optimizations: use vectors instead of move-procs, avoid mapping symbols, tighten loops, use bytes, keep only min+max solutions etc
svn: r11624
This commit is contained in:
Eli Barzilay
parent
9c928f7e82
commit
bb470554a5
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@ -4,105 +4,95 @@
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;; Based on a Python version:
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;; contributed by Olof Kraigher
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;; modified by Tupteq
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;; contributed by Matthew Flatt
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;; optimized by Eli Barzilay
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#lang scheme/base
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(require scheme/cmdline)
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(require scheme/cmdline scheme/list)
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(define width 5)
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(define height 10)
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(define size (* width height))
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(define (rotate dir)
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(case dir
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[(E) 'NE]
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[(NE) 'NW]
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[(NW) 'W]
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[(W) 'SW]
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[(SW) 'SE]
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[(SE) 'E]))
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(define (flip dir)
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(case dir
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[(E) 'W]
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[(NE) 'NW]
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[(NW) 'NE]
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[(W) 'E]
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[(SW) 'SE]
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[(SE) 'SW]))
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(define move
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(make-immutable-hash
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(list
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(cons 'E (lambda (x y) (values (add1 x) y)))
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(cons 'W (lambda (x y) (values (sub1 x) y)))
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(cons 'NE (lambda (x y) (values (+ x (bitwise-and y 1)) (sub1 y))))
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(cons 'NW (lambda (x y) (values (sub1 (+ x (bitwise-and y 1))) (sub1 y))))
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(cons 'SE (lambda (x y) (values (+ x (bitwise-and y 1)) (add1 y))))
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(cons 'SW (lambda (x y) (values (sub1 (+ x (bitwise-and y 1))) (add1 y)))))))
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(define move-procs
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(hash-map move (lambda (k v) v)))
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(define (valid? x y)
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(define (valid-xy? x y)
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(and (0 . <= . x)
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(x . < . width)
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(0 . <= . y)
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(y . < . height)))
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(define (mover fun)
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(let ([t (make-vector size)])
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(for ([p (in-range size)])
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(vector-set! t p (let*-values ([(y x) (quotient/remainder p width)]
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[(x y) (fun x y)])
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(if (valid-xy? x y) (+ x (* y width)) -1))))
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t))
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(define E
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(mover (lambda (x y) (values (add1 x) y))))
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(define W
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(mover (lambda (x y) (values (sub1 x) y))))
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(define NE
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(mover (lambda (x y) (values (+ x (bitwise-and y 1)) (sub1 y)))))
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(define NW
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(mover (lambda (x y) (values (sub1 (+ x (bitwise-and y 1))) (sub1 y)))))
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(define SE
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(mover (lambda (x y) (values (+ x (bitwise-and y 1)) (add1 y)))))
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(define SW
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(mover (lambda (x y) (values (sub1 (+ x (bitwise-and y 1))) (add1 y)))))
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(define rotate-list (list E NE NW W SW SE E))
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(define (rotate dir)
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(cadr (memq dir rotate-list)))
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(define flip-alist (list (cons E W) (cons NE NW) (cons NW NE)
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(cons W E) (cons SW SE) (cons SE SW)))
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(define (flip dir) (cdr (assq dir flip-alist)))
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(define movers (list E W NE NW SE SW))
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(define (valid? p)
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(p . >= . 0))
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(define (clear? board pos)
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(not (bitwise-bit-set? board pos)))
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(define (set board pos)
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(bitwise-ior board (arithmetic-shift 1 pos)))
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(define (zero-count board)
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(for/fold ([count 0])
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([i (in-range (* width height))])
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(if (clear? board i)
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(add1 count)
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count)))
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(for/fold ([count 0]) ([i (in-range size)])
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(if (clear? board i) (add1 count) count)))
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(define (find-free-cell board)
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(let yloop ([y 0])
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(let xloop ([x 0])
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(if (= x width)
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(yloop (add1 y))
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(if (clear? board (+ x (* width y)))
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(values x y)
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(xloop (add1 x)))))))
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(for/or ([p (in-range 0 size)])
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(and (clear? board p) p)))
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(define (flood-fill board x y)
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(if (valid? x y)
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(let ([pos (+ x (* y width))])
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(if (clear? board pos)
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(for/fold ([board (set board pos)])
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([move-proc move-procs])
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(let-values ([(x y) (move-proc x y)])
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(flood-fill board x y)))
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board))
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board))
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(define (flood-fill board p)
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(for/fold ([board (set board p)]) ([mover (in-list movers)])
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(let ([p (vector-ref mover p)])
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(if (and (valid? p) (clear? board p))
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(flood-fill board p)
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board))))
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(define (no-islands? mask)
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(let ([zeros (zero-count mask)])
