Problem - Cracking the Safe

Problem: A safe has a password of $n$ digits where each digit is $0$ to $k-1$. Find the shortest string that contains all possible passwords as substrings.

Link: LeetCode 753

Example: $n = 2$, $k = 2$. Passwords: $00, 01, 10, 11$. Answer: "$01100$" (length $5$).

Connection: This is the De Bruijn sequence problem generalized to alphabet size $k$. Build a De Bruijn graph and find an Euler circuit.