which of the following is TRUEGroup of answer choicesits running time is Ω(n^3)its running time is Ω(n log n)its running time is Ω(n)its running time is Ω(n^2)
Solution
The correct answer is "its running time is Ω(n^2)".
Here's why:
The time complexity of an algorithm, denoted as Θ(n^2), describes the upper and lower bounds of the time taken by the algorithm to run. In other words, it gives us an estimation of the running time in the best and worst-case scenarios.
Ω notation, on the other hand, provides an asymptotic lower bound. This means that the running time of the algorithm is at least Ω(n^2), but it could be more.
Therefore, the statement "its running time is Ω(n^2)" is true because the running time of the algorithm is at least n^2 for large inputs n. The other options suggest that the algorithm could run faster than Θ(n^2), which contradicts the given time complexity.
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