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(if (zeros . < . 5)
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#f
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(let loop ([mask mask][zeros zeros])
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(and (zeros . >= . 5)
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(let loop ([mask mask] [zeros zeros])
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(if (= mask #x3FFFFFFFFFFFF)
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#t
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(let*-values ([(x y) (find-free-cell mask)]
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[(mask) (flood-fill mask x y)]
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[(new-zeros) (zero-count mask)])
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(if ((- zeros new-zeros) . < . 5)
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#f
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(let* ([p (find-free-cell mask)]
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[mask (flood-fill mask p)]
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[new-zeros (zero-count mask)])
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(and ((- zeros new-zeros) . >= . 5)
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(loop mask new-zeros))))))))
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(define (get-bitmask x y piece)
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(let ([mask (arithmetic-shift 1 (+ x (* y width)))])
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(let loop ([x x][y y][cells piece][mask mask])
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(define (get-bitmask p piece)
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(let ([mask (arithmetic-shift 1 p)])
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(let loop ([p p] [cells piece] [mask mask])
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(if (null? cells)
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mask
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(let-values ([(x y) ((hash-ref move (car cells)) x y)])
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(if (valid? x y)
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(loop x y (cdr cells) (set mask (+ x (* width y))))
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#f))))))
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(let ([p (vector-ref (car cells) p)])
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(and (valid? p) (loop p (cdr cells) (set mask p))))))))
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(define (all-bitmasks piece color)
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(let ([pieces
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@ -111,43 +101,39 @@
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([orientations (in-range 2)])
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(let-values ([(accum piece)
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(for/fold ([accum accum] [piece piece])
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([orientations (in-range (- 6 (* 3 (if (= color 4)
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1
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0))))])
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([orientations (in-range (- 6 (* 3 (if (= color 4) 1 0))))])
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(values (cons piece accum)
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(map rotate piece)))])
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(values accum (map flip piece))))])
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accum)])
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(for*/list ([piece (in-list pieces)]
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[y (in-range height)]
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[x (in-range width)]
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[mask (:do-in ([(mask) (get-bitmask x y piece)]) ; should be in-value
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#t () #t () #t #f ())]
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#:when (and mask (no-islands? mask)))
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mask)))
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(reverse
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(for*/fold ([accum null])
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([piece (in-list pieces)]
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[p (in-range 0 size)])
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(let ([mask (get-bitmask p piece)])
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(if (and mask (no-islands? mask)) (cons mask accum) accum))))))
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(define generate-bitmasks-pieces
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(list (list E E E SE)
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(list SE SW W SW)
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(list W W SW SE)
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(list E E SW SE)
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(list NW W NW SE SW)
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(list E E NE W)
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(list NW NE NE W)
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(list NE SE E NE)
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(list SE SE E SE)
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(list E NW NW NW)))
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(define (generate-bitmasks)
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(let ([pieces '((E E E SE)
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(SE SW W SW)
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(W W SW SE)
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(E E SW SE)
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(NW W NW SE SW)
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(E E NE W)
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(NW NE NE W)
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(NE SE E NE)
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(SE SE E SE)
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(E NW NW NW))]
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[masks-at-cell
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(let ([masks-at-cell
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(list->vector
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(for/list ([i (in-range (* width height))])
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(list->vector
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(for/list ([j (in-range 10)])
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null))))])
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(for ([piece (in-list pieces)]
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(for/list ([i (in-range size)])
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(list->vector (for/list ([j (in-range 10)]) null))))])
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(for ([piece (in-list generate-bitmasks-pieces)]
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[color (in-naturals)])
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(let loop ([masks (sort (all-bitmasks piece color) >)]
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[cell-bit (sub1 (* width height))]
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[cell-counter (sub1 (* width height))])
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[cell-bit (sub1 size)]
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[cell-counter (sub1 size)])
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(if (null? masks)
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masks-at-cell
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(if (bitwise-bit-set? (car masks) cell-bit)
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@ -165,14 +151,12 @@
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(define masks (make-vector 10 0))
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(define to-go 0)
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(define solutions null)
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(define solutions (mcons #f #f)) ; keeps (min max) solutions
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(define (solve-cell! cell board)
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(when (and (positive? to-go)
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(not (negative? cell)))
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(when (and (positive? to-go) (not (negative? cell)))
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;; Need solutions and not off board
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(cond
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[(= board #x3FFFFFFFFFFFF)
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(cond [(= board #x3FFFFFFFFFFFF)
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;; Solved
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(add-solutions!)]
