Algorithm: Find the minimum number of sets containing your entire domain

Question

Given few sets and a number n:

Here assume n is 5:
a - (0,1,2)
b - (0,1,2,3)
c - (1,3,4,5)
d - (0,1,2,4)
e - (2,3,4,5)
f - (3,5)

Now if we take just b and c we get the entire range from 0 to 5.

I was thinking of a greedy approach but that does not seems to fit here.

Answer 1

This is the set cover problem and, as such, NP-complete, meaning you have to consider every possible solution and choose the minimum.