Algorithms · Question 15 · Hard
Using the Master theorem, what is the solution of T(n) = 3T(n/2) + n?
- Θ(n^(log2 3)), about Θ(n^1.585)
- Θ(n log n)
- Θ(n²)
- Θ(n^1.5)
Answer and explanation
Answer: A. Θ(n^(log2 3)), about Θ(n^1.585)
Explanation: Here a = 3 and b = 2, so n^(log_b a) = n^(log2 3) ≈ n^1.585. Since f(n) = n grows polynomially slower, case 1 applies and T(n) = Θ(n^(log2 3)).
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