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168 lines
5.7 KiB
Racket
168 lines
5.7 KiB
Racket
#lang at-exp racket
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(require "csp.rkt" rackunit)
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(define demo (make-csp))
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(add-vars! demo '(t w) (range 7))
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(add-var! demo 'o '(2 6 7))
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(define (sum-three t w o) (= 3 (+ t w o)))
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(add-constraint! demo sum-three '(t w o))
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(add-pairwise-constraint! demo alldiff= '(t w o))
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(add-pairwise-constraint! demo < '(t w o))
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(check-equal? (time (solve demo)) ($csp (list ($var 't '(0)) ($var 'w '(1)) ($var 'o '(2))) '()))
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;; TWO + TWO = FOUR
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(define ttf (make-csp))
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(add-vars! ttf '(t w o f u r) (reverse (range 10)))
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(define (word-value . xs)
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(let ([xs (reverse xs)])
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(for/sum ([i (in-range (length xs))])
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(* (list-ref xs i) (expt 10 i)))))
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(add-pairwise-constraint! ttf alldiff= '(t w o f u r))
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(add-constraint! ttf (λ (o r) (= (modulo (+ o o) 10) r)) '(o r))
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(add-constraint! ttf (λ (t w o f u r) (= (+ (word-value t w o) (word-value t w o))
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(word-value f o u r))) '(t w o f u r))
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(add-constraint! ttf positive? '(t))
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(add-constraint! ttf positive? '(f))
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(define ttf-solution (time (solve ttf)))
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(check-equal? ttf-solution
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($csp
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(list
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($var 't '(7))
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($var 'w '(3))
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($var 'o '(4))
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($var 'f '(1))
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($var 'u '(6))
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($var 'r '(8)))
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'()))
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(define (ttf-print csp)
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(format "~a~a~a + ~a~a~a = ~a~a~a~a" ($csp-ref csp 't) ($csp-ref csp 'w) ($csp-ref csp 'o) ($csp-ref csp 't) ($csp-ref csp 'w) ($csp-ref csp 'o) ($csp-ref csp 'f) ($csp-ref csp 'o) ($csp-ref csp 'u) ($csp-ref csp 'r)))
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(check-equal? (time (solve ttf-solution ttf-print)) "734 + 734 = 1468")
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;; ABC problem:
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;; what is the minimum value of
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;; ABC
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;; -------
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;; A+B+C
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(define abc (make-csp))
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(add-vars! abc '(a b c) (range 1 10))
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(define (solution-score sol)
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(let ([a ($csp-ref sol 'a)]
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[b ($csp-ref sol 'b)]
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[c ($csp-ref sol 'c)])
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(/ (+ (* 100 a) (* 10 b) c) (+ a b c))))
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(define abc-sols (time (solve* abc)))
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(check-equal? (* 9 9 9) (length abc-sols))
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(check-equal?
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(argmin solution-score abc-sols)
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($csp (list ($var 'a '(1)) ($var 'b '(9)) ($var 'c '(9))) '()))
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;; quarter problem:
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;; 26 dollars and quarters
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;; that add up to $17.
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(define quarters (make-csp))
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(add-vars! quarters '(dollars quarters) (range 26))
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(add-constraint! quarters (λ (d q) (= 26 (+ d q))) '(dollars quarters))
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(add-constraint! quarters (λ (d q) (= 17 (+ d (* 0.25 q)))) '(dollars quarters))
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(check-equal? (time (solve quarters))
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($csp (list ($var 'dollars '(14)) ($var 'quarters '(12))) '()))
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;; nickel problem
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#|
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A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many coins of each kind are there?
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|#
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(define nickels (make-csp))
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(add-vars! nickels '(n d q) (range 33))
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(add-constraint! nickels (λ (n d q) (= 33 (+ n d q))) '(n d q) 'count-33)
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(add-constraint! nickels (λ (n d q) (= 330 (+ (* n 5) (* d 10) (* q 25)))) '(n d q) 'total-3.30)
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(add-constraint! nickels (λ (n q) (= (* 3 q) n)) '(n q) 'triple-nickel)
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(add-constraint! nickels (λ (d n) (= (* 2 d) n)) '(d n) 'double-nickel)
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(check-equal? (time (solve nickels))
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($csp (list ($var 'n '(18)) ($var 'd '(9)) ($var 'q '(6))) '()))
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;; xsum
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#|
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# Reorganize the following numbers in a way that each line of
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# 5 numbers sum to 27.
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#
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# 1 6
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# 2 7
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# 3
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# 8 4
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# 9 5
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#
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|#
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(define xsum (make-csp))
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(add-vars! xsum '(l1 l2 l3 l4 r1 r2 r3 r4 x) (range 1 10))
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(add-pairwise-constraint! xsum < '(l1 l2 l3 l4))
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(add-pairwise-constraint! xsum < '(r1 r2 r3 r4))
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(add-constraint! xsum (λ (l1 l2 l3 l4 x) (= 27 (+ l1 l2 l3 l4 x))) '(l1 l2 l3 l4 x))
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(add-constraint! xsum (λ (r1 r2 r3 r4 x) (= 27 (+ r1 r2 r3 r4 x))) '(r1 r2 r3 r4 x))
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(add-pairwise-constraint! xsum alldiff= '(l1 l2 l3 l4 r1 r2 r3 r4 x))
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(check-equal? (length (time (solve* xsum))) 8)
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;; send more money problem
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#|
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# Assign equal values to equal letters, and different values to
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# different letters, in a way that satisfies the following sum:
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#
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# SEND
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# + MORE
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# ------
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# MONEY
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|#
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(define smm (make-csp))
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(add-vars! smm '(s e n d m o r y) (λ () (reverse (range 10))))
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(add-constraint! smm positive? '(s))
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(add-constraint! smm positive? '(m))
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(add-constraint! smm (λ (d e y) (= (modulo (+ d e) 10) y)) '(d e y))
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(add-constraint! smm (λ (n d r e y)
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(= (modulo (+ (word-value n d) (word-value r e)) 100)
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(word-value e y))) '(n d r e y))
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(add-constraint! smm (λ (e n d o r y)
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(= (modulo (+ (word-value e n d) (word-value o r e)) 1000) (word-value n e y))) '(e n d o r y))
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(add-constraint! smm (λ (s e n d m o r y)
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(= (+ (word-value s e n d) (word-value m o r e))
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(word-value m o n e y))) '(s e n d m o r y))
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(add-pairwise-constraint! smm alldiff= '(s e n d m o r y))
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;; todo: too slow
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;(solve smm)
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;; queens problem
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;; place queens on chessboard so they do not intersect
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(define queens (make-csp))
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(define qs (for/list ([q 8]) (string->symbol (format "q~a" q))))
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(define rows (range (length qs)))
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(add-vars! queens qs rows)
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(define (q-col q) (string->number (string-trim (symbol->string q) "q")))
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(for* ([qs (in-combinations qs 2)])
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(match-define (list qa qb) qs)
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(match-define (list qa-col qb-col) (map q-col qs))
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(add-constraint! queens
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(λ (qa-row qb-row)
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(and
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(not (= (abs (- qa-row qb-row)) (abs (- qa-col qb-col)))) ; same diagonal?
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(not (= qa-row qb-row)))) ; same row?
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(list qa qb)))
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(check-equal? 92 (length (time (solve* queens)))) |