Interesting interview questions

Prob.

Sampling from random

Q: use a uniform random generator rand(7) to produce uniform random rand(10).

Combine 2 rand(7) ($X$ and $Y$) as $Z = 7 \times X + Y$, we can obtain a uniform sampling $[1, 49]$. Then reject if $Z > 40$, and finally $Z' = Z \mod 10$.

Coding

Coding is the basic skills for a software engineer, no matter how LLM/agent powerful is.

All permutations

Q: if we have a next_permutation function, how to obtain all possible values of combination $\mathrm{C}_n^k$ based on this?

Compare a 0-1 array with $k$ ones and $n - k$ zeros. Run next_permutation on this array, each result means a snapshot of combination.