complexity of recursive string permutation function

Question

From: Are there any better methods to do permutation of string?

what is the complexity of this function???

void permute(string elems, int mid, int en         


        

Answer 1

Ignoring the print, the recurrence relation satisfied is

T(n) = n*T(n-1) + O(n)

If G(n) = T(n)/n! we get

G(n) = G(n-1) + O(1/(n-1)!)

which gives G(n) = Theta(1).

Thus T(n) = Theta(n!).

Assuming that the print happens exactly n! times, we get the time complexity as

Theta(n * n!)