Challenge: Digit Set Edge Cases

What if the digit set doesn't include 0? We can't form numbers like $101$. The DP handles this naturally by only trying available digits. What if $N = 0$? The answer is 0 (or 1 if we count 0 as valid). Check your base case. What if the digit set is $\{0\}$? Only 0 is valid.

But leading zeros mean we only count actual 0, not "00" or "000". What if $N <$ smallest digit? Answer is 0. The DP will find no valid paths at the first position.