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[(not (clear? board cell))
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@ -180,56 +164,57 @@
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(solve-cell! (sub1 cell) board)]
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[else
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;; Recur
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(for ([color (in-range 10)])
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(when (zero? (vector-ref masks color))
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(for ([mask (in-list (vector-ref
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(vector-ref masks-at-cell cell)
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color))])
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(when (zero? (bitwise-and mask board))
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(for* ([color (in-range 10)]
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#:when (zero? (vector-ref masks color))
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[mask (in-list (vector-ref (vector-ref masks-at-cell cell)
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color))]
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#:when (zero? (bitwise-and mask board)))
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(vector-set! masks color mask)
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(solve-cell! (sub1 cell) (bitwise-ior board mask))
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(vector-set! masks color 0)))))])))
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(vector-set! masks color 0))])))
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(define (add-solutions!)
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(let ([digits
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(for/list ([pos (in-range (* width height))])
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(define (add! solution)
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(cond [(not (mcar solutions))
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(set-mcar! solutions solution)
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(set-mcdr! solutions solution)]
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[(bytes<? solution (mcar solutions))
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(set-mcar! solutions solution)]
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[(bytes>? solution (mcdr solutions))
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(set-mcdr! solutions solution)]))
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(let* ([s (list->bytes
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(for/list ([pos (in-range size)])
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(for/or ([color (in-range 10)])
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(and (not (clear? (vector-ref masks color) pos))
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color)))])
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(let ([s (list->string
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(map (lambda (digit)
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(if digit
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(integer->char (+ digit (char->integer #\0)))
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#\.))
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digits))]
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[ns (make-string (* width height))])
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(+ color (char->integer #\0))))))]
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[ns (make-bytes size)])
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;; Inverse
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(for* ([y (in-range height)]
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[x (in-range width)])
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(string-set! ns (+ x (* y width))
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(string-ref s (+ (- width (+ x 1))
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(bytes-set! ns (+ x (* y width))
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(bytes-ref s (+ (- width (+ x 1))
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(* width (- height (+ y 1)))))))
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;; Append
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(set! solutions (cons s solutions))
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(set! solutions (cons ns solutions))
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(set! to-go (- to-go 2)))))
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;; Keep first and last only
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(add! s)
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(add! ns)
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(set! to-go (- to-go 2))))
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(define (print-solution solution)
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(let ([solution (bytes->string/utf-8 solution)])
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(for ([y (in-range height)])
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(when (odd? y) (display " "))
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(for ([x (in-range width)])
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(display (string-ref solution (+ x (* y width))))
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(display " "))
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(display "\n")
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(when (even? y)
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(display " ")))
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(newline))
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(printf "~a " (string-ref solution (+ x (* y width)))))
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(printf "\n"))
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(newline)))
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(define (solve! n)
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(set! to-go n)
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(solve-cell! (sub1 (* width height)) 0))
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(solve-cell! (sub1 size) 0))
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(command-line #:args (n) (solve! (string->number n)))
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(let ([solutions (sort solutions string<?)])
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(printf "~a solutions found\n\n" (length solutions))
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(print-solution (car solutions))
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(print-solution (list-ref solutions (sub1 (length solutions)))))
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(command-line #:args (n)
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(let ([n (string->number n)])
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(solve! n)
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(printf "~a solutions found\n\n" (- n to-go))
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(print-solution (mcar solutions))
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(print-solution (mcdr solutions))))
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