typesetting/csp/hacs-test.rkt

#lang debug racket
(require "hacs.rkt" rackunit sugar/list sugar/debug)

(current-inference forward-check)
(current-select-variable mrv-degree-hybrid)
(current-order-values shuffle)
(current-random #true)

(check-equal? (first-unassigned-variable ($csp (list ($var 'a (range 3)) ($var 'b (range 3))) null))
              ($var 'a (range 3)))
(check-equal? (first-unassigned-variable ($csp (list ($avar 'a (range 3)) ($var 'b (range 3))) null))
              ($var 'b (range 3)))
(check-false (first-unassigned-variable ($csp (list ($avar 'a (range 3)) ($avar 'b (range 3))) null)))

(check-equal?
 ;; no forward checking when no constraints
 ($csp-vars (forward-check ($csp (list ($avar 'a '(1)) ($var 'b (range 2))) null) 'a))
 (list ($avar 'a '(1)) ($var 'b '(0 1))))

(check-equal?
 ($csp-vars (forward-check (forward-check ($csp (list ($avar 'a '(1))  ($avar 'b '(0)) ($var 'c '(0 1 2)))
                                                (list ($constraint '(a c) (negate =))
                                                      ($constraint '(b c) (negate =)))) 'a) 'b))
 (list ($avar 'a '(1)) ($avar 'b '(0)) ($cvar 'c '(2) '(b a))))

(check-equal?
 ;; no inconsistency: b≠c not checked when fc is relative to a
 ($csp-vars (forward-check ($csp (list ($avar 'a '(1))  ($var 'b (range 2)) ($var 'c '(0)))
                                 (list ($constraint '(a b) (negate =))
                                       ($constraint '(b c) (negate =)))) 'a))
 (list ($avar 'a '(1)) ($cvar 'b '(0) '(a)) ($var 'c '(0))))

(check-equal?
 ;; no inconsistency: a≠b not checked when fc ignores a, which is already assigned
 ($csp-vars (forward-check ($csp (list ($avar 'a '(1))  ($avar 'b '(1)) ($var 'c (range 2)))
                                 (list ($constraint '(a b) (negate =))
                                       ($constraint '(b c) (negate =)))) 'b))
 (list ($avar 'a '(1)) ($avar 'b '(1)) ($cvar 'c '(0) '(b))))

(check-exn $backtrack?
           (λ () ($csp-vars (forward-check ($csp (list ($avar 'a '(1))
                                                       ($var 'b '(1)))
                                                 (list ($constraint '(a b) (negate =)))) 'a))))


(check-equal? ($csp-vars (forward-check ($csp (list ($var 'a '(0))
                                                    ($var 'b (range 3)))
                                              (list ($constraint '(a b) <))) 'a))
              (list ($var 'a '(0)) ($cvar 'b '(1 2) '(a))))

(check-equal?
 (parameterize ([current-inference forward-check])
   (length (solve* ($csp (list ($var 'x (range 3))
                               ($var 'y (range 3))
                               ($var 'z (range 3)))
                         (list ($constraint '(x y) <>)
                               ($constraint '(x z) <>)
                               ($constraint '(y z) <>)))))) 6)

(parameterize ([current-inference forward-check])
  (define vds (for/list ([k '(wa nt nsw q t v sa)])
                        ($var k '(red green blue))))
  (define cs (list
              ($constraint '(wa nt) neq?)
              ($constraint '(wa sa) neq?)
              ($constraint '(nt sa) neq?)
              ($constraint '(nt q) neq?)
              ($constraint '(q sa) neq?)
              ($constraint '(q nsw) neq?)
              ($constraint '(nsw sa) neq?)
              ($constraint '(nsw v) neq?)
              ($constraint '(v sa) neq?)))
  (define csp ($csp vds cs))
  (check-equal? (length (solve* csp)) 18))


(define quarters (make-csp))
(add-vars! quarters '(dollars quarters) (range 26))
(add-constraint! quarters (λ (d q) (= 26 (+ d q))) '(dollars quarters))
(add-constraint! quarters (λ (d q) (= 17 (+ d (* 0.25 q)))) '(dollars quarters))
(check-equal? (time-named (solve quarters))
              '((dollars . 14) (quarters . 12)))


