main
Matthew Butterick 6 years ago
parent 65a512c077
commit b7f829760c

@ -2,7 +2,7 @@
(require sugar/debug "hacs.rkt")
(define names (for/list ([i (in-range 81)])
(string->symbol (format "c~a" i))))
(string->symbol (format "c~a" i))))
(define (make-sudoku)
(define sudoku (make-csp))
@ -11,26 +11,26 @@
(define (not= . xs) (= (length xs) (length (remove-duplicates xs =))))
(for ([i (in-range 9)])
(define row-cells (for/list ([(name idx) (in-indexed names)]
#:when (= (quotient idx 9) i))
name))
(add-pairwise-constraint! sudoku not= row-cells)
(define col-cells (for/list ([(name idx) (in-indexed names)]
#:when (= (remainder idx 9) i))
name))
(add-pairwise-constraint! sudoku not= col-cells))
(define row-cells (for/list ([(name idx) (in-indexed names)]
#:when (= (quotient idx 9) i))
name))
(add-pairwise-constraint! sudoku not= row-cells)
(define col-cells (for/list ([(name idx) (in-indexed names)]
#:when (= (remainder idx 9) i))
name))
(add-pairwise-constraint! sudoku not= col-cells))
(for ([i '(0 3 6 27 30 33 54 57 60)])
(define box-cells (for/list ([j '(0 1 2 9 10 11 18 19 20)])
(string->symbol (format "c~a" (+ i j)))))
(add-pairwise-constraint! sudoku not= box-cells))
(define box-cells (for/list ([j '(0 1 2 9 10 11 18 19 20)])
(string->symbol (format "c~a" (+ i j)))))
(add-pairwise-constraint! sudoku not= box-cells))
sudoku)
(require racket/sequence)
(define (print-grid sol)
(displayln (string-join (map ~a (for/list ([row (in-slice 9 (csp->assocs sol))])
(map cdr row))) "\n")))
(map cdr row))) "\n")))
(define (board . strs)
(define sudoku (make-sudoku))
@ -38,11 +38,11 @@
(for*/list ([str strs]
[c (in-port read-char (open-input-string str))]
#:unless (memv c '(#\- #\|)))
(string->number (string c))))
(string->number (string c))))
(for ([name names]
[val vals]
#:when val)
(add-constraint! sudoku (curry = val) (list name) (string->symbol (format "is-~a" val))))
(add-constraint! sudoku (curry = val) (list name) (string->symbol (format "is-~a" val))))
sudoku)
;; http://jeapostrophe.github.io/2013-10-23-sudoku-post.html
@ -97,23 +97,27 @@
(current-random #true)
(current-node-consistency #t)
(current-arity-reduction #t)
#;(time-avg 10 (solve b1 #:finish-proc print-grid))
#;(time-avg 10 (solve b2 #:finish-proc print-grid))
#;(time-avg 10 (solve b3 #:finish-proc print-grid))
(time-avg 10 (void (solve b1)))
(time-avg 10 (void (solve b2)))
(time-avg 10 (void (solve b3)))
(define (euler-value sol)
(match sol
[(list (cons (== 'c0) h) (cons (== 'c1) t) (cons (== 'c2) d) _ ...)
(+ (* 100 h) (* 10 t) d)]))
(require rackunit)
(check-equal? (euler-value (solve b1)) 534)
(check-equal? (euler-value (solve b2)) 378)
(check-equal? (euler-value (solve b3)) 938)
;; https://projecteuler.net/problem=96
;; todo: parsing of these is wrong
(define bstrs
(for/list ([puz (in-slice 10 (string-split (port->string (open-input-file "euler-sudoku-grids.txt")) "\n"))])
(map (λ (str) (string-replace str "0" " ")) (cdr puz))))
(car bstrs)
(define bboard (apply board (car bstrs)))
(solve bboard #:finish-proc print-grid)
#;(for/fold ([sum 0])
([(bstr idx) (in-indexed bstrs)])
(define sol (solve (apply board bstr)))
(+ sum #R (+ (* 100 (cdr (assq 'c0 sol)))
(* 10 (cdr (assq 'c1 sol)))
(* 1 (cdr (assq 'c2 sol))))))
;; answer 24702
(define (do-euler)
(define bstrs
(for/list ([puz (in-slice 10 (string-split (port->string (open-input-file "euler-sudoku-grids.txt")) "\n"))])
(map (λ (str) (string-replace str "0" " ")) (cdr puz))))
(for/sum ([bstr bstrs])
(euler-value (solve (apply board bstr)))))

@ -20,7 +20,7 @@
(if (null? argss)
(yield (reverse acc))
(for ([arg (car argss)])
(loop (cdr argss) (cons arg acc))))))))
(loop (cdr argss) (cons arg acc))))))))
(struct csp (vars constraints) #:mutable #:transparent)
(define constraints csp-constraints)
@ -36,7 +36,7 @@
(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))))
(apply (constraint-proc const) args))))
(define name? symbol?)
