|
|
#lang debug racket
|
|
|
(require racket/generator graph racket/set)
|
|
|
(provide (except-out (all-defined-out) define/contract))
|
|
|
|
|
|
(define-syntax-rule (define/contract EXPR CONTRACT . BODY)
|
|
|
(define EXPR . BODY))
|
|
|
|
|
|
(define-syntax when-debug
|
|
|
(let ()
|
|
|
(define debug #t)
|
|
|
(if debug
|
|
|
(make-rename-transformer #'begin)
|
|
|
(λ (stx) (syntax-case stx ()
|
|
|
[(_ . rest) #'(void)])))))
|
|
|
|
|
|
(define (print-debug-info)
|
|
|
(when-debug
|
|
|
(displayln (format "assignments: ~a forward checks: ~a checks: ~a " nassns nchecks nfchecks))))
|
|
|
|
|
|
(define-syntax-rule (in-cartesian x)
|
|
|
(in-generator (let ([argss x])
|
|
|
(let loop ([argss argss][acc empty])
|
|
|
(if (null? argss)
|
|
|
(yield (reverse acc))
|
|
|
(for ([arg (in-stream (car argss))])
|
|
|
(loop (cdr argss) (cons arg acc))))))))
|
|
|
|
|
|
(struct csp (vars constraints) #:mutable #:transparent)
|
|
|
(define constraints csp-constraints)
|
|
|
(define vars csp-vars)
|
|
|
(define-syntax-rule (in-constraints csp) (in-list (csp-constraints csp)))
|
|
|
(define-syntax-rule (in-vars csp) (in-list (vars csp)))
|
|
|
(define-syntax-rule (in-var-names csp) (in-list (map var-name (vars csp))))
|
|
|
|
|
|
(struct constraint (names proc) #:transparent
|
|
|
#:property prop:procedure
|
|
|
(λ (const prob)
|
|
|
(unless (csp? prob)
|
|
|
(raise-argument-error 'constraint "csp" prob))
|
|
|
;; apply proc in many-to-many style
|
|
|
(for/and ([args (in-cartesian (map (λ (name) (find-domain prob name)) (constraint-names const)))])
|
|
|
(apply (constraint-proc const) args))))
|
|
|
|
|
|
(define/contract (make-constraint [names null] [proc values])
|
|
|
(() ((listof name?) procedure?) . ->* . constraint?)
|
|
|
(constraint names proc))
|
|
|
|
|
|
(define/contract (csp->graphviz prob)
|
|
|
(csp? . -> . string?)
|
|
|
(define g (csp->graph prob))
|
|
|
(graphviz g #:colors (coloring/brelaz g)))
|
|
|
|
|
|
(define/contract (csp->graph prob)
|
|
|
(csp? . -> . graph?)
|
|
|
(for*/fold ([gr (unweighted-graph/undirected (map var-name (vars prob)))])
|
|
|
([constraint (in-constraints prob)]
|
|
|
[edge (in-combinations (constraint-names constraint) 2)])
|
|
|
(apply add-edge! gr edge)
|
|
|
gr))
|
|
|
|
|
|
(struct var (name domain) #:transparent)
|
|
|
(define (var-name? x) #true) ; anything is ok for now
|
|
|
(define domain var-domain)
|
|
|
|
|
|
(struct checked-variable var (history) #:transparent)
|
|
|
(define history checked-variable-history)
|
|
|
(define cvar checked-variable)
|
|
|
(define cvar? checked-variable?)
|
|
|
|
|
|
(struct assigned-var var () #:transparent)
|
|
|
(define avar assigned-var)
|
|
|
(define avar? assigned-var?)
|
|
|
|
|
|
(define/contract (make-csp [vars null] [consts null])
|
|
|
(() ((listof var?) (listof constraint?)) . ->* . csp?)
|
|
|
(csp vars consts))
|
|
|
|
|
|
(define (varvals->set vals)
|
|
|
(match vals
|
|
|
[(list (or (? fixnum?) (? symbol?)) ...) (list->seteq vals)]
|
|
|
[_ (list->set vals)]))
|
|
|
|
|
|
(define/contract (make-var name [vals null])
|
|
|
((name?) ((listof any/c)) . ->* . var?)
|
|
|
(var name (varvals->set vals)))
|
|
|
|
|
|
(define (make-checked-var name vals history)
|
|
|
(checked-variable name (varvals->set vals) history))
|
|
|
|
|
|
(define/contract (make-var-names prefix vals [suffix ""])
|
|
|
((string? (listof any/c)) ((string?)) . ->* . (listof name?))
|
|
|
(for/list ([val (in-list vals)])
|
|
|
(string->symbol (format "~a~a~a" prefix val suffix))))
|
|
|
|
|
|
(define/contract (add-vars! prob names [vals-or-procedure empty])
|
|
|
((csp? (listof name?)) ((or/c (listof any/c) procedure?)) . ->* . void?)
