Digitmask

Digitmask, sometimes written as DIGITMASK, is a compact data representation used in computing to encode a subset of decimal digits 0 through 9 as a bitmask. The concept uses a ten-bit field, where bit i corresponds to digit i and is set if that digit occurs in the input. This allows a quick, space-efficient way to track which digits appear in a number, string, or sequence of symbols.

To construct a digitmask, each digit in the input is examined and the corresponding bit is turned on. For example, the number 4132 contains digits 4, 1, 3, and 2. The resulting mask has bits 1, 2, 3, and 4 set, which equals 2 + 4 + 8 + 16 = 30 (binary 00000011110 in a 10-bit field). Digit 0 is represented by the least significant bit, so its presence would add 1 to the mask. Operations on digitmasks typically use bitwise arithmetic, such as testing for a digit with (mask >> d) & 1, or combining masks with OR and intersecting with AND. The population count (popcount) of a mask reveals how many distinct digits are present.

DIGITMASKs are widely used in algorithmic problems, such as digit-based constraints, digit DP, and fast membership tests where duplicates are irrelevant. They provide a compact and fast method to compare digit sets and detect the presence or absence of particular digits. Limitations include that they only capture digit presence, not frequency, and are specific to decimal digits, not arbitrary symbols.