Problem 91

src/euler/p091/data.cljc

@@ -0,0 +1,4 @@
+(ns euler.p091.data)
+
+(def answer "e8dc153260a59d4f236cfd7439d5dfd3")
+

src/euler/p091/dfuenzalida.cljc

@@ -0,0 +1,54 @@
+(ns euler.p091.dfuenzalida
+  (:refer-clojure :exclude [read-string format])
+  (:require
+   [euler.utils :as u :refer [deftest md5 primes]]
+   [euler.p091.data :refer [answer]]
+   [clojure.test :as t :refer [is]]))
+
+(defn slope [xa ya xb yb]
+  [(- yb ya) (- xb xa)]) ;; not division, numerator over denominator
+
+(defn right-angle? [x1 y1 x2 y2 x3 y3] ;; (x2, y2) is the vertex of the angle
+  (cond
+    (and (= x1 x2) (= y2 y3)) true
+    (and (= y1 y2) (= x2 x3)) true
+    (or  (= x1 x2) (= x2 x3)) false
+    :else (let [[s1a s1b] (slope x1 y1 x2 y2)
+                [s2a s2b] (slope x2 y2 x3 y3)]
+            (= (* -1 s1a s2a) (* s1b s2b)))))
+
+(defn right-triangle? [[x1 y1] [x2 y2] [x3 y3]]
+  (->> (cycle [x1 y1 x2 y2 x3 y3])
+       (partition 6 2)
+       (take 3)
+       (map (partial apply right-angle?))
+       (some true?)))
+
+(defn div2 [n] (quot n 2))
+
+(defn solve [n]
+  (->> (for [x1 (range 0 (inc n))
+             y1 (range 0 (inc n))
+             x2 (range 0 (inc n))
+             y2 (range 0 (inc n))]
+         (set [[0 0] [x1 y1] [x2 y2]]))
+       (filter #(= 3 (count %))) ;; 3 different points
+       ;; set ;; A triangle as a set of 3 points on any order: triangle BCA == triangle ABC
+       (filter #(apply right-triangle? %))
+       count
+       div2))
+
+(deftest tests
+  (is (= 14 (solve 2)))
+  (is (right-triangle? [0 0] [1 1] [0 2]))
+  (is (= (str answer)
+         (md5 (str (solve 50))))))
+
+;;;; Scratch
+
+(comment
+  ; (time (solve 50))
+  ; "Elapsed time: 41760.5671 msecs"
+  (t/run-tests)
+  )
+