|
|
|
(for/fold ([vrs (vars prob)]
|
|
|
#:result (set-csp-vars! prob vrs))
|
|
|
([name (in-list names)])
|
|
|
(when (memq name (map var-name vrs))
|
|
|
(raise-argument-error 'add-vars! "var that doesn't already exist" name))
|
|
|
(append vrs (list (make-var name
|
|
|
(match vals-or-procedure
|
|
|
[(? procedure? proc) (proc)]
|
|
|
[vals vals]))))))
|
|
|
|
|
|
(define/contract (add-var! prob name [vals-or-procedure empty])
|
|
|
((csp? name?) ((or/c (listof any/c) procedure?)) . ->* . void?)
|
|
|
(add-vars! prob (list name) vals-or-procedure))
|
|
|
|
|
|
(define/contract (add-constraints! prob proc namess [proc-name #false]
|
|
|
#:caller [caller-id 'add-constraints!])
|
|
|
((csp? procedure? (listof (listof name?))) ((or/c #false name?)) . ->* . void?)
|
|
|
(unless (procedure? proc)
|
|
|
(raise-argument-error caller-id "procedure" proc))
|
|
|
(unless (and (list? namess) (andmap list? namess))
|
|
|
(raise-argument-error caller-id "list of lists of names" namess))
|
|
|
(set-csp-constraints! prob (append (constraints prob)
|
|
|
(for/list ([names (in-list namess)])
|
|
|
(for ([name (in-list names)])
|
|
|
(check-name-in-csp! 'add-constraints! prob name))
|
|
|
(make-constraint names (if proc-name
|
|
|
(procedure-rename proc proc-name)
|
|
|
proc))))))
|
|
|
|
|
|
(define/contract (add-pairwise-constraint! prob proc names [proc-name #false])
|
|
|
((csp? procedure? (listof name?)) (name?) . ->* . void?)
|
|
|
(unless (list? names)
|
|
|
(raise-argument-error 'add-pairwise-constraint! "list of names" names))
|
|
|
(add-constraints! prob proc (combinations names 2) proc-name #:caller 'add-pairwise-constraint!))
|
|
|
|
|
|
(define/contract (add-transitive-constraint! prob proc names [proc-name #false])
|
|
|
((csp? procedure? (listof name?)) (name?) . ->* . void?)
|
|
|
(unless (and (list? names) (>= (length names) 2))
|
|
|
(raise-argument-error 'add-transitive-constraint! "list of two or more names" names))
|
|
|
(add-constraints! prob proc (for/list ([name (in-list names)]
|
|
|
[next (in-list (cdr names))])
|
|
|
(list name next)) proc-name #:caller 'add-transitive-constraint!))
|
|
|
|
|
|
(define/contract (add-constraint! prob proc names [proc-name #false])
|
|
|
((csp? procedure? (listof name?)) (name?) . ->* . void?)
|
|
|
(unless (list? names)
|
|
|
(raise-argument-error 'add-constraint! "list of names" names))
|
|
|
(add-constraints! prob proc (list names) proc-name #:caller 'add-constraint!))
|
|
|
|
|
|
(define/contract (alldiff x y)
|
|
|
(any/c any/c . -> . boolean?)
|
|
|
(not (= x y)))
|
|
|
(define alldiff= alldiff)
|
|
|
|
|
|
(define (add-all-diff-constraint! prob [names (map var-name (csp-vars prob))]
|
|
|
#:same [equal-proc equal?])
|
|
|
(add-pairwise-constraint! prob (λ (x y) (not (equal-proc x y))) names
|
|
|
(string->symbol (format "all-diff-~a" (object-name equal-proc)))))
|
|
|
|
|
|
(struct backtrack (histories) #:transparent)
|
|
|
(define (backtrack! [names null]) (raise (backtrack names)))
|
|
|
|
|
|
(define/contract (check-name-in-csp! caller prob name)
|
|
|
(symbol? csp? name? . -> . void?)
|
|
|
(define names (map var-name (vars prob)))
|
|
|
(unless (memq name names)
|
|
|
(raise-argument-error caller (format "one of these existing csp var names: ~v" names) name)))
|
|
|
|
|
|
(define/contract (find-var prob name)
|
|
|
(csp? name? . -> . var?)
|
|
|
(check-name-in-csp! 'find-var prob name)
|
|
|
(for/first ([vr (in-vars prob)]
|
|
|
#:when (eq? name (var-name vr)))
|
|
|
vr))
|
|
|
|
|
|
(define/contract (find-domain prob name)
|
|
|
(csp? name? . -> . (listof any/c))
|
|
|
(check-name-in-csp! 'find-domain prob name)
|
|
|
(domain (find-var prob name)))
|
|
|
|
|
|
(define order-domain-values values)
|
|
|
|
|
|
(define/contract (assigned-name? prob name)
|
|
|
(csp? name? . -> . any/c)
|
|
|
(assigned-var? (find-var prob name)))
|
|
|
|
|
|
(define/contract (reduce-function-arity proc pattern)
|
|
|
(procedure? (listof any/c) . -> . procedure?)
