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