ummels-4clojure-solution127.clj

;; ummels's solution to Love Triangle
;; https://4clojure.com/problem/127

(fn [mine]
  (let [n (count mine)
        ln #(loop [r 1 v %] (if (< v 2) r (recur (inc r) (quot v 2))))
        m (apply max (map ln mine))
        mineral? (fn [mine [x y]]
                   (and (>= x 0)
                        (< x (count mine))
                        (>= y 0)
                        (loop [i y n (mine x)]
                          (if (zero? i) (odd? n) (recur (dec i) (quot n 2))))))
        area (fn [mine corner [x y] w]
               (let [sgn #(max (min % 1) -1)
                     lft [(sgn (+ x y)) (sgn (- y x))] ; [x y] turned ccw by 45
                     rt  [(sgn (- x y)) (sgn (+ x y))] ; [x y] turned cw by 45
                     points (for [k (range (inc w))
                                  i (range (inc k))
                                  b (if (and (some zero? [x y]) (< k w)) [0 1] [0])]
                              (map + corner
                                     (map * [i i] lft)
                                     (map * [(- k i) (- k i)] rt)
                                     (map * [b b] [x y])))]
                 (if (every? #(mineral? mine %) points) (count points) 0)))
        res (apply max (for [x (range n)
                             y (range m)
                             d [[-1 -1] [-1 0] [-1 1] [0 -1] [0 1] [1 -1] [1 0] [1 1]]
                              w (range (* 2 n))]
                         (area mine [x y] d w)))]
    (if (> res 2) res nil)))