UK Postcode Data Structure
Overview
- Type safe representation of only those strings that are valid postcodes
- Stack allocated 4 byte struct instead of a .NET string (26 - 30 byte heap allocation + 4 bytes for a reference)
- Fast postcode validation and parsing, ignoring spaces and treating all letters case in-sensitively
Background
Every UK address is associated with a postcode. This consists of between 5 and 7 letters and digits in one of these formats:
| Area | District | Sector | Unit | Example |
|---|---|---|---|---|
| A | 1 | 1 | AA | M1 1AE |
| A | 11 | 1 | AA | B33 8TH |
| A | 1A | 1 | AA | W1A 0AX |
| AA | 1 | 1 | AA | CR2 6XH |
| AA | 11 | 1 | AA | DN55 1PT |
| AA | 1A | 1 | AA | EC1A 1BB |
Where A represents an upper case letter A-Z and 1 represents a digit 0-9. A single space is placed between the sector and unit for a total of between 6 and 8 characters.
Description of Representation
- 1st character of the Area is a letter (26 possibilities)
- 2nd character of the Area is a letter or missing (26 + 1 = 27 possibilities)
- 1st character of the District is a digit (10 possibilities)
- 2nd character of the District is a letter, a digit or missing (26 + 10 + 1 = 37 possibilities)
- 1st character of the Sector is a digit (10 possibilities)
- 1st character of the Unit is a letter (26 possibilities)
- 2nd character of the Unit is a letter (26 possibilities)
The number of possible postcodes is 26 · 27 · 10 · 37 · 10 · 26 · 26 = 1,755,842,400 ≤ 2³². Therefore it is possible to represent a postcode in a 4 byte (32 bit) word by using this scheme:
| Value | 0 | 1 | 2 | 3 | … | 9 | 10 | 11 | 12 | 13 | … | 25 | 26 | … | 36 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Digit | 0 | 1 | 2 | 3 | … | 9 | |||||||||
| Letter | A | B | C | D | … | J | K | L | M | N | … | Z | |||
| Letter or missing | A | B | C | … | K | L | M | N | O | … | Y | Z | |||
| Letter, digit or missing | 0 | 1 | 2 | … | 8 | 9 | A | B | C | … | M | N | … | Z |
Parsing Algorithm
public static bool TryParse(string s, out Postcode postcode)The algorithm can be understood as a special case of multi-dimensional array indexing:
- Imagine each valid postcode is placed in a 7 dimensional array with the indexes for each dimension given by the scheme above
- This array might be represented in memory by a single dimensional array
- By calculating the index for a given postcode in this single dimensional array we have an integer that uniquely specifies any valid postcode
- It is not necessary to store the hypothetical array since the element the index represents can be easily computed using the reverse calculation
Package available on Nuget