 Step number

A step number is a positive integer whose adjacent decimal digits differ by exactly $1$. For example, $3210$ and $101$ are step numbers, while $112$ is not: its first two numerical digits have difference zero. Repetition is allowed; only neighboring differences are constrained.

The numerical digits form a walk on the path graph $0-1-\cdots -9$, starting at a nonzero digit. From a last digit $d$, the possible extensions are $d-1,d+1$ within the range $0,\dots ,9$. At endpoints there is only one extension.

For digit dynamic programming, record the last digit and a bit mask encoding the set of digits already visited. Appending $d^{\prime }$ updates the visited set by set union with $\{d^{\prime }\}$. Here pandigital means that every decimal digit appears at least once; repetitions are allowed. Accept only final states whose visited set contains all ten numerical digits. This separates local adjacency from the global requirement to have seen every digit.