base62

Base62 is a base-62 numeral system that encodes integers using 62 distinct characters. The most common alphabet consists of the digits 0 through 9, followed by uppercase letters A through Z, and then lowercase letters a through z. Some implementations swap the order of uppercase and lowercase letters; others use alternative alphabets. Regardless of order, the concept remains: each position represents a power of 62 and a number is represented by a sequence of characters.

Encoding and decoding: To encode a nonnegative integer, repeatedly divide by 62 and record the remainders; map each remainder to the corresponding character; the final encoded string is the remainders read in reverse. The value zero is typically encoded as '0'. Decoding reverses the process by interpreting each character's index in the alphabet and accumulating value = value*62 + index. For example, with the common alphabet '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz', the integer 125 encodes to '21' (2*62 + 1).

Applications: Base62 is widely used in URL shortening, database keys, and other tokens where a compact, URL-safe representation is beneficial. It is not encryption; it is reversible given the alphabet and mapping.

Considerations: Because the alphabet includes both uppercase and lowercase letters, base62 strings are case-sensitive. It is efficient for compact representations, but the length scales with the logarithm of the input. Implementations are straightforward; many languages provide libraries or simple routines to encode and decode.