Given $$$L,R (1 \leq L \leq R \leq 10^{18})$$$.
Count how many number $$$n=\overline{d_1d_2...d_k}$$$ that have $$$Q = n * d_1 * d_2 * \dots * d_k$$$ and $$$L \leq Q \leq R.$$$
I have done some calculation and found out that there are about $$$40000$$$ to $$$60000$$$ different possible product of digits: $$$d_1 * d_2 * \dots * d_k$$$. But I don't know any possible algorithm at all. Please help me! Thanks <3.
This blog post might be helpful: https://codeforces.me/blog/entry/84354
TL;DR: for your problem, just store the prime factorization of the digit product in the DP state. That's it!
Wow thanks. I missed that $$$d_1 * d_2 * \dots * d_k \lt n$$$ so there is only about 5000 different $$$d_1 * d_2 * \dots * d_k$$$.