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This is a Chicken Scheme egg which solves constraint satisfaction problems.
A CSP is composed of a number of domain-variables that have a domain, a set of bindings they can assume, along with a number of constraints. This egg supports 5 kinds of constraints: efd (early failure detection), fc (forward checking), vp (value propagation), gfc (generalized forward checking) and ac (arc consistency).
- csp-solution domain-variables selectprocedure
Given a list of domain variables and a function to select which one to try to bind next, one can simply pass in first, this produces a solution to the CSP.
- create-domain-variable domainprocedure
Create a domain variable whose domain is domain.
- assert-constraint! constraint domain-variablesprocedure
Assert a constraint, a function that returns a boolean, between a number of domain variables. The kind of constraint is determined by inspecting *csp-strategy*. Valid types are: efd (early failure detection), fc (forward checking), vp (value propagation), gfc (generalized forward checking) and ac (arc consistency). The default is ac. For constraints of low arity, a small number of domain variables, it will use an optimized version of the constraint propagation code.
- bound? domain-variableprocedure
- binding domain-variableprocedure
Determine if the domain variable is bound and what its binding is.
- assert-unary-constraint-efd! constraint xprocedure
- assert-binary-constraint-efd! constraint x yprocedure
- assert-ternary-constraint-efd! constraint x y zprocedure
- assert-unary-constraint-fc! constraint xprocedure
- assert-binary-constraint-fc! constraint x yprocedure
- assert-ternary-constraint-fc! constraint x y zprocedure
- assert-unary-constraint-vp! constraint xprocedure
- assert-binary-constraint-vp! constraint x yprocedure
- assert-ternary-constraint-vp! constraint x y zprocedure
- assert-unary-constraint-gfc! constraint xprocedure
- assert-binary-constraint-gfc! constraint x yprocedure
- assert-ternary-constraint-gfc! constraint x y zprocedure
- assert-unary-constraint-ac! constraint xprocedure
- assert-binary-constraint-ac! constraint x yprocedure
- assert-ternary-constraint-ac! constraint x y zprocedure
Assert each of the 5 kinds of constraints between domain-variables x, y and z. You can always use assert-constraint! instead and it will default to these functions if your constraint is of low arity.
- assert-constraint-efd! constraint dsprocedure
- assert-constraint-fc! constraint dsprocedure
- assert-constraint-vp! constraint dsprocedure
- assert-constraint-gfc! constraint dsprocedure
- assert-constraint-ac! constraint dsprocedure
Assert each of the 5 kinds of constraints between the list of domain-variables ds. You can always use assert-constraint! instead as it will pick an optimized version for each of the above if the arity of the constraint is low.
- attach-before-demon! demon xprocedure
- attach-after-demon! demon xprocedure
- restrict-domain! x domainprocedure
Only of interest to implementers.
This solves Project Euler problem 43.
(use traversal nondeterminism csp) (let* ((ds (map-n (lambda _ (create-domain-variable (map-n identity 10))) 10)) (d3 (lambda (ns) (+ (* (first ns) 100) (* (second ns) 10) (third ns)))) (div (lambda (n) (lambda ns (= (modulo (d3 ns) n) 0)))) (nthd (lambda (a b) (sublist ds (- a 1) b)))) (assert-constraint! (div 17) (nthd 8 10)) (assert-constraint! (div 13) (nthd 7 9)) (assert-constraint! (div 11) (nthd 6 8)) (assert-constraint! (div 7) (nthd 5 7)) (assert-constraint! (div 5) (nthd 4 6)) (assert-constraint! (div 3) (nthd 3 5)) (assert-constraint! (div 2) (nthd 2 4)) (map-all-pairs (lambda l (assert-constraint! (lambda (a b) (not (= a b))) l)) ds) (foldl + 0 (map (lambda (l) (foldl (lambda (a b) (+ (* a 10) b)) 0 l)) (all-values (csp-solution ds last)))))
Copyright 1993-1995 University of Toronto. All rights reserved. Copyright 1996 Technion. All rights reserved. Copyright 1996 and 1997 University of Vermont. All rights reserved. Copyright 1997-2001 NEC Research Institute, Inc. All rights reserved. Copyright 2002-2013 Purdue University. All rights reserved.
Contact Andrei Barbu, email@example.com. Originally written by Jeff Siskind.
This program is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this program. If not, see http://www.gnu.org/licenses.