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typesetting/csp/constraint.rkt

548 lines
22 KiB
Racket

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#lang racket/base
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(require racket/class racket/contract racket/match racket/list racket/generator)
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(require sugar/container sugar/debug)
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(require "helpers.rkt")
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(module+ test (require rackunit))
;; Adapted from work by Gustavo Niemeyer
#|
# Copyright (c) 2005-2014 - Gustavo Niemeyer <gustavo@niemeyer.net>
#
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
#
# 1. Redistributions of source code must retain the above copyright notice, this
# list of conditions and the following disclaimer.
# 2. Redistributions in binary form must reproduce the above copyright notice,
# this list of conditions and the following disclaimer in the documentation
# and/or other materials provided with the distribution.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
# DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE
# FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
# SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
# OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|#
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(provide (all-defined-out) (all-from-out "helpers.rkt"))
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;(provide Problem Variable Domain Unassigned Solver BacktrackingSolver RecursiveBacktrackingSolver MinConflictsSolver Constraint FunctionConstraint AllDifferentConstraint AllEqualConstraint MaxSumConstraint ExactSumConstraint MinSumConstraint InSetConstraint NotInSetConstraint SomeInSetConstraint SomeNotInSetConstraint)
;(define Problem/c (λ(x) (is-a x Problem)))
(define/contract Problem
;; Class used to define a problem and retrieve solutions
(class/c [reset (->m void?)]
;; todo: tighten `object?` contracts
[setSolver (object? . ->m . void?)]
[getSolver (->m object?)]
;; todo: tighten `object?` contract
[addVariable (any/c (or/c list? object?) . ->m . void?)]
[getSolutions (->m list?)])
(class* object% (printable<%>)
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(super-new)
(init-field [solver #f])
(field [_solver (or solver (new BacktrackingSolver))]
[_constraints null]
[_variables (make-hash)])
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(define (repr) (format "<Problem ~a>" (hash-keys _variables)))
(define/public (custom-print out quoting-depth) (print (repr) out))
(define/public (custom-display out) (displayln (repr) out))
(define/public (custom-write out) (write (repr) out))
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(define/public (reset)
;; Reset the current problem definition
(set! _constraints null)
(hash-clear! _variables))
(define/public (setSolver solver)
;; Change the problem solver currently in use
(set! _solver solver))
(define/public (getSolver)
;; Obtain the problem solver currently in use
_solver)
(define/public (addVariable variable domain)
;; Add a variable to the problem
(when (variable . in? . _variables)
(error 'addVariable (format "Tried to insert duplicated variable ~a" variable)))
(cond
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[(list? domain) (set! domain (new Domain [set domain]))]
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;; todo: test for `instance-of-Domain?` ; how to copy domain?
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[(object? domain) (set! domain '(copy.copy domain))]
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[else (error 'addVariable "Domains must be instances of subclasses of Domain")])
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(when (not (object? domain)) (error 'fudge))
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(when (not domain) ; todo: check this test
(error 'addVariable "Domain is empty"))
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(hash-set! _variables variable domain))
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(define/public (addVariables variables domain)
;; Add one or more variables to the problem
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(define listified-variables
(cond
[(string? variables) (map (λ(c) (format "~a" c)) (string->list variables))]
[else variables]))
(for-each (λ(var) (addVariable var domain)) listified-variables))
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(define/public (addConstraint constraint [variables null])
;; Add a constraint to the problem
(when (not (Constraint? constraint))
(if (procedure? constraint)
(set! constraint (new FunctionConstraint [func constraint]))
(error 'addConstraint "Constraints must be instances of class Constraint")))
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(py-append! _constraints (list constraint variables)))
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(define/public (getSolution)
;; Find and return a solution to the problem
(define-values (domains constraints vconstraints) (_getArgs))
(if (not domains)
null
(send _solver getSolution domains constraints vconstraints)))
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(define/public (getSolutions)
;; Find and return all solutions to the problem
(define-values (domains constraints vconstraints) (_getArgs))
(if (not domains)
null
(send _solver getSolutions domains constraints vconstraints)))
(define/public (_getArgs)
(define domains (hash-copy _variables))
(define allvariables (hash-keys domains))
(define constraints null)
(for ([constraint-variables-pair (in-list _constraints)])
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(match-define (list constraint variables) constraint-variables-pair)
(when (null? variables)
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(set! variables allvariables))
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(set! constraints (append constraints (list (list constraint variables)))))