|
|
|
(unless (match (procedure-arity proc)
|
|
|
[(arity-at-least val) (<= val (length pattern))]
|
|
|
[(? number? val) (= val (length pattern))])
|
|
|
(raise-argument-error 'reduce-function-arity (format "list of length ~a, same as procedure arity" (procedure-arity proc)) pattern))
|
|
|
(define reduced-arity-name (string->symbol (format "reduced-arity-~a" (object-name proc))))
|
|
|
(define-values (boxed-id-names vals) (partition box? pattern))
|
|
|
(define new-arity (length boxed-id-names))
|
|
|
(procedure-rename
|
|
|
(λ xs
|
|
|
(unless (= (length xs) new-arity)
|
|
|
(apply raise-arity-error reduced-arity-name new-arity xs))
|
|
|
(apply proc (for/fold ([acc empty]
|
|
|
[xs xs]
|
|
|
[vals vals]
|
|
|
#:result (reverse acc))
|
|
|
([pat-item (in-list pattern)])
|
|
|
(if (box? pat-item)
|
|
|
(values (cons (car xs) acc) (cdr xs) vals)
|
|
|
(values (cons (car vals) acc) xs (cdr vals))))))
|
|
|
reduced-arity-name))
|
|
|
|
|
|
(define/contract (reduce-constraint-arity prob [minimum-arity 3])
|
|
|
((csp?) ((or/c #false natural?)) . ->* . csp?)
|
|
|
(define assigned? (curry assigned-name? prob))
|
|
|
(define (partially-assigned? constraint)
|
|
|
(ormap assigned? (constraint-names constraint)))
|
|
|
(make-csp (vars prob)
|
|
|
(for/list ([const (in-constraints prob)])
|
|
|
(cond
|
|
|
;; no point reducing 2-arity functions because they will be consumed by forward checking
|
|
|
[(and (or (not minimum-arity) (<= minimum-arity (constraint-arity const)))
|
|
|
(partially-assigned? const))
|
|
|
(match-define (constraint cnames proc) const)
|
|
|
;; pattern is mix of values and boxed symbols (indicating variables to persist)
|
|
|
;; use boxes here as cheap way to distinguish id symbols from value symbols
|
|
|
(define arity-reduction-pattern (for/list ([cname (in-list cnames)])
|
|
|
(if (assigned? cname)
|
|
|
(first (find-domain prob cname))
|
|
|
(box cname))))
|
|
|
(constraint (filter-not assigned? cnames)
|
|
|
(reduce-function-arity proc arity-reduction-pattern))]
|
|
|
[else const]))))
|
|
|
|
|
|
(define nassns 0)
|
|
|
(define nfchecks 0)
|
|
|
(define nchecks 0)
|
|
|
|
|
|
(define (reset-nassns!) (set! nassns 0))
|
|
|
(define (reset-nfchecks!) (set! nfchecks 0))
|
|
|
(define (reset-nchecks!) (set! nchecks 0))
|
|
|
|
|
|
(define/contract (assign-val prob name val)
|
|
|
(csp? name? any/c . -> . csp?)
|
|
|
(begin0
|
|
|
(make-csp
|
|
|
(for/list ([vr (in-vars prob)])
|
|
|
(if (eq? name (var-name vr))
|
|
|
(assigned-var name (list val))
|
|
|
vr))
|
|
|
(constraints prob))
|
|
|
(when-debug (set! nassns (add1 nassns)))))
|
|
|
|
|
|
(define/contract (assigned-vars prob [invert? #f])
|
|
|
((csp?) (any/c) . ->* . (listof var?))
|
|
|
((if invert? filter-not filter) assigned-var? (vars prob)))
|
|
|
|
|
|
(define/contract (unassigned-vars prob)
|
|
|
(csp? . -> . (listof var?))
|
|
|
(assigned-vars prob 'invert))
|
|
|
|
|
|
(define/contract (first-unassigned-variable csp)
|
|
|
(csp? . -> . (or/c #false (and/c var? (not/c assigned-var?))))
|
|
|
(match (unassigned-vars csp)
|
|
|
[(== empty) #false]
|
|
|
[uvars (first uvars)]))
|
|
|
|
|
|
(define/contract (argmin* proc xs [max-style? #f])
|
|
|
((procedure? (listof any/c)) (any/c) . ->* . (listof any/c))
|
|
|
;; return all elements that have min value.
