Range Queries

Digit DP naturally counts from $0$ to $N$. But problems often ask for a range $[L, R]$. Use inclusion-exclusion: $count(L, R) = count(0, R) - count(0, L-1)$ Compute the count up to $R$, subtract the count up to $L-1$.

You run digit DP twice with different limits. Watch for edge cases: if $L = 0$, you might need to handle it specially since $L-1 = -1$ is invalid. Some problems exclude $0$ from the count.