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(define vconstraints (make-hash))
(for ([variable (in-hash-keys domains)])
(hash-set! vconstraints variable null))
(for ([constraint-variables-pair (in-list constraints)])
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(match-define (list constraint variables) constraint-variables-pair)
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(for ([variable (in-list variables)])
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(hash-update! vconstraints variable (λ(val) (append val (list (list constraint variables)))))))
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(for ([constraint-variables-pair (in-list constraints)])
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(match-define (list constraint variables) constraint-variables-pair)
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(send constraint preProcess variables domains constraints vconstraints))
(define result #f)
(let/ec done
(for ([domain (in-list (hash-values domains))])
(send domain resetState)
(when (not domain)
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(set! result (list null null null))
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(done)))
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(set! result (list domains constraints vconstraints)))
(apply values result))
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))
(module+ test
(check-equal? (get-field _solver (new Problem [solver 'solver-in])) 'solver-in)
(check-equal? (get-field _constraints (new Problem)) null)
(check-equal? (get-field _variables (new Problem)) (make-hash))
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(define problem (new Problem)) ;; test from line 125
(send problem addVariable "a" '(1))
(check-equal? (get-field _list (hash-ref (get-field _variables problem) "a")) '(1))
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(send problem reset)
(check-equal? (get-field _variables problem) (make-hash))
(send problem addVariables '("a" "b") '(1 2 3))
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(check-equal? (get-field _list (hash-ref (get-field _variables problem) "a")) '(1 2 3))
(check-equal? (get-field _list (hash-ref (get-field _variables problem) "b")) '(1 2 3)))
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;; ----------------------------------------------------------------------
;; Domains
;; ----------------------------------------------------------------------
(define Domain
;; Class used to control possible values for variables
;; When list or tuples are used as domains, they are automatically
;; converted to an instance of that class.
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(class* object% (printable<%>)
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(super-new)
(init-field set)
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(field [_list set][_hidden null][_states null])
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(define (repr) (format "<Domain ~v>" _list))
(define/public (custom-print out quoting-depth) (print (repr) out))
(define/public (custom-display out) (displayln (repr) out))
(define/public (custom-write out) (write (repr) out))
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(define/public (resetState)
;; Reset to the original domain state, including all possible values
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(py-extend! _list _hidden)
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(set! _hidden null)
(set! _states null))
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(define/public (pushState)
;; Save current domain state
;; Variables hidden after that call are restored when that state
;; is popped from the stack.
(py-append! _states (length _list)))
(define/public (popState)
;; Restore domain state from the top of the stack
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;; Variables hidden since the last popped state are then available
;; again.
(define diff (- (py-pop! _states) (length _list)))
(when (not (= 0 diff))
(py-extend! _list (take-right _hidden diff))
(set! _hidden (take _hidden (- (length _hidden) diff)))))
(define/public (hideValue value)
;; Hide the given value from the domain
;; After that call the given value won't be seen as a possible value
;; on that domain anymore. The hidden value will be restored when the
;; previous saved state is popped.
(set! _list (remove value _list))
(py-append! _hidden value))
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(define/public (domain-pop!)
(py-pop! _list))
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(define/public (copy)
(define copied-domain (new Domain [set _list]))
(set-field! _hidden copied-domain _hidden)
(set-field! _states copied-domain _states)
copied-domain)
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))
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(define Domain? (is-a?/c Domain))
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;; ----------------------------------------------------------------------
;; Constraints
;; ----------------------------------------------------------------------
(define Constraint
(class object%
(super-new)
(define/public (call variables domains assignments [forwardcheck #f])
;; Perform the constraint checking
;; If the forwardcheck parameter is not false, besides telling if
;; the constraint is currently broken or not, the constraint
;; implementation may choose to hide values from the domains of
;; unassigned variables to prevent them from being used, and thus
;; prune the search space.
#t)
(define/public (preProcess variables domains constraints vconstraints)
;; Preprocess variable domains
;; This method is called before starting to look for solutions,
;; and is used to prune domains with specific constraint logic
;; when possible. For instance, any constraints with a single
;; variable may be applied on all possible values and removed,
;; since they may act on individual values even without further
;; knowledge about other assignments.