|
|
|
(match xs
|
|
|
[(== empty) xs]
|
|
|
[(list x) xs]
|
|
|
[xs
|
|
|
(define vals (map proc xs))
|
|
|
(define target-val (apply (if max-style? max min) vals))
|
|
|
(for/list ([x (in-list xs)]
|
|
|
[val (in-list vals)]
|
|
|
#:when (= val target-val))
|
|
|
x)]))
|
|
|
|
|
|
(define/contract (argmax* proc xs)
|
|
|
(procedure? (listof any/c) . -> . (listof any/c))
|
|
|
;; return all elements that have max value.
|
|
|
(argmin* proc xs 'max-mode!))
|
|
|
|
|
|
(define/contract (minimum-remaining-values prob)
|
|
|
(csp? . -> . (or/c #false (and/c var? (not/c assigned-var?))))
|
|
|
(match (unassigned-vars prob)
|
|
|
[(== empty) #false]
|
|
|
[uvars (random-pick (argmin* domain-length uvars))]))
|
|
|
|
|
|
(define/contract (max-degree prob)
|
|
|
(csp? . -> . (or/c #false (and/c var? (not/c assigned-var?))))
|
|
|
(match (unassigned-vars prob)
|
|
|
[(== empty) #false]
|
|
|
[uvars (random-pick (argmax* (λ (var) (var-degree prob var)) uvars))]))
|
|
|
|
|
|
(define mrv minimum-remaining-values)
|
|
|
|
|
|
(define/contract (var-degree prob var)
|
|
|
(csp? var? . -> . natural?)
|
|
|
(for/sum ([const (in-constraints prob)]
|
|
|
#:when (memq (var-name var) (constraint-names const)))
|
|
|
1))
|
|
|
|
|
|
(define/contract (domain-length var)
|
|
|
(var? . -> . natural?)
|
|
|
(set-count (domain var)))
|
|
|
|
|
|
(define/contract (state-count csp)
|
|
|
(csp? . -> . natural?)
|
|
|
(for/product ([vr (in-vars csp)])
|
|
|
(domain-length vr)))
|
|
|
|
|
|
(define/contract (mrv-degree-hybrid prob)
|
|
|
(csp? . -> . (or/c #f var?))
|
|
|
(match (unassigned-vars prob)
|
|
|
[(== empty) #false]
|
|
|
[uvars
|
|
|
(max-degree (make-csp (argmin* domain-length uvars) (constraints prob)))]))
|
|
|
|
|
|
(define first-domain-value values)
|
|
|
|
|
|
(define (no-inference prob name) prob)
|
|
|
|
|
|
(define/contract (relating-only constraints names)
|
|
|
((listof constraint?) (listof name?) . -> . (listof constraint?))
|
|
|
(for*/list ([const (in-list constraints)]
|
|
|
[cnames (in-value (constraint-names const))]
|
|
|
#:when (and (= (length names) (length cnames))
|
|
|
(for/and ([name (in-list names)])
|
|
|
(memq name cnames))))
|
|
|
const))
|
|
|
|
|
|
(define (one-arity? const) (= 1 (constraint-arity const)))
|
|
|
(define (two-arity? const) (= 2 (constraint-arity const)))
|
|
|
|
|
|
(define (constraint-relates? const name)
|
|
|
(memq name (constraint-names const)))
|
|
|
|
|
|
(struct arc (name const) #:transparent)
|
|
|
|
|
|
(define/contract (two-arity-constraints->arcs constraints)
|
|
|
((listof (and/c constraint? two-arity?)) . -> . (listof arc?))
|
|
|
(for*/list ([const (in-list constraints)]
|
|
|
[name (in-list (constraint-names const))])
|
|
|
(arc name const)))
|
|
|
|
|
|
(require sugar/debug)
|
|
|
(define/contract (reduce-domain prob ark)
|
|
|
(csp? arc? . -> . csp?)
|
|
|
(match-define (arc name (constraint names constraint-proc)) ark)
|
|
|
(match-define (list other-name) (remove name names))
|
|
|
(define proc (if (eq? name (first names)) ; name is on left
|
|
|
constraint-proc ; so val stays on left
|
|
|
(λ (val other-val) (constraint-proc other-val val)))) ; otherwise reverse arg order
|
|
|
(define (satisfies-arc? val)
|
|
|
(for/or ([other-val (in-set (find-domain prob other-name))])
|
|
|
(proc val other-val)))
|
|
|
(make-csp
|
|
|
(for/list ([vr (in-vars prob)])
|
|
|
(cond
|
|
|
[(assigned-var? vr) vr]
|
|
|
[(eq? name (var-name vr))
|
|
|
(make-var name (match (filter satisfies-arc? (set->list (domain vr)))
|
|
|
[(? empty?) (backtrack!)]
|
|
|
[vals vals]))]
|
|
|
[else vr]))
|
|
|
(constraints prob)))
|
|
|
|
|
|
(define/contract (terminating-at? arcs name)
|
|
|
((listof arc?) name? . -> . (listof arc?))
