The asymptotic complexities of four functions are: f1(n) = 2n f2(n) = n3/2…

2023

The asymptotic complexities of four functions are:

  • f1(n) = 2n

  • f2(n) = n3/2

  • f3(n) = n log n

  • f4(n) = nlog n

Which option gives the functions in increasing order of asymptotic growth (lowest to highest)?

  1. A.

    f2, f3, f4, f1

  2. B.

    f1, f2, f3, f4

  3. C.

    f3, f2, f4, f1

  4. D.

    f3, f1, f2, f4

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Correct answer: C

Increasing-order comparison:

  • f3(n) = n log n grows slower than any fixed polynomial nk where k > 1.

  • f2(n) = n3/2 is a fixed polynomial.

  • f4(n) = nlog n grows faster than any fixed polynomial but slower than 2n.

  • f1(n) = 2n is exponential and grows fastest here.

Order: f3, f2, f4, f1

Final answer: Option C

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