(when (= (length variables) 1)
(define variable (list-ref variables 0))
(define domain (hash-ref domains variable))
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(for ([value (in-list (get-field _list domain))])
(when (not (call variables domains (make-hash (list (cons variable value)))))
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(set-field! _list domain (remove value (get-field _list domain)))))
(set! constraints (remove (list this variables) constraints))
(hash-update! vconstraints variable (λ(val) (remove (list this variables) val)))))
(define/public (forwardCheck variables domains assignments [_unassigned Unassigned])
;; Helper method for generic forward checking
;; Currently, this method acts only when there's a single
;; unassigned variable.
(define return-result #t)
(define unassignedvariable _unassigned)
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;(report assignments)
(let/ec break
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(for ([variable (in-list variables)])
(when (not (variable . in? . assignments))
(if (equal? unassignedvariable _unassigned)
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(set! unassignedvariable variable)
(break))))
(when (not (equal? unassignedvariable _unassigned))
;; Remove from the unassigned variable domain's all
;; values which break our variable's constraints.
(define domain (hash-ref domains unassignedvariable))
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;(report domain domain-fc)
(when (not (null? (get-field _list domain)))
(for ([value (in-list (get-field _list domain))])
(hash-set! assignments unassignedvariable value)
(when (not (send this call variables domains assignments))
(send domain hideValue value)))
(hash-remove! assignments unassignedvariable))
(when (null? (get-field _list domain))
(set! return-result #f)
(break))))
return-result)
))
(define Constraint? (is-a?/c Constraint))
(define FunctionConstraint
(class Constraint
(super-new)
(init-field func [assigned #t])
(field [_func func][_assigned assigned])
(inherit forwardCheck)
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(define/override (call variables domains assignments [forwardcheck #f] [_unassigned Unassigned])
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;(report assignments assignments-before)
(define parms (for/list ([x (in-list variables)])
(if (hash-has-key? assignments x) (hash-ref assignments x) _unassigned)))
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;(report assignments assignments-after)
(define missing (length (filter (λ(v) (equal? v _unassigned)) parms)))
(if (> missing 0)
(begin
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;(report missing)
;(report _assigned)
;(report parms)
;(report (apply _func parms))
;(report forwardcheck)
;(report assignments assignments-to-fc)
(and (or _assigned (apply _func parms))
(or (not forwardcheck) (not (= missing 1))
(forwardCheck variables domains assignments))))
(apply _func parms)))
))
(define FunctionConstraint? (is-a?/c FunctionConstraint))
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(define AllDifferentConstraint
;; Constraint enforcing that values of all given variables are different
(class Constraint
(super-new)
(define/override (call variables domains assignments [forwardcheck #f] [_unassigned Unassigned])
(define seen (make-hash))
(define value #f)
(define domain #f)
(define return-value (void))
(let/ec return-k
(for ([variable (in-list variables)])
(set! value (if (hash-has-key? assignments variable)
(hash-ref assignments variable)
_unassigned))
(when (not (equal? value _unassigned))
(when (value . in? . seen)
(set! return-value #f)
(return-k))
(hash-set! seen value #t)))
(when forwardcheck
(for ([variable (in-list variables)])
(when (not (variable . in? . assignments))
(set! domain (hash-ref domains variable))
(for ([value (in-hash-keys seen)])
(when (value . in? . (get-field _list (hash-ref domains variable)))
(send domain hideValue value)
(when (null? (get-field _list (hash-ref domains variable)))
(set! return-value #f)
(return-k)))))))
(set! return-value #t)
(return-k))
return-value)))
(define AllDifferentConstraint? (is-a?/c AllDifferentConstraint))
;; ----------------------------------------------------------------------
;; Variables
;; ----------------------------------------------------------------------
(define Variable
(class* object% (printable<%>)
(super-new)
(define (repr) (format "<Variable ~a>" _name))
(define/public (custom-print out quoting-depth) (print (repr) out))
(define/public (custom-display out) (displayln (repr) out))
(define/public (custom-write out) (write (repr) out))
(init-field name)
(field [_name name])))
(define Variable? (is-a?/c Variable))
(define Unassigned (new Variable [name "Unassigned"]))
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;; ----------------------------------------------------------------------
;; Solvers
;; ----------------------------------------------------------------------
(define Solver
;; Abstract base class for solvers
(class object%
(super-new)
(abstract getSolution)
(abstract getSolutions)
(abstract getSolutionIter)))
(define BacktrackingSolver
;; Problem solver with backtracking capabilities
(class Solver
(super-new)
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(init-field [forwardcheck #t])
(field [_forwardcheck forwardcheck])
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(define/override (getSolutionIter domains constraints vconstraints)
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(define forwardcheck _forwardcheck)
(define assignments (make-hash))
(define queue null)
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(define values null)
