2019-12-10 08:16:52 +00:00
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#lang racket
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(require "../lib.rkt")
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(define input
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(problem-input 10))
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(define width (string-length (car input)))
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(define height (length input))
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2019-12-10 21:18:04 +00:00
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(define (out-of-range? x y)
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(or (< x 0)
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(< y 0)
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(>= x width)
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(>= y height)))
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(define (coprime? i j)
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(= 1 (gcd i j)))
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2019-12-10 08:16:52 +00:00
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(define (offsets x y)
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2019-12-10 21:18:04 +00:00
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(let ([is (range (negate x) (- width x))]
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[js (range (negate y) (- height y))])
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(filter (uncurry coprime?) (cartesian-product is js))))
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(define (asteroid? x y)
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(define row (list-ref input y))
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(eq? #\# (string-ref row x)))
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(define (asteroid-offset x y i j)
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(let loop ([m 1])
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(let ([x* (+ x (* i m))]
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[y* (+ y (* j m))])
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(cond
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[(out-of-range? x* y*) #f]
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[(asteroid? x* y*) (list x* y*)]
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[else (loop (add1 m))]))))
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(define (asteroids x y)
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(filter-map (uncurry (curry asteroid-offset x y)) (offsets x y)))
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(define-values (part1 location in-view)
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2019-12-10 08:16:52 +00:00
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(let* ([cols (range width)]
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[rows (range height)]
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2019-12-10 21:18:04 +00:00
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[locations (filter (uncurry asteroid?) (cartesian-product cols rows))]
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[in-views (map (uncurry asteroids) locations)]
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[counts (map length in-views)]
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[maximum (apply max counts)]
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[index (index-of counts maximum)])
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(values maximum
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(list-ref locations index)
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(list-ref in-views index))))
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(define (offset<? xy1 xy2)
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(let ([x1 (first xy1)]
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[y1 (second xy1)]
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[x2 (first xy2)]
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[y2 (second xy2)])
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(or ; (0, -) < (+, y) < (0, +) < (-, y)
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(and (zero? x1) (negative? y1))
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(and (positive? x1)
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(or (negative? x2)
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(and (zero? x2) (positive? y2))))
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(and (zero? x1) (negative? x2))
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(and (nzero? x1) (nzero? x2)
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(< (atan (/ y1 x1)) (atan (/ y2 x2)))))))
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(define part2
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(let* ([offsets (map (λ (ast) (zip - ast location)) in-view)]
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[offsets (sort offsets offset<?)]
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[200th (zip + location (list-ref offsets (sub1 200)))])
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(+ (* (first 200th) 100) (second 200th))))
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(show-solution part1 part2)
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