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degree tiebreaker

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Matthew Butterick 6 years ago
parent 56d975667f
commit 9629c000eb
2 changed files with 64 additions and 43 deletions
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99
csp/csp.rkt
Unescape Escape View File

@ -20,8 +20,8 @@
[else
(match-define (cons name other-names) names)
(for/and ([val (in-list ($csp-vals csp name))])
;; todo: reconsider efficiency of currying every value
(($constraint other-names (curry proc val)) csp))])))
;; todo: reconsider efficiency of currying every value
(($constraint other-names (curry proc val)) csp))])))
(define/contract (check-name-in-csp! caller csp name)
(symbol? $csp? $var-name? . -> . void?)
@ -61,11 +61,11 @@
(($csp? procedure? (listof (listof $var-name?))) ((or/c #false $var-name?)) . ->* . void?)
(set-$csp-constraints! csp (append ($csp-constraints csp)
(for/list ([names (in-list namess)])
(for ([name (in-list names)])
(check-name-in-csp! 'add-constraint! csp name))
($constraint names (if proc-name
(procedure-rename proc proc-name)
proc))))))
(for ([name (in-list names)])
(check-name-in-csp! 'add-constraint! csp name))
($constraint names (if proc-name
(procedure-rename proc proc-name)
proc))))))
(define/contract (add-pairwise-constraint! csp proc var-names [proc-name #false])
(($csp? procedure? (listof $var-name?)) ($var-name?) . ->* . void?)
@ -78,7 +78,7 @@
(define/contract (no-solutions? csp)
($csp? . -> . boolean?)
(for/or ([var (in-list ($csp-vars csp))])
(empty? ($var-vals var))))
(zero? (remaining-values var))))
(struct inconsistency-error () #:transparent)
@ -86,14 +86,14 @@
($csp? unary-constraint? . -> . $csp?)
(match-define ($constraint (list constraint-name) proc) constraint)
(define new-csp ($csp (for/list ([var (in-list ($csp-vars csp))])
(match-define ($var name vals) var)
(if (eq? name constraint-name)
;; special rule: use promise for a constant value
;; to skip the filtering
($var name (if (promise? proc)
(force proc)
(filter proc vals)))
var))
(match-define ($var name vals) var)
(if (eq? name constraint-name)
;; special rule: use promise for a constant value
;; to skip the filtering
($var name (if (promise? proc)
(force proc)
(filter proc vals)))
var))
;; once the constraint is applied, it can go away
;; ps this is not the same as an "assigned" constraint
;; because the var may still have multiple values
@ -113,7 +113,7 @@
(check-name-in-csp! '$csp-vals csp name)
(for/first ([var (in-list ($csp-vars csp))]
#:when (eq? name ($var-name var)))
($var-vals var)))
($var-vals var)))
(struct $arc (name constraint) #:transparent)
@ -126,7 +126,7 @@
(λ (val other-val) (constraint-proc other-val val)))) ; otherwise reverse arg order
(define (satisfies-arc? val)
(for/or ([other-val (in-list ($csp-vals csp other-name))])
(proc val other-val)))
(proc val other-val)))
(apply-unary-constraint csp ($constraint (list name)
(procedure-rename
satisfies-arc?
@ -136,18 +136,18 @@
((listof binary-constraint?) . -> . (listof $arc?))
(for*/list ([constraint (in-list constraints)]
[name (in-list ($constraint-names constraint))])
($arc name constraint)))
($arc name constraint)))
(define/contract (terminating-at arcs name)
((listof $arc?) $var-name? . -> . (listof $arc?))
(for/list ([arc (in-list arcs)]
#:when (eq? name (second ($constraint-names ($arc-constraint arc)))))
arc))
arc))
(define/contract (constraint-assigned? csp constraint)
($csp? $constraint? . -> . any/c)
(for/and ([name (in-list ($constraint-names constraint))])
(memq name (map $var-name (assigned-vars csp)))))
(memq name (map $var-name (assigned-vars csp)))))
(define/contract (remove-assigned-constraints csp [arity #false])
(($csp?) ((or/c #false exact-nonnegative-integer?)) . ->* . $csp?)
@ -156,7 +156,7 @@
(for/list ([constraint (in-list ($csp-constraints csp))]
#:unless (and (if arity (= (length ($constraint-names constraint)) arity) #true)
(constraint-assigned? csp constraint)))
constraint)))
constraint)))
(define (remove-assigned-binary-constraints csp)
(remove-assigned-constraints csp 2))
@ -187,7 +187,7 @@
(define/contract (var-assigned? var)
($var? . -> . boolean?)
(= 1 (length ($var-vals var))))
(= 1 (remaining-values var)))
(define/contract (solution-complete? csp)
($csp? . -> . boolean?)
@ -205,13 +205,24 @@
(match-define-values (assigned unassigned) (assigned-helper csp))
assigned)
(define/contract (var-degree csp var)