@ -95,11 +95,11 @@
((csp? procedure? (listof (listof name?))) ((or/c #false name?)) . ->* . void?)
(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))))))
(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?)
@ -138,7 +138,7 @@
(check-name-in-csp! 'find-var prob name)
(for/first ([vr (in-vars prob)]
#:when (eq? name (var-name vr)))
vr))
vr))
(define/contract (find-domain prob name)
(csp? name? . -> . (listof any/c))
@ -151,7 +151,7 @@
(csp? name? . -> . any/c)
(for/or ([vr (in-vars prob)]
#:when (assigned-var? vr))
(eq? name (var-name vr))))
(eq? name (var-name vr))))
(define/contract (reduce-function-arity proc pattern)
(procedure? (listof any/c) . -> . procedure?)
@ -183,20 +183,20 @@
(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]))))
(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)
@ -211,9 +211,9 @@
(when-debug (set! nassns (add1 nassns)))
(make-csp
(for/list ([vr (in-vars prob)])
(if (eq? name (var-name vr))
(assigned-var name (list val))
vr))
(if (eq? name (var-name vr))
(assigned-var name (list val))
vr))
(constraints prob)))
(define/contract (unassigned-vars prob)
@ -238,7 +238,7 @@
(csp? var? . -> . natural?)
(for/sum ([const (in-constraints prob)]
#:when (memq (var-name var) (constraint-names const)))
1))
1))
(define/contract (domain-length var)
(var? . -> . natural?)
@ -247,7 +247,7 @@
(define/contract (state-count csp)
(csp? . -> . natural?)
(for/product ([vr (in-vars csp)])
(domain-length vr)))
(domain-length vr)))
(define/contract (mrv-degree-hybrid prob)
(csp? . -> . (or/c #f var?))
@ -267,7 +267,7 @@
(random-pick (for/list ([uv (in-list mrv-uvars)]
[degree (in-list degrees)]
#:when (= max-degree degree))
uv))])]))
uv))])]))
(define first-domain-value values)
@ -279,8 +279,8 @@
[cnames (in-value (constraint-names const))]
#:when (and (= (length names) (length cnames))
(for/and ([name (in-list names)])
(memq name cnames))))
const))
(memq name cnames))))
const))
(define (one-arity? const) (= 1 (constraint-arity const)))
(define (two-arity? const) (= 2 (constraint-arity const)))
@ -294,7 +294,7 @@
((listof (and/c constraint? two-arity?)) . -> . (listof arc?))
(for*/list ([const (in-list constraints)]
[name (in-list (constraint-names const))])
(arc name const)))
(arc name const)))
(require sugar/debug)
(define/contract (reduce-domain prob ark)
@ -306,16 +306,16 @@
(λ (val other-val) (constraint-proc other-val val)))) ; otherwise reverse arg order
(define (satisfies-arc? val)
(for/or ([other-val (in-list (find-domain prob other-name))])
(proc val other-val)))
(proc val other-val)))
(make-csp
(for/list ([vr (in-vars prob)])
(cond
[(assigned-var? vr) vr]
[(eq? name (var-name vr))
(var name (match (filter satisfies-arc? (domain vr))
[(? empty?) (backtrack!)]
[vals vals]))]
[else vr]))
(cond
[(assigned-var? vr) vr]
[(eq? name (var-name vr))
(var name (match (filter satisfies-arc? (domain vr))
[(? empty?) (backtrack!)]
[vals vals]))]
[else vr]))
(constraints prob)))
(define/contract (terminating-at? arcs name)
@ -324,7 +324,7 @@
#:when (and
(memq name (constraint-names (arc-const arc)))
(not (eq? name (arc-name arc)))))
arc))
arc))
(define/contract (ac-3 prob ref-name)
(csp? name? . -> . csp?)
