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148 lines
5.7 KiB
Racket
148 lines
5.7 KiB
Racket
#lang racket
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(require "main.rkt")
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(require rackunit)
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(define-simple-check (check-hash-items h1 h2)
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(for/and ([(k1 v1) (in-hash h1)])
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(equal? (hash-ref h2 k1) v1)))
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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-problem (new Problem))
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(send abc-problem addVariables '("a" "b" "c") (range 1 10))
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(define (test-solution s) (let ([a (hash-ref s "a")]
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[b (hash-ref s "b")]
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[c (hash-ref s "c")])
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(/ (+ (* 100 a) (* 10 b) c) (+ a b c))))
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(check-hash-items (argmin test-solution (send abc-problem getSolutions))
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#hash(("c" . 9) ("b" . 9) ("a" . 1)))
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;; quarter problem:
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;; 26 coins, dollars and quarters
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;; that add up to $17.
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(define quarter-problem (new Problem))
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(send quarter-problem addVariables '("dollars" "quarters") (range 1 27))
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(send quarter-problem addConstraint (λ(d q) (= 17 (+ d (* 0.25 q)))) '("dollars" "quarters"))
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(send quarter-problem addConstraint (λ(d q) (= 26 (+ d q))) '("dollars" "quarters"))
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(check-hash-items (send quarter-problem getSolution) '#hash(("dollars" . 14) ("quarters" . 12)))
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;; coin problem 2
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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 nickel-problem (new Problem))
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(send nickel-problem addVariables '(nickels dimes quarters) (range 1 34))
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(send nickel-problem addConstraint (λ(n d q) (= 33 (+ n d q))) '(nickels dimes quarters))
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(send nickel-problem addConstraint (λ(n d q) (= 3.30 (+ (* 0.05 n) (* 0.1 d) (* 0.25 q)))) '(nickels dimes quarters))
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(send nickel-problem addConstraint (λ(n q) (= n (* 3 q))) '(nickels quarters))
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(send nickel-problem addConstraint (λ(d n) (= n (* 2 d))) '(dimes nickels))
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(check-hash-items (send nickel-problem getSolution) #hash((nickels . 18) (quarters . 6) (dimes . 9)))
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;; word math
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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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# TWO
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# + TWO
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# -----
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# FOUR
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|#
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(define two-four-problem (new Problem))
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(send two-four-problem addVariables '(t w o f u r) (range 10))
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(send two-four-problem addConstraint (new AllDifferentConstraint))
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(send two-four-problem addConstraint (λ(t w o) (> (word-value t w o) 99)) '(t w o))
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(send two-four-problem addConstraint (λ(f o u r) (> (word-value f o u r) 999)) '(f o u r))
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(send two-four-problem addConstraint
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(λ (t w o f u r)
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(let ([two (word-value t w o)]
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[four (word-value f o u r)])
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((two . + . two) . = . four))) '(t w o f u r))
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(check-equal? (length (send two-four-problem getSolutions)) 7)
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(send two-four-problem addConstraint (λ(r) (= r 0)) '(r))
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(check-hash-items (send two-four-problem getSolution) #hash((o . 5) (w . 6) (u . 3) (f . 1) (r . 0) (t . 7)))
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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-problem (new Problem))
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(send xsum-problem addVariables '(l1 l2 l3 l4 r1 r2 r3 r4 x) (range 10))
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(send xsum-problem addConstraint (λ (l1 l2 l3 l4 x)
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(and (< l1 l2 l3 l4)
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(= 27 (+ l1 l2 l3 l4 x)))) '(l1 l2 l3 l4 x))
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(send xsum-problem addConstraint (λ (r1 r2 r3 r4 x)
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(and (< r1 r2 r3 r4)
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(= 27 (+ r1 r2 r3 r4 x)))) '(r1 r2 r3 r4 x))
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(send xsum-problem addConstraint (new AllDifferentConstraint))
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(check-equal? (length (send xsum-problem getSolutions)) 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 sm-problem (new Problem))
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(send sm-problem addVariables '(s e n d m o r y) (range 10))
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(send sm-problem addConstraint (λ(x) (> x 0)) '(s))
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(send sm-problem addConstraint (λ(x) (> x 0)) '(m))
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(send sm-problem addConstraint (λ(d e y) (= (modulo (+ d e) 10) y)) '(d e y))
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(send sm-problem addConstraint (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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(send sm-problem addConstraint (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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(send sm-problem addConstraint (λ(s e n d m o r y) (=
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(+ (word-value s e n d)
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(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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(send sm-problem addConstraint (new AllDifferentConstraint))
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(check-hash-items (send sm-problem getSolution) '#hash((m . 1) (e . 5) (r . 8) (n . 6) (y . 2) (o . 0) (d . 7) (s . 9)))
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;; queens problem
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;; place queens on chessboard so they do not intersect
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(define qp (new Problem))
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(define cols (range 8))
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(define rows (range 8))
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(send qp addVariables cols rows)
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(for* ([col1 (in-list cols)] [col2 (in-list cols)] #:when (< col1 col2))
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(send qp addConstraint (λ(row1 row2 [col1 col1][col2 col2])
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(and
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;; test if two cells are on a diagonal
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(not (= (abs (- row1 row2)) (abs (- col1 col2))))
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;; test if two cells are in same row
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(not (= row1 row2)))) (list col1 col2)))
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(check-equal? (length (send qp getSolutions)) 92) |