Understanding Big O notation - Cracking the Coding Interview

Question

I need help understanding how the author got the answer of problem 11 in the Big O chapter.

The problem goes like this:

The following code prints

Answer 1

In general the printing of a constant length string is considered constant as well, but if we want to be precise let's consider the print of a single character as the basic operation: this means that to print a k length string we have O(k).

Since we have O(c^k) possible strings and for each of them we have to check if it is sorted (with O(k)) and to print them (another O(k)), the total complexity became O(c^k(k + k)) = O(2c^kk).

But multiplying a function for a constant factor doesn't change it's complexity, and therefore the answer remains O(c^kk).