;; xsum
#|
# Reorganize the following numbers in a way that each line of
# 5 numbers sum to 27.
#
#       1   6
#        2 7
#         3
#        8 4
#       9   5
#
|#
(define xsum (make-csp))
(add-vars! xsum '(l1 l2 l3 l4 r1 r2 r3 r4 x) (range 1 10))
(add-pairwise-constraint! xsum < '(l1 l2 l3 l4))
(add-pairwise-constraint! xsum < '(r1 r2 r3 r4))
(add-constraint! xsum (λ (l1 l2 l3 l4 x) (= 27 (+ l1 l2 l3 l4 x))) '(l1 l2 l3 l4 x))
(add-constraint! xsum (λ (r1 r2 r3 r4 x)  (= 27 (+ r1 r2 r3 r4 x))) '(r1 r2 r3 r4 x))
(add-pairwise-constraint! xsum alldiff= '(l1 l2 l3 l4 r1 r2 r3 r4 x))

(check-equal? (length (time-named (solve* xsum))) 8)



;; send more money problem
#|
# Assign equal values to equal letters, and different values to
# different letters, in a way that satisfies the following sum:
#
#    SEND
#  + MORE
#  ------
#   MONEY
|#

(define (word-value . xs)
  (for/sum ([(x idx) (in-indexed (reverse xs))])
           (* x (expt 10 idx))))

(define smm (make-csp))
(add-vars! smm '(s e n d m o r y) (λ () (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))
(add-pairwise-constraint! smm alldiff= '(s e n d m o r y))
(check-equal? (parameterize ([current-select-variable mrv-degree-hybrid]) ; todo: why is plain mrv so bad on this problem?
                (time-named (solve smm))) '((s . 9) (e . 5) (n . 6) (d . 7) (m . 1) (o . 0) (r . 8) (y . 2)))


;; queens problem
;; place queens on chessboard so they do not intersect
(define queens (make-csp))
(define qs (for/list ([q 8]) (string->symbol (format "q~a" q))))
(define rows (range (length qs)))
(add-vars! queens qs rows)
(define (q-col q) (string->number (string-trim (symbol->string q) "q")))
(for* ([qs (in-combinations qs 2)])
      (match-define (list qa qb) qs)
      (match-define (list qa-col qb-col) (map q-col qs))
      (add-constraint! queens
                       (λ (qa-row qb-row)
                         (and 
                          (not (= (abs (- qa-row qb-row)) (abs (- qa-col qb-col)))) ; same diagonal?
                          (not (= qa-row qb-row)))) ; same row?
                       (list qa qb)))

(check-equal? 92 (length (time-named (solve* queens))))

#|
# There are no tricks, just pure logic, so good luck and don't give up. 
# 
# 1. In a street there are five houses, painted five different colours. 
# 2. In each house lives a person of different nationality 
# 3. These five homeowners each drink a different kind of beverage, smoke 
# different brand of cigar and keep a different pet. 
# 
# THE QUESTION: WHO OWNS THE zebra? 
# 
# HINTS 
# 
# 1. The englishman lives in a red house. 
# 2. The spaniard keeps dogs as pets. 
# 5. The owner of the Green house drinks coffee. 
# 3. The ukrainian drinks tea. 
# 4. The Green house is on the left of the ivory house. 
# 6. The person who smokes oldgold rears snails. 
# 7. The owner of the Yellow house smokes kools. 
# 8. The man living in the centre house drinks milk. 
# 9. The Norwegian lives in the first house. 
# 10. The man who smokes chesterfields lives next to the one who keeps foxes. 
# 11. The man who keeps horses lives next to the man who smokes kools. 
# 12. The man who smokes luckystrike drinks orangejuice. 
# 13. The japanese smokes parliaments. 
# 14. The Norwegian lives next to the blue house. 
# 15. The man who smokes chesterfields has a neighbour who drinks water. 
|#

(define (sym . args) (string->symbol (apply format args)))

(define zebra (make-csp))

(define ns (map (curry sym "nationality-~a") (range 5)))
(define cs (map (curry sym "color-~a") (range 5)))
(define ds (map (curry sym "drink-~a") (range 5)))
(define ss (map (curry sym "smoke-~a") (range 5)))
(define ps (map (curry sym "pet-~a") (range 5)))

(add-vars! zebra ns '(englishman spaniard ukrainian norwegian japanese))
(add-vars! zebra cs '(red ivory green yellow blue))
(add-vars! zebra ds '(tea coffee milk orange-juice water))
(add-vars! zebra ss '(oldgold kools chesterfields luckystrike parliaments))
(add-vars! zebra ps '(dogs snails foxes horses zebra))