@ -334,8 +334,8 @@
(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)))
(memq cname checkable-names))))
const)))
(for/fold ([prob prob]
[arcs (sort starting-arcs < #:key (λ (a) (length (find-domain prob (arc-name a)))) #:cache-keys? #true)]
#:result (prune-singleton-constraints prob))
@ -366,11 +366,11 @@
(define new-vals
(for/list ([val (in-list vals)]
#:when (for/and ([const (in-list constraints)])
(let ([proc (constraint-proc const)])
(if (eq? name (first (constraint-names const)))
(proc val ref-val)
(proc ref-val val)))))
val))
(let ([proc (constraint-proc const)])
(if (eq? name (first (constraint-names const)))
(proc val ref-val)
(proc ref-val val)))))
val))
(checked-variable name new-vals (cons (cons ref-name ref-val) (match vr
[(checked-variable _ _ history) history]
[else null])))])]))
@ -379,15 +379,15 @@
((csp?) ((or/c #false name?)) . ->* . csp?)
(define singleton-var-names (for/list ([vr (in-vars prob)]
#:when (singleton-var? vr))
(var-name 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)))
(memq cname singleton-var-names))))
const)))
(define/contract (forward-check prob ref-name)
(csp? name? . -> . csp?)
@ -396,7 +396,7 @@
;; 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 (empty? (domain cvr)))
(history 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.
@ -413,7 +413,7 @@
;; constraint is checkable if all constraint names
;; are in target list of names.
(for/and ([cname (in-list (constraint-names const))])
(memq cname names)))
(memq cname names)))
(define/contract (constraint-arity const)
(constraint? . -> . natural?)
@ -430,26 +430,26 @@
;; we also want to use "singleton" vars (that is, vars that have been reduced to a single domain value by forward checking)
(define singleton-varnames (for/list ([vr (in-vars prob)]
#:when (singleton-var? vr))
(var-name vr)))
(var-name vr)))
(define-values (checkable-consts other-consts)
(partition (λ (const) (and (constraint-checkable? const singleton-varnames)
(or (not mandatory-names)
(for/and ([name (in-list mandatory-names)])
(constraint-relates? const name)))))
(constraint-relates? const name)))))
(constraints prob)))
(cond
[conflict-count?
(define conflict-count
(for/sum ([constraint (in-list checkable-consts)]
#:unless (constraint prob))
1))
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!))
(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)]))
@ -461,28 +461,18 @@
prob
(make-csp
(for/list ([vr (in-vars prob)])
(match-define (var name vals) vr)
(var name (for/fold ([vals vals])
([const (in-list unary-constraints)]
#:when (constraint-relates? const name))
(filter (constraint-proc const) vals))))
(match-define (var name vals) vr)
(var name (for/fold ([vals vals])
([const (in-list unary-constraints)]
#:when (constraint-relates? const name))
(filter (constraint-proc const) vals))))
other-constraints)))
(define ((make-hist-proc assocs) . xs)
(not
(for/and ([x (in-list xs)]
[val (in-list (map cdr assocs))])
(equal? x val))))
(define (history->constraint hst)
(constraint (map car hst) (make-hist-proc hst)))
(define/contract (assign-singletons prob)
(csp? . -> . csp?)
(for/fold ([prob prob])
([vr (in-vars prob)]
#:when (singleton-var? vr))
(assign-val prob (var-name vr) (first (var-domain vr)))))
(equal? x val))))
(define/contract (backtracking-solver
prob
@ -493,10 +483,8 @@
((csp?) (#:select-variable procedure? #:order-values procedure? #:inference procedure?) . ->* . generator?)
(generator ()
(define reduce-arity-proc (if (current-arity-reduction) reduce-constraint-arity values))
(define learned-constraints null)
(define learning? (current-learning))
(let* ([prob ((if (current-node-consistency) make-nodes-consistent values) prob)]
[prob (assign-singletons prob)])
(let* ([prob ((if (current-node-consistency) make-nodes-consistent values) prob)])
(let loop ([prob prob])
(match (select-unassigned-variable prob)
[#false (yield prob)]
@ -505,30 +493,18 @@
(and (backtrack? exn) (or (let ([bths (backtrack-histories exn)])
(or (empty? bths) (for*/or ([bth bths]
[rec bth])
(eq? name (car rec))))))))
(eq? name (car rec))))))))
(for/fold ([conflicts null]
#:result (void))
([val (in-list (order-domain-values domain))])
(with-handlers ([wants-backtrack?