|
|
|
(for/list ([arc (in-list arcs)]
|
|
|
#:when (and
|
|
|
(memq name (constraint-names (arc-const arc)))
|
|
|
(not (eq? name (arc-name arc)))))
|
|
|
arc))
|
|
|
|
|
|
(define/contract (ac-3 prob ref-name)
|
|
|
(csp? name? . -> . csp?)
|
|
|
;; csp is arc-consistent if every pair of variables (x y)
|
|
|
;; has values in their domain that satisfy every binary constraint
|
|
|
(define checkable-names (cons ref-name (filter-not (λ (vn) (assigned-name? prob vn)) (map var-name (vars prob)))))
|
|
|
(define starting-arcs
|
|
|
(two-arity-constraints->arcs
|
|
|
(for/list ([const (in-constraints prob)]
|
|
|
#:when (and (two-arity? const)
|
|
|
(for/and ([cname (in-list (constraint-names const))])
|
|
|
(memq cname checkable-names))))
|
|
|
const)))
|
|
|
(for/fold ([prob prob]
|
|
|
[arcs (sort starting-arcs < #:key (λ (a) (domain-length (find-var prob (arc-name a)))) #:cache-keys? #true)]
|
|
|
#:result (prune-singleton-constraints prob))
|
|
|
([i (in-naturals)]
|
|
|
#:break (empty? arcs))
|
|
|
(match-define (cons (and first-arc (arc name _)) other-arcs) arcs)
|
|
|
(define reduced-csp (reduce-domain prob first-arc))
|
|
|
(define domain-reduced?
|
|
|
(< (domain-length (find-var reduced-csp name)) (domain-length (find-var prob name))))
|
|
|
(values reduced-csp
|
|
|
(if domain-reduced?
|
|
|
;; revision reduced the domain, so supplement the list of arcs
|
|
|
(remove-duplicates (append (starting-arcs . terminating-at? . name) other-arcs))
|
|
|
;; revision did not reduce the domain, so keep going
|
|
|
other-arcs))))
|
|
|
|
|
|
(define/contract (forward-check-var prob ref-name vr)
|
|
|
(csp? name? var? . -> . var?)
|
|
|
(match vr
|
|
|
;; don't check against assigned vars, or the reference var
|
|
|
;; (which is probably assigned but maybe not)
|
|
|
[(? assigned-var? vr) vr]
|
|
|
[(var (== ref-name eq?) _) vr]
|
|
|
[(var name vals)
|
|
|
(match ((constraints prob) . relating-only . (list ref-name name))
|
|
|
[(? empty?) vr]
|
|
|
[constraints
|
|
|
(define ref-val (first (find-domain prob ref-name)))
|
|
|
(define new-vals
|
|
|
(for/list ([val (in-set vals)]
|
|
|
#:when (for/and ([const (in-list constraints)])
|
|
|
(match const
|
|
|
[(constraint (list (== name eq?) _) proc) (proc val ref-val)]
|
|
|
[(constraint _ proc) (proc ref-val val)])))
|
|
|
val))
|
|
|
(make-checked-var name new-vals (cons (cons ref-name ref-val) (match vr
|
|
|
[(checked-variable _ _ history) history]
|
|
|
[_ null])))])]))
|
|
|
|
|
|
(define/contract (prune-singleton-constraints prob [ref-name #false])
|
|
|
((csp?) ((or/c #false name?)) . ->* . csp?)
|
|
|
(define singleton-var-names (for/list ([vr (in-vars prob)]
|
|
|
#:when (singleton-var? vr))
|
|
|
(var-name vr)))
|
|
|
(make-csp
|
|
|
(vars prob)
|
|
|
(for/list ([const (in-constraints prob)]
|
|
|
#:unless (and (two-arity? const)
|
|
|
(or (not ref-name) (constraint-relates? const ref-name))
|
|
|
(for/and ([cname (in-list (constraint-names const))])
|
|
|
(memq cname singleton-var-names))))
|
|
|
const)))
|
|
|
|
|
|
(define/contract (forward-check prob ref-name)
|
|
|
(csp? name? . -> . csp?)
|
|
|
(define checked-vars (map (λ (vr) (forward-check-var prob ref-name vr)) (vars prob)))
|
|
|
(when-debug (set! nfchecks (+ (length checked-vars) nchecks)))
|
|
|
;; conflict-set will be empty if there are no empty domains (as we would hope)
|
|
|
(define conflict-set (for/list ([cvr (in-list checked-vars)]
|
|
|
#:when (set-empty? (domain cvr)))
|
|
|
(history cvr)))
|
|
|
;; for conflict-directed backjumping it's essential to forward-check ALL vars
|
|
|
;; (even after an empty domain is generated) and combine their conflicts
|
|
|
;; so we can discover the *most recent past var* that could be the culprit.
