90 lines
2.8 KiB
Scheme
90 lines
2.8 KiB
Scheme
; -*- scheme -*-
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; dictionaries ----------------------------------------------------------------
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(define (dict-new) ())
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(define (dict-extend dl key value)
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(cond ((null? dl) (list (cons key value)))
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((equal? key (caar dl)) (cons (cons key value) (cdr dl)))
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(else (cons (car dl) (dict-extend (cdr dl) key value)))))
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(define (dict-lookup dl key)
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(cond ((null? dl) ())
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((equal? key (caar dl)) (cdar dl))
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(else (dict-lookup (cdr dl) key))))
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(define (dict-keys dl) (map car dl))
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; graphs ----------------------------------------------------------------------
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(define (graph-empty) (dict-new))
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(define (graph-connect g n1 n2)
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(dict-extend
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(dict-extend g n2 (cons n1 (dict-lookup g n2)))
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n1
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(cons n2 (dict-lookup g n1))))
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(define (graph-adjacent? g n1 n2) (member n2 (dict-lookup g n1)))
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(define (graph-neighbors g n) (dict-lookup g n))
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(define (graph-nodes g) (dict-keys g))
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(define (graph-add-node g n1) (dict-extend g n1 ()))
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(define (graph-from-edges edge-list)
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(if (null? edge-list)
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(graph-empty)
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(graph-connect (graph-from-edges (cdr edge-list))
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(caar edge-list)
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(cdar edge-list))))
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; graph coloring --------------------------------------------------------------
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(define (node-colorable? g coloring node-to-color color-of-node)
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(not (member
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color-of-node
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(map
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(lambda (n)
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(let ((color-pair (assq n coloring)))
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(if (pair? color-pair) (cdr color-pair) ())))
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(graph-neighbors g node-to-color)))))
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(define (try-each f lst)
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(if (null? lst) #f
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(let ((ret (f (car lst))))
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(if ret ret (try-each f (cdr lst))))))
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(define (color-node g coloring colors uncolored-nodes color)
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(cond
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((null? uncolored-nodes) coloring)
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((node-colorable? g coloring (car uncolored-nodes) color)
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(let ((new-coloring
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(cons (cons (car uncolored-nodes) color) coloring)))
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(try-each (lambda (c)
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(color-node g new-coloring colors (cdr uncolored-nodes) c))
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colors)))))
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(define (color-graph g colors)
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(if (null? colors)
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(and (null? (graph-nodes g)) ())
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(color-node g () colors (graph-nodes g) (car colors))))
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(define (color-pairs pairs colors)
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(color-graph (graph-from-edges pairs) colors))
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; queens ----------------------------------------------------------------------
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(define (can-attack x y)
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(let ((x1 (mod x 5))
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(y1 (truncate (/ x 5)))
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(x2 (mod y 5))
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(y2 (truncate (/ y 5))))
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(or (= x1 x2) (= y1 y2) (= (abs (- y2 y1)) (abs (- x2 x1))))))
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(define (generate-5x5-pairs)
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(let ((result ()))
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(dotimes (x 25)
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(dotimes (y 25)
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(if (and (/= x y) (can-attack x y))
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(set! result (cons (cons x y) result)) ())))
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result))
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