($csp? $var? . -> . exact-nonnegative-integer?)
(for/sum ([constraint (in-list ($csp-constraints csp))]
#:when (constraint-contains-name? constraint ($var-name var)))
1))
(define/contract (select-unassigned-var csp)
($csp? . -> . $var?)
(define uvars (unassigned-vars csp))
(when (empty? uvars)
(raise-argument-error 'select-unassigned-var "csp with unassigned vars" csp))
;; minimum remaining values (MRV) rule
(argmin (λ (var) (length ($var-vals var))) uvars))
(define uvars-by-rv (sort uvars < #:key remaining-values))
(define minimum-remaining-values (remaining-values (first uvars-by-rv)))
(match (takef uvars-by-rv (λ (var) (= minimum-remaining-values (remaining-values var))))
[(list sole-winner) sole-winner]
[(list mrv-vars ...) ;; use degree as tiebreaker
(first (sort mrv-vars > #:key (λ (var) (var-degree csp var))))]))
(define/contract (order-domain-values vals)
((listof any/c) . -> . (listof any/c))
@ -226,7 +237,7 @@
($csp? . -> . $csp?)
(for ([constraint (in-list ($csp-constraints csp))]
#:when (constraint-assigned? csp constraint))
(unless (constraint csp) (raise (inconsistency-error))))
(unless (constraint csp) (raise (inconsistency-error))))
(reduce-constraint-arity (remove-assigned-constraints csp)))
(define/contract (assign-val csp name val)
@ -270,19 +281,19 @@
(define assigned-names (map $var-name (assigned-vars csp)))
($csp ($csp-vars csp)
(for/list ([constraint (in-list ($csp-constraints csp))])
(match-define ($constraint cnames proc) constraint)
(cond
[(and (<= minimum-arity (length cnames))
(for/or ([cname (in-list cnames)])
(memq cname assigned-names)))
($constraint (for/list ([cname (in-list cnames)]
#:unless (memq cname assigned-names))
cname)
(reduce-arity proc (for/list ([cname (in-list cnames)])
(if (memq cname assigned-names)
(car ($csp-vals csp cname))
cname))))]
[else constraint]))))
(match-define ($constraint cnames proc) constraint)
(cond
[(and (<= minimum-arity (length cnames))
(for/or ([cname (in-list cnames)])
(memq cname assigned-names)))
($constraint (for/list ([cname (in-list cnames)]
#:unless (memq cname assigned-names))
cname)
(reduce-arity proc (for/list ([cname (in-list cnames)])
(if (memq cname assigned-names)
(car ($csp-vals csp cname))
cname))))]
[else constraint]))))
(module+ test
(define creduce (assign-val ($csp (list ($var 'a '(1 2 3)) ($var 'b '(2 3)) ($var 'c '(1 2 3 4 5))) (list ($constraint '(a b c) (procedure-rename (λ (a b c) (= (+ a b c) 4)) 'summer)))) 'a 1))
@ -304,15 +315,15 @@
[else ;; we have at least 1 unassigned var
(match-define ($var name vals) (select-unassigned-var csp))
(for ([val (in-list (order-domain-values vals))])
(with-handlers ([inconsistency-error? void])
(backtrack (infer (assign-val csp name val)))))]))))
(with-handlers ([inconsistency-error? void])
(backtrack (infer (assign-val csp name val)))))]))))
(define/contract (solve* csp [finish-proc values][solution-limit +inf.0])
(($csp?) (procedure? integer?) . ->* . (listof any/c))
(define solutions
(for/list ([solution (in-producer (backtracking-solver csp) (void))]
[idx (in-range solution-limit)])
(finish-proc solution)))
(finish-proc solution)))
(unless (pair? solutions) (raise (inconsistency-error)))
solutions)
@ -330,7 +341,11 @@
(any/c any/c . -> . boolean?)
(not (= x y)))
(define/contract (remaining-values var)
($var? . -> . exact-nonnegative-integer?)
(length ($var-vals var)))
(define/contract (state-count csp)
($csp? . -> . exact-nonnegative-integer?)
(for/product ([var (in-list ($csp-vars csp))])
(length ($var-vals var))))
(remaining-values var)))

8
csp/test.rkt
Unescape Escape View File

@ -131,9 +131,15 @@ A collection of 33 coins, consisting of nickels, dimes, and quarters, has a valu
|#
(define smm (make-csp))
(add-vars! smm '(s e n d m o r y) (λ () (shuffle (range 10))))
(add-vars! smm '(s e n d m o r y) (range 10))
(add-constraint! smm positive? '(s))
(add-constraint! smm positive? '(m))
(add-constraint! smm (λ (d e y) (= (modulo (+ d e) 10) y)) '(d e y))
(add-constraint! smm (λ (n d r e y)
(= (modulo (+ (word-value n d) (word-value r e)) 100)
(word-value e y))) '(n d r e y))
(add-constraint! smm (λ (e n d o r y)
(= (modulo (+ (word-value e n d) (word-value o r e)) 1000) (word-value n e y))) '(e n d o r y))
(add-constraint! smm (λ (s e n d m o r y)
(= (+ (word-value s e n d) (word-value m o r e))
(word-value m o n e y))) '(s e n d m o r y))

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