|
|
|
;; If we just bail out at the first conflict, we may backjump too far based on its history
|
|
|
;; (and thereby miss parts of the search tree)
|
|
|
(unless (empty? conflict-set)
|
|
|
(backtrack! conflict-set))
|
|
|
;; Discard constraints that have produced singleton domains
|
|
|
;; (they have no further use)
|
|
|
(prune-singleton-constraints (make-csp checked-vars (constraints prob)) ref-name))
|
|
|
|
|
|
(define/contract (constraint-checkable? const names)
|
|
|
(constraint? (listof name?) . -> . any/c)
|
|
|
;; constraint is checkable if all constraint names
|
|
|
;; are in target list of names.
|
|
|
(for/and ([cname (in-list (constraint-names const))])
|
|
|
(memq cname names)))
|
|
|
|
|
|
(define/contract (constraint-arity const)
|
|
|
(constraint? . -> . natural?)
|
|
|
(length (constraint-names const)))
|
|
|
|
|
|
(define/contract (singleton-var? var)
|
|
|
(var? . -> . boolean?)
|
|
|
(= 1 (domain-length var)))
|
|
|
|
|
|
(define/contract (check-constraints prob [mandatory-names #f] #:conflicts [conflict-count? #f])
|
|
|
((csp?) ((listof name?) #:conflicts boolean?) . ->* . (or/c csp? natural?))
|
|
|
(define assigned-varnames (map var-name (assigned-vars prob)))
|
|
|
(define-values (checkable-consts other-consts)
|
|
|
(partition (λ (const) (and (constraint-checkable? const assigned-varnames)
|
|
|
(or (not mandatory-names)
|
|
|
(for/and ([name (in-list mandatory-names)])
|
|
|
(constraint-relates? const name)))))
|
|
|
(constraints prob)))
|
|
|
(cond
|
|
|
[conflict-count?
|
|
|
(define conflict-count
|
|
|
(for/sum ([constraint (in-list checkable-consts)]
|
|
|
#:unless (constraint prob))
|
|
|
1))
|
|
|
(when-debug (set! nchecks (+ conflict-count nchecks)))
|
|
|
conflict-count]
|
|
|
[else
|
|
|
(for ([(constraint idx) (in-indexed checkable-consts)]
|
|
|
#:unless (constraint prob))
|
|
|
(when-debug (set! nchecks (+ (add1 idx) nchecks)))
|
|
|
(backtrack!))
|
|
|
;; discard checked constraints, since they have no further reason to live
|
|
|
(make-csp (vars prob) other-consts)]))
|
|
|
|
|
|
(define/contract (make-nodes-consistent prob)
|
|
|
(csp? . -> . csp?)
|
|
|
(define-values (unary-constraints other-constraints)
|
|
|
(partition one-arity? (constraints prob)))
|
|
|
(if (empty? unary-constraints)
|
|
|
prob
|
|
|
(make-csp
|
|
|
(for/list ([vr (in-vars prob)])
|
|
|
(match-define (var name vals) vr)
|
|
|
(define name-constraints (filter (λ (const) (constraint-relates? const name)) unary-constraints))
|
|
|
(make-var name (for/list ([val (in-set vals)]
|
|
|
#:when (for/and ([const (in-list name-constraints)])
|
|
|
((constraint-proc const) val)))
|
|
|
val)))
|
|
|
other-constraints)))
|
|
|
|
|
|
(define ((make-hist-proc assocs) . xs)
|
|
|
(not
|
|
|
(for/and ([x (in-list xs)]
|
|
|
[val (in-list (map cdr assocs))])
|
|
|
(equal? x val))))
|
|
|
|
|
|
(struct solver (generator kill) #:transparent
|
|
|
#:property prop:procedure 0)
|
|
|
|
|
|
(define/contract (backtracking-solver
|
|
|
prob
|
|
|
#:select-variable [select-unassigned-variable
|
|
|
(or (current-select-variable) first-unassigned-variable)]
|
|
|
#:order-values [order-domain-values (or (current-order-values) first-domain-value)]
|
|
|
#:inference [inference (or (current-inference) no-inference)])
|
|
|
((csp?) (#:select-variable procedure? #:order-values procedure? #:inference procedure?) . ->* . solver?)
|
|
|
(solver
|
|
|
(generator ()
|
|
|
(define starting-state-count (state-count prob))
|
|
|
(define states-examined 0)
|
|
|
(define reduce-arity-proc (if (current-arity-reduction) reduce-constraint-arity values))
|
|
|
(let loop ([prob ((if (current-node-consistency) make-nodes-consistent values) prob)])
|
|
|
(match (select-unassigned-variable prob)
|
|
|
[#false (yield prob)]
|
|
|
[(var name domain)
|
|
|
(define (wants-backtrack? exn)
|
|
|
(and (backtrack? exn) (or (let ([bths (backtrack-histories exn)])
|
|
|
(or (empty? bths) (for*/or ([bth (in-list bths)]
|
|
|
[rec (in-list bth)])
|
|
|
(eq? name (car rec))))))))
|
|
|
(for/fold ([conflicts null]
|
|
|
#:result (void))
|
|
|
([val (in-list (order-domain-values (set->list domain)))])
|
|
|
(with-handlers ([wants-backtrack?
