Constraint Satisfaction Problem Solver for Dart




Constraint Satisfaction Problem Solver for Dart that uses a basic backtracking algorithm. It has no external dependencies and currently works. It is quite slow due to unimplemented optimizations like MAC3 and LCV.

It does however support the MRV optimization.


Constraints are defined with an object hierarchy that begins with the primitive abstract class Constraint. All Constraint objects must implement one method - isSatisfied() - which returns a bool indicating whether the constraint has been satisfied by the provided assignment. The abstract subclasses UnaryConstraint, BinaryConstraint, and ListConstraint should typically be subclassed by a program using constraineD with an implementation of isSatisfied() being the primary definition of a problem.


A CSP is an object that defines a (C)onstraint (S)atisfaction (P)roblem. It holds all of the variables and constraints utilizing those variables that make up a problem. It also holds a domain for each variables through a map called domains.

Solving a CSP

A CSP is solved using a simple backtracking algorithm via the function backtrackingSearch(). It takes a CSP and a Map called assignment. Typically assignment will just be a blank map when you start up backtrackingSearch. backtrackingSearch returns a Future that represents a Map of the resulting assignments from successfully solving the CSP. If no result could be found this Future will hold a null value (equivalent of new Future.value(null)).

backtrackingSearch() has optional placeholders for the MRV, LCV, and MAC3 backtracking search constraint satisfaction problem optimizations that can be turned on via optional boolean parameters. A buggy implemention of MRV is already written, but for now LCV and MAC3 are just true placeholders.


There are examples of SEND + MORE = MONEY, the Australian Map Coloring Problem, and a couple circuit board layout problems in the test directory. There is also an example of using constraineD for creating a non-overlapping wordsearch grid in Chapter 16 of Dart for Absolute Beginners.