Arrange by growth: n log n, n^2, 2^n, log n!, n^0.5, log^2 n
Analyze the arrange by growth: n log n, n^2, 2^n, log n!, n^0.5, log^2 n.
Examples
Input:"test_input_1"
Output:"output_1"
Input:"test_input_2"
Output:"output_2"
Hints
Recall the definitions of Big-O, Big-Theta, and Big-Omega notations, and how they relate to the growth rates of functions.
Compare the given functions by taking their logarithms (or using other transformations) to simplify the comparison, especially for functions like n log n, n^2, and log^2 n.
For factorial-based growth (log n!), apply Stirling's approximation to approximate n! and then take the logarithm to compare it with the other functions.
Arrange by growth: n log n, n^2, 2^n, log n!, n^0.5, log^2 n
Analyze the arrange by growth: n log n, n^2, 2^n, log n!, n^0.5, log^2 n.