Question-33

Time complexity

Let \(g(n) = 6n^4 + 20n^3\) and \(f(n) = 5762n^3\log{n} + 436n^2\). Which of the following is true?

\(f(n)\) is \(O(g(n))\) and \(g(n)\) is \(O(f(n))\)
\(f(n)\) is \(O(g(n))\), but \(g(n)\) is not \(O(f(n))\)
\(f(n)\) is not \(O(g(n))\) and \(g(n)\) is not \(O(f(n))\)
\(g(n)\) is \(O(f(n))\), but \(f(n)\) is not \(O(g(n))\)

Answer

\(f(n)\) is \(O(g(n))\) and \(g(n)\) is \(O(f(n))\)
\(f(n)\) is \(O(g(n))\), but \(g(n)\) is not \(O(f(n))\)
\(f(n)\) is not \(O(g(n))\) and \(g(n)\) is not \(O(f(n))\)
\(g(n)\) is \(O(f(n))\), but \(f(n)\) is not \(O(g(n))\)