; dictionaries ----------------------------------------------------------------(def (dict-new) NIL) (def (dict-extend dl key value) (cond ((not 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))))) (def (dict-lookup dl key) (cond ((not dl) NIL) ((equal? key (caar dl)) (cdar dl)) (else (dict-lookup (cdr dl) key)))) (def (dict-keys dl) (map car dl)) ; graphs ----------------------------------------------------------------------(def (graph-empty) (dict-new)) (def (graph-connect g n1 n2) (dict-extend (dict-extend g n2 (cons n1 (dict-lookup g n2))) n1 (cons n2 (dict-lookup g n1)))) (def (graph-adjacent? g n1 n2) (member n2 (dict-lookup g n1))) (def (graph-neighbors g n) (dict-lookup g n)) (def (graph-nodes g) (dict-keys g)) (def (graph-add-node g n1) (dict-extend g n1 NIL)) (def (graph-from-edges edge-list) (if (not edge-list) (graph-empty) (graph-connect (graph-from-edges (cdr edge-list)) (caar edge-list) (cdar edge-list)))) ; graph coloring --------------------------------------------------------------(def (node-colorable? g coloring node-to-color color-of-node) (not (member color-of-node (map (λ (n) (let ((color-pair (assq n coloring))) (and (cons? color-pair) (cdr color-pair)))) (graph-neighbors g node-to-color))))) (def (try-each f lst) (if (not lst) NIL (let ((ret (f (car lst)))) (if ret ret (try-each f (cdr lst)))))) (def (color-node g coloring colors uncolored-nodes color) (cond ((not uncolored-nodes) coloring) ((node-colorable? g coloring (car uncolored-nodes) color) (let ((new-coloring (cons (cons (car uncolored-nodes) color) coloring))) (try-each (λ (c) (color-node g new-coloring colors (cdr uncolored-nodes) c)) colors))))) (def (color-graph g colors) (if (not colors) (and (not (graph-nodes g)) NIL) (color-node g NIL colors (graph-nodes g) (car colors)))) (def (color-pairs pairs colors) (color-graph (graph-from-edges pairs) colors)) ; queens ----------------------------------------------------------------------(def (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)))))) (def (generate-5x5-pairs) (let ((result NIL)) (dotimes (x 25) (dotimes (y 25) (when (and (not (= x y)) (can-attack x y)) (set! result (cons (cons x y) result))))) result))
; dictionaries ----------------------------------------------------------------
(def (dict-new) NIL)
(def (dict-extend dl key value)
(cond ((not 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)))))
(def (dict-lookup dl key)
(cond ((not dl) NIL)
((equal? key (caar dl)) (cdar dl))
(else (dict-lookup (cdr dl) key))))
(def (dict-keys dl) (map car dl))
; graphs ----------------------------------------------------------------------
(def (graph-empty) (dict-new))
(def (graph-connect g n1 n2)
(dict-extend
(dict-extend g n2 (cons n1 (dict-lookup g n2)))
n1
(cons n2 (dict-lookup g n1))))
(def (graph-adjacent? g n1 n2) (member n2 (dict-lookup g n1)))
(def (graph-neighbors g n) (dict-lookup g n))
(def (graph-nodes g) (dict-keys g))
(def (graph-add-node g n1) (dict-extend g n1 NIL))
(def (graph-from-edges edge-list)
(if (not edge-list)
(graph-empty)
(graph-connect (graph-from-edges (cdr edge-list))
(caar edge-list)
(cdar edge-list))))
; graph coloring --------------------------------------------------------------
(def (node-colorable? g coloring node-to-color color-of-node)
(not (member
color-of-node
(map
(λ (n)
(let ((color-pair (assq n coloring)))
(and (cons? color-pair) (cdr color-pair))))
(graph-neighbors g node-to-color)))))
(def (try-each f lst)
(if (not lst) NIL
(let ((ret (f (car lst))))
(if ret ret (try-each f (cdr lst))))))
(def (color-node g coloring colors uncolored-nodes color)
(cond
((not uncolored-nodes) coloring)
((node-colorable? g coloring (car uncolored-nodes) color)
(let ((new-coloring
(cons (cons (car uncolored-nodes) color) coloring)))
(try-each (λ (c)
(color-node g new-coloring colors (cdr uncolored-nodes) c))
colors)))))
(def (color-graph g colors)
(if (not colors)
(and (not (graph-nodes g)) NIL)
(color-node g NIL colors (graph-nodes g) (car colors))))
(def (color-pairs pairs colors)
(color-graph (graph-from-edges pairs) colors))
; queens ----------------------------------------------------------------------
(def (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))))))
(def (generate-5x5-pairs)
(let ((result NIL))
(dotimes (x 25)
(dotimes (y 25)
(when (and (not (= x y)) (can-attack x y))
(set! result (cons (cons x y) result)))))
result))