Question

Arrange the following functions in ascending order; f(n) should come before g(n) in your list only...

Arrange the following functions in ascending order; f(n) should come before g(n) in your list only if f(n) is O(g(n)).

                        10n2 + 100n, (log n)3, 2n, 99999, log n, n0.1+100, 0.1n3-50n, log n1000, 3n, n log n

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Answer #1

Arrange the following functions in ascending order:

10n2 + 100n, (log n)3, 2n, 99999, log n, n0.1+100, 0.1n3-50n, log n1000, 3n, n log n

Ascending Order:

  • 99999
  • logn
  • (log n)3
  • log n1000
  • n0.1+100
  • n log n
  • 10n2 + 100n
  • 0.1n3-50n
  • 2n
  • 3n

Description:

• The above can be written as:

99999 < logn < (log n)3 < log n1000 < n0.1+100 < n log n < 10n2 + 100n < 0.1n3-50n < 2n < 3n

• Order of the following functions:

• 99999 is the constant function which is the O(1).

• logn, (log n)3,  log n1000 is the O(log(n)).

• n log n is the O(nlogn).

• 10n2 + 100n is the O(n2).

• 0.1n3-50n is the O(n3).

• 2n is the O(2n) and 3n is the O(3n).

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