|
|
|
(λ (bt)
|
|
|
(define bths (backtrack-histories bt))
|
|
|
(append conflicts (remq name (remove-duplicates
|
|
|
(for*/list ([bth (in-list bths)]
|
|
|
[rec (in-list bth)])
|
|
|
(car rec)) eq?))))])
|
|
|
(let* ([prob (assign-val prob name val)]
|
|
|
;; reduce constraints before inference,
|
|
|
;; to create more forward-checkable (binary) constraints
|
|
|
[prob (reduce-arity-proc prob)]
|
|
|
[prob (inference prob name)]
|
|
|
[prob (check-constraints prob)])
|
|
|
(loop prob))
|
|
|
;; conflicts goes inside the handler expression
|
|
|
;; so raises can supersede it
|
|
|
conflicts))])))
|
|
|
void))
|
|
|
|
|
|
(define/contract (random-pick xs)
|
|
|
((non-empty-listof any/c) . -> . any/c)
|
|
|
(match xs
|
|
|
[(list x) x]
|
|
|
[(app set->list xs) (list-ref xs (random (length xs)))]))
|
|
|
|
|
|
(define (assign-random-vals prob)
|
|
|
(for/fold ([new-csp prob])
|
|
|
([name (in-var-names prob)])
|
|
|
(assign-val new-csp name (random-pick (find-domain prob name)))))
|
|
|
|
|
|
(define (make-min-conflcts-thread prob-start thread-count max-steps [main-thread (current-thread)])
|
|
|
(thread
|
|
|
(λ ()
|
|
|
(let loop ()
|
|
|
;; Generate a complete assignment for all variables (probably with conflicts)
|
|
|
(for/fold ([prob (assign-random-vals prob-start)])
|
|
|
([nth-step (in-range max-steps)])
|
|
|
;; Now repeatedly choose a random conflicted variable and change it
|
|
|
(match (conflicted-variable-names prob)
|
|
|
[(? empty?) (thread-send main-thread prob) (loop)]
|
|
|
[names
|
|
|
(define name (random-pick names))
|
|
|
(define val (min-conflicts-value prob name (find-domain prob-start name)))
|
|
|
(assign-val prob name val)]))))))
|
|
|
|
|
|
(define/contract (min-conflicts-solver prob [max-steps 100])
|
|
|
((csp?) (exact-positive-integer?) . ->* . solver?)
|
|
|
; todo: what is ideal thread count?
|
|
|
(define threads (for/list ([thread-count (or (current-thread-count) 1)])
|
|
|
(make-min-conflcts-thread prob thread-count max-steps)))
|
|
|
(solver
|
|
|
(generator ()
|
|
|
(let loop ()
|
|
|
(yield (thread-receive))
|
|
|
(loop)))
|
|
|
(λ () (for-each kill-thread threads) )))
|
|
|
|
|
|
(define/contract (optimal-stop-min proc xs)
|
|
|
(procedure? (listof any/c) . -> . any/c)
|
|
|
;; coefficient from
|
|
|
;; https://www.math.ucla.edu/~tom/Stopping/sr2.pdf
|
|
|
(define optimal-stopping-coefficient .458)
|
|
|
(define-values (sample candidates)
|
|
|
(split-at xs (inexact->exact (floor (* optimal-stopping-coefficient (length xs))))))
|
|
|
(define threshold (argmin proc sample))
|
|
|
(or (for/first ([candidate (in-list candidates)]
|
|
|
#:when (<= (proc candidate) threshold))
|
|
|
candidate)
|
|
|
(last candidates)))
|
|
|
|
|
|
(define/contract (conflicted-variable-names prob)
|
|
|
(csp? . -> . (listof name?))
|
|
|
;; Return a list of variables in current assignment that are conflicted
|
|
|
(for/list ([name (in-var-names prob)]
|
|
|
#:when (positive? (nconflicts prob name)))
|
|
|
name))
|
|
|
|
|
|
(define/contract (min-conflicts-value prob name vals)
|
|
|
(csp? name? (listof any/c) . -> . any/c)
|
|
|
;; Return the value that will give var the least number of conflicts
|
|
|
(define vals-by-conflict (sort (set->list vals) < #:key (λ (val) (nconflicts prob name val))
|
|
|
#:cache-keys? #true))
|
|
|
(for/first ([val (in-list vals-by-conflict)]
|
|
|
#:unless (equal? val (first (find-domain prob name)))) ;; but change the value
|
|
|
val))
|
|
|
|
|
|
(define no-value-sig (gensym))
|
|
|
|
|
|
(define/contract (nconflicts prob name [val no-value-sig])
|
|
|
((csp? name?) (any/c) . ->* . natural?)
