Question

If positive function f(n) is given below as:

f(n) = a₀ + a₁n + a₂n² + a₃n³ + .......a_mn^m then for positive n and a_m > 0, f(n) is:

1. θ(n^a)
2. θ(mⁿ)
3. θ(a^m)
4. θ(n^m)

Answer 1

Correct Answer - Option 4 : θ(n^m)

f(n) = a0 + a1n + a2n2 + a3n3 + .......amnm

a0 , a1,  a2 ,a3 are constants & highest power of n is nm

So the complexity will be θ(nm)

Important Point 

Big-Θ notation to asymptotically bound the growth of a running time to within constant factors above and below.