A constraint-satisfaction problem (CSP) models a problem with variables, domains of possible values, and constraints that restrict compatible assignments. A solver searches for an assignment satisfying every constraint. In languages without built-in CSP facilities, a reusable framework commonly combines recursive backtracking with performance heuristics. section 3.0
Model a problem by identifying:
- Variables: the things that need values, such as meeting participants, Australian regions, queens, words, or cryptarithm letters. section 3.0 section 3.5
- Domains: the possible values for each variable, such as available hours, colors, board rows, grid locations, or digits. section 3.2 section 3.4
- Constraints: rules that reject incompatible assignments while allowing partial assignments to continue until enough values are known. section 3.2 section 3.5
One framework, several problems
A generic Swift CSP framework solves Australian map coloring by assigning red, green, or blue to regions while preventing equal colors on borders. Reusing the same framework, the eight queens problem assigns rows to fixed columns and rejects equal rows or diagonals. Other applications place nonoverlapping words in a grid and assign distinct digits to SEND+MORE=MONEY. section 3.2 section 3.3 section 3.4 section 3.5
Implement constraints by:
- Returning true for incomplete assignments when no conflict is yet possible, then checking the full rule once relevant values exist. section 3.2 section 3.5
The approach favors generic reuse over problem-specific code, but domain generation can dominate runtime: word-search placement examines many grid locations, and preassigning SEND+MORE=MONEY values can make brute-force search practical in a Swift Playground. section 3.3 section 3.4 section 3.5
Use the scheduling diagram to connect variables, availability domains, and attendance constraints before implementing a solver. section 3.0