(λ (bt)
(define bths (backtrack-histories bt))
(when learning?
(set! learned-constraints (append
(map history->constraint (filter (λ (bth) (<= 2 (length bth) 4)) bths))
learned-constraints)))
(append conflicts (remq name (remove-duplicates
(for*/list ([bth bths]
[rec bth])
(car rec)) eq?))))])
(car rec)) eq?))))])
(let* ([prob (assign-val prob name val)]
[prob (if learning?
(and (for ([lc learned-constraints]
#:when (for/and ([cname (constraint-names lc)])
(memq cname (map var-name (filter assigned-var? (vars prob))))))
(unless (lc prob)
(println 'boing)
(backtrack!))) prob)
prob)]
;; reduce constraints before inference,
;; to create more forward-checkable (binary) constraints
[prob (reduce-arity-proc prob)]
@ -565,9 +541,9 @@
(generator ()
(for ([thread-count (or (current-thread-count) 1)]) ; todo: what is ideal thread count?
(make-min-conflcts-thread prob thread-count max-steps))
(make-min-conflcts-thread prob thread-count max-steps))
(for ([i (in-naturals)])
(yield (thread-receive)))))
(yield (thread-receive)))))
(define/contract (optimal-stop-min proc xs)
(procedure? (listof any/c) . -> . any/c)
@ -575,7 +551,7 @@
(define threshold (argmin proc sample))
(or (for/first ([candidate (in-list candidates)]
#:when (<= (proc candidate) threshold))
candidate)
candidate)
(last candidates)))
(define/contract (conflicted-variable-names prob)
@ -583,7 +559,7 @@
;; Return a list of variables in current assignment that are conflicted
(for/list ([name (in-var-names prob)]
#:when (positive? (nconflicts prob name)))
name))
name))
(define/contract (min-conflicts-value prob name vals)
(csp? name? (listof any/c) . -> . any/c)
@ -592,7 +568,7 @@
#:cache-keys? #true))
(for/first ([val (in-list vals-by-conflict)]
#:unless (equal? val (first (find-domain prob name)))) ;; but change the value
val))
val))
(define no-value-sig (gensym))
@ -607,11 +583,11 @@
((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)])))
(match vr
[(var name (list val)) (cons name val)])))
(if keys
(for/list ([key (in-list keys)])
(assq key assocs))
(assq key assocs))
assocs))
(define/contract (combine-csps probs)
@ -626,11 +602,11 @@
(make-csp
(for/list ([vr (in-vars prob)]
#:when (memq (var-name vr) names))
vr)
vr)
(for/list ([const (in-constraints prob)]
#:when (for/and ([cname (in-list (constraint-names const))])
(memq cname names)))
const)))
(memq cname names)))
const)))
(define/contract (solve* prob
#:finish-proc [finish-proc (λ (p) (csp->assocs p (map var-name (vars prob))))]
@ -643,17 +619,17 @@
(define subcsps ; decompose into independent csps. `cc` determines "connected components"
(if (current-decompose)
(for/list ([nodeset (in-list (cc (csp->graph prob)))])
(extract-subcsp prob nodeset))
(extract-subcsp prob nodeset))
(list prob)))
(define solgens (map solver subcsps))
(define solstreams (for/list ([solgen (in-list solgens)])
(for/stream ([sol (in-producer solgen (void))])
sol)))
(for/stream ([sol (in-producer solgen (void))])
sol)))
(for/list ([solution-pieces (in-cartesian solstreams)]
[idx (in-range max-solutions)])
(finish-proc (combine-csps solution-pieces))))
(finish-proc (combine-csps solution-pieces))))
(define/contract (solve prob
#:finish-proc [finish-proc (λ (p) (csp->assocs p (map var-name (vars prob))))]

@ -272,8 +272,7 @@
(on-tick move-right 1/8)
(on-draw draw-draw-state)))
(module+ main
;; Wikipedia Example
;; Wikipedia Example
(define b1
(board
"53 | 7 | "
@ -318,7 +317,13 @@
" 7| 6 | "
"65 | |3 "))
(draw-state-i
#;(draw-state-i
(draw-it!
(solve-it
b2))))
b2)))
(require sugar/debug)
(time-avg 10 (void (solve-it b1)))
(time-avg 10 (void (solve-it b2)))
(time-avg 10 (void (solve-it b3)))
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