Time complexity of a powerset generating function
- by Lirik
I'm trying to figure out the time complexity of a function that I wrote (it generates a power set for a given string):
public static HashSet<string> GeneratePowerSet(string input)
{
HashSet<string> powerSet = new HashSet<string>();
if (string.IsNullOrEmpty(input))
return powerSet;
int powSetSize = (int)Math.Pow(2.0, (double)input.Length);
// Start at 1 to skip the empty string case
for (int i = 1; i < powSetSize; i++)
{
string str = Convert.ToString(i, 2);
string pset = str;
for (int k = str.Length; k < input.Length; k++)
{
pset = "0" + pset;
}
string set = string.Empty;
for (int j = 0; j < pset.Length; j++)
{
if (pset[j] == '1')
{
set = string.Concat(set, input[j].ToString());
}
}
powerSet.Add(set);
}
return powerSet;
}
So my attempt is this:
let the size of the input string be n
in the outer for loop, must iterate 2^n times (because the set size is 2^n).
in the inner for loop, we must iterate 2*n times (at worst).
1. So Big-O would be O((2^n)*n) (since we drop the constant 2)... is that correct?
And n*(2^n) is worse than n^2.
if n = 4 then
(4*(2^4)) = 64
(4^2) = 16
if n = 100 then
(10*(2^10)) = 10240
(10^2) = 100
2. Is there a faster way to generate a power set, or is this about optimal?
