Pattern - Digit DP

When you see a problem counting numbers in a range with digit-based constraints, think digit DP. The pattern:

$1.$ Convert the limit to a string (base $10$) or binary.

$2.$ State: $(pos, tight, started, ...extra)$ where extra depends on the constraint.

$3.$ Transition: try each valid digit, update state, recurse.

$4.$ Base case: return $1$ when you've placed all digits (and satisfied constraints). Common extra states: bitmask (distinct digits), running sum (digit sum), remainder (divisibility), previous digit (adjacency constraints).