Numbers of length N and value less than K

• Time : O(Alog₁₀C)
• Space : O(1)

c++

int helper(vector<int>& A, int len, int pos, string limit, bool fl) {
    if(len == pos) return pos == limit.length() ? fl : 1;
    if(pos >= limit.length()) return 0;
    else {
        if(fl) return pow(A.size(), limit.length() - pos);
        int res = 0;
        for(int i = 0; i < A.size() and A[i] <= limit[pos] - '0'; i++) {
            if(pos == 0 and A[i] == 0 and limit.length() != 1) continue;
            if(A[i] == (limit[pos] - '0')) res += helper(A,len,pos+1,limit,false);
            else res += helper(A,len,pos+1,limit,true);
        } 
        return res;
    }
}
int Solution::solve(vector<int> &A, int B, int C) {
    string s = to_string(C);
    if(s.length() < B) return 0;
    if(s.length() > B) return pow(A.size(), B - 1) * (B != 1 ? (A.size() - count(begin(A), end(A), 0)) : A.size());
    return helper(A,B,0,s, false);
}