|
|
|
;; How many conflicts var: val assignment has with other variables.
|
|
|
(check-constraints (if (eq? val no-value-sig)
|
|
|
prob
|
|
|
(assign-val prob name val)) (list name) #:conflicts #true))
|
|
|
|
|
|
(define/contract (csp->assocs prob [keys #f])
|
|
|
((csp?) ((listof name?)) . ->* . (listof (cons/c name? any/c)))
|
|
|
(define assocs
|
|
|
(for/list ([vr (in-vars prob)])
|
|
|
(match vr
|
|
|
[(var name (list val)) (cons name val)])))
|
|
|
(if keys
|
|
|
(for/list ([key (in-list keys)])
|
|
|
(assq key assocs))
|
|
|
assocs))
|
|
|
|
|
|
(define/contract (combine-csps probs)
|
|
|
((listof csp?) . -> . csp?)
|
|
|
(make-csp
|
|
|
(apply append (map vars probs))
|
|
|
(apply append (map csp-constraints probs))))
|
|
|
|
|
|
|
|
|
(define/contract (extract-subcsp prob names)
|
|
|
(csp? (listof name?) . -> . csp?)
|
|
|
(make-csp
|
|
|
(for/list ([vr (in-vars prob)]
|
|
|
#:when (memq (var-name vr) names))
|
|
|
vr)
|
|
|
(for/list ([const (in-constraints prob)]
|
|
|
#:when (constraint-checkable? const names))
|
|
|
const)))
|
|
|
|
|
|
(define (decompose-prob prob)
|
|
|
; decompose into independent csps. `cc` determines "connected components"
|
|
|
(if (current-decompose)
|
|
|
(for/list ([nodeset (in-list (cc (csp->graph prob)))])
|
|
|
(extract-subcsp prob nodeset))
|
|
|
(list prob)))
|
|
|
|
|
|
(define (make-solution-generator prob [max-solutions #false])
|
|
|
(generator ()
|
|
|
(define subprobs (decompose-prob prob))
|
|
|
(define solgens (map (current-solver) subprobs))
|
|
|
(define solstreams (for/list ([solgen (in-list solgens)])
|
|
|
(for/stream ([sol (in-producer solgen (void))])
|
|
|
sol)))
|
|
|
(for ([solution-pieces (in-cartesian solstreams)]
|
|
|
[count (in-range (or max-solutions +inf.0))])
|
|
|
(yield (combine-csps solution-pieces)))
|
|
|
(for-each solver-kill solgens)))
|
|
|
|
|
|
(define-syntax (in-solutions stx)
|
|
|
(syntax-case stx ()
|
|
|
[(_ PROB) #'(in-solutions PROB #false)]
|
|
|
[(_ PROB MAX-SOLUTIONS) #'(in-producer (make-solution-generator PROB MAX-SOLUTIONS) (void))]))
|
|
|
|
|
|
(define/contract (solve* prob [max-solutions #false]
|
|
|
#:finish-proc [finish-proc (λ (p) (csp->assocs p (map var-name (vars prob))))]
|
|
|
#:solver [solver #f])
|
|
|
((csp?) (natural? #:finish-proc procedure? #:solver procedure?) . ->* . (listof any/c))
|
|
|
(when-debug (reset-nassns!) (reset-nfchecks!) (reset-nchecks!))
|
|
|
|
|
|
(parameterize ([current-solver (or solver (current-solver))])
|
|
|
(for/list ([sol (in-solutions prob max-solutions)])
|
|
|
(finish-proc sol))))
|
|
|
|
|
|
(define/contract (solve prob
|
|
|
#:finish-proc [finish-proc (λ (p) (csp->assocs p (map var-name (vars prob))))]
|
|
|
#:solver [solver #f])
|
|
|
((csp?) (#:finish-proc procedure? #:solver procedure?)
|
|
|
. ->* . (or/c #false any/c))
|
|
|
(match (solve* prob 1 #:finish-proc finish-proc #:solver solver)
|
|
|
[(list solution) solution]
|
|
|
[_ #false]))
|
|
|
|
|
|
(define (<> a b) (not (= a b)))
|
|
|
(define (neq? a b) (not (eq? a b)))
|
|
|
|
|
|
(define current-select-variable (make-parameter #f))
|
|
|
(define current-order-values (make-parameter #f))
|
|
|
(define current-inference (make-parameter forward-check))
|
|
|
(define current-solver (make-parameter backtracking-solver))
|
|
|
(define current-decompose (make-parameter #t))
|
|
|
(define current-thread-count (make-parameter 4))
|
|
|
(define current-node-consistency (make-parameter #f))
|
|
|
(define current-arity-reduction (make-parameter #t))
|
|
|
(define current-learning (make-parameter #f)) |