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(define pushdomains null)
(define variable #f)
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(define lst null)
(define want-to-return #f)
(define return-k #f)
(let/ec break-loop1
(set! return-k break-loop1)
(let loop1 ()
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;(displayln "starting while loop 1")
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;; Mix the Degree and Minimum Remaing Values (MRV) heuristics
(set! lst (sort (for/list ([variable (in-hash-keys domains)])
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(list (* -1 (length (hash-ref vconstraints variable)))
(length (get-field _list (hash-ref domains variable)))
variable)) list-comparator))
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;(report lst)
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(let/ec break-for-loop
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(for ([item (in-list lst)])
(when (not ((last item) . in? . assignments))
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; Found unassigned variable
(set! variable (last item))
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;(report variable unassigned-variable)
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(set! values (send (hash-ref domains variable) copy))
(set! pushdomains
(if forwardcheck
(for/list ([x (in-hash-keys domains)]
#:when (and (not (x . in? . assignments))
(not (x . equal? . variable))))
(hash-ref domains x))
null))
(break-for-loop)))
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;; if it makes it through the loop without breaking, then there are
;; No unassigned variables. We've got a solution. Go back
;; to last variable, if there's one.
(yield (hash-copy assignments))
(when (null? queue) (begin
(set! want-to-return #t)
(return-k)))
(define variable-values-pushdomains (py-pop! queue))
(set! variable (first variable-values-pushdomains))
(set-field! _list values (second variable-values-pushdomains))
(set! pushdomains (third variable-values-pushdomains))
(for ([domain (in-list pushdomains)])
(send domain popState)))
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;(report variable variable-preloop-2)
;(report assignments assignments-preloop-2)
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(let/ec break-loop2
(let loop2 ()
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;(displayln "starting while loop 2")
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;; We have a variable. Do we have any values left?
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;(report values values-tested)
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(when (null? (get-field _list values))
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;; No. Go back to last variable, if there's one.
(hash-remove! assignments variable)
(let/ec break-loop3
(let loop3 ()
(if (not (null? queue))
(let ()
(define variable-values-pushdomains (py-pop! queue))
(set! variable (first variable-values-pushdomains))
(set-field! _list values (second variable-values-pushdomains))
(set! pushdomains (third variable-values-pushdomains))
(when (not (null? pushdomains))
(for ([domain (in-list pushdomains)])
(send domain popState)))
(when (not (null? (get-field _list values))) (break-loop3))
(hash-remove! assignments variable)
(loop3))
(begin
(set! want-to-return #t)
(return-k))))))
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;; Got a value. Check it.
(hash-set! assignments variable (send values domain-pop!))
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(for ([domain (in-list pushdomains)])
(send domain pushState))
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;(report pushdomains pushdomains1)
;(report domains domains1)
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(let/ec break-for-loop
(for ([cvpair (in-list (hash-ref vconstraints variable))])
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(match-define (list constraint variables) cvpair)
(define the_result (send constraint call variables domains assignments pushdomains))
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;(report pushdomains pushdomains2)
;(report domains domains2)
;(report the_result)
(when (not the_result)
;; Value is not good.
(break-for-loop)))
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(begin ;(displayln "now breaking loop 2")
(break-loop2)))
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(for ([domain (in-list pushdomains)])
(send domain popState))
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(loop2)))
;; Push state before looking for next variable.
(py-append! queue (list variable (get-field _list (send values copy)) pushdomains))
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;(report queue new-queue)
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(loop1)))
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(if want-to-return
(void)
(error 'getSolutionIter "Whoops, broken solver")))
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(define (call-solution-generator domains constraints vconstraints #:first-only [first-only #f])
(for/list ([solution (in-generator (getSolutionIter domains constraints vconstraints))] #:final first-only)
solution))
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(define/override (getSolution . args)
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(car (apply call-solution-generator #:first-only #t args)))
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(define/override (getSolutions . args)
(apply call-solution-generator args))
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))
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