(for ([vars (list ns cs ds ss ps)])
     (add-pairwise-constraint! zebra neq? vars))

(define (xnor lcond rcond)
  (or (and lcond rcond) (and (not lcond) (not rcond))))
(define (paired-with lval left rval right)
  (add-constraint! zebra (λ (left right) (xnor (eq? left lval) (eq? rval right))) (list left right)))

(define (paired-with* lval lefts rval rights)
  (for ([left lefts][right rights])
       (paired-with lval left rval right)))

;# 1. The englishman lives in a red house. 
('englishman ns . paired-with* . 'red cs)

;# 2. The spaniard keeps dogs as pets. 
('spaniard ns . paired-with* . 'dogs ps)

;# 5. The owner of the Green house drinks coffee. 
('green cs . paired-with* . 'coffee ds)

;# 3. The ukrainian drinks tea.
('ukrainian ns . paired-with* . 'tea ds)

;# 4. The Green house is on the left of the ivory house.
('green (drop-right cs 1) . paired-with* . 'ivory (drop cs 1))
(add-constraint! zebra (curry neq? 'ivory) (list 'color-0))
(add-constraint! zebra (curry neq? 'green) (list 'color-4))

;# 6. The person who smokes oldgold rears snails.
('oldgold ss . paired-with* . 'snails ps)

;# 7. The owner of the Yellow house smokes kools.
('yellow cs . paired-with* . 'kools ss)

;# 8. The man living in the centre house drinks milk.
(add-constraint! zebra (λ (d) (eq? d 'milk)) (list 'drink-2))

;# 9. The Norwegian lives in the first house.
(add-constraint! zebra (λ (x) (eq? x 'norwegian)) (list 'nationality-0))

(define (next-to lval lefts rval rights)
  (for ([righta (drop-right rights 2)]
        [left (cdr lefts)]
        [rightb (drop rights 2)])
       (add-constraint! zebra (λ (left righta rightb)
                                (or (not (eq? left lval)) (eq? righta rval) (eq? rval rightb)))
                        (list left righta rightb)))
  (for ([left (list (first lefts) (last lefts))]
        [right (list (second rights) (fourth rights))])
       (add-constraint! zebra (λ (left right) (xnor (eq? left lval) (eq? rval right)))
                        (list left right))))

;# 10. The man who smokes chesterfields lives next to the one who keeps foxes.
('chesterfields ss . next-to . 'foxes ps)

;# 11. The man who keeps horses lives next to the man who smokes kools.
('horses ps . next-to . 'kools ss)

;# 12. The man who smokes luckystrike drinks orangejuice.
('luckystrike ss . paired-with* . 'orange-juice ds)

;# 13. The japanese smokes parliaments.
('japanese ns . paired-with* . 'parliaments ss)

;# 14. The Norwegian lives next to the blue house.
('norwegian ns . next-to . 'blue cs)

;# 15. The man who smokes chesterfields has a neighbour who drinks water. 
('chesterfields ss . next-to . 'water ds)

(define (finish x)
  (apply map list (slice-at x 5)))

(check-equal? (parameterize ([current-select-variable mrv]
                             [current-random #f])
                (finish (time-named (solve zebra))))
              '(((nationality-0 . norwegian) (color-0 . yellow) (drink-0 . water) (smoke-0 . kools) (pet-0 . foxes))
                ((nationality-1 . ukrainian) (color-1 . blue) (drink-1 . tea) (smoke-1 . chesterfields) (pet-1 . horses))
                ((nationality-2 . englishman) (color-2 . red) (drink-2 . milk) (smoke-2 . oldgold) (pet-2 . snails))
                ((nationality-3 . japanese) (color-3 . green) (drink-3 . coffee) (smoke-3 . parliaments) (pet-3 . zebra))
                ((nationality-4 . spaniard) (color-4 . ivory) (drink-4 . orange-juice) (smoke-4 . luckystrike) (pet-4 . dogs))))

(module+ main
  (when-debug
   (define-syntax n (λ (stx) #'10))
   (time-avg n (void (solve quarters)))
   (time-avg n (void (solve* xsum)))
   (time-avg n (void (solve smm)))
   (time-avg n (void (solve* queens)))
   (time-avg n (void (solve zebra)))))