p138.clj

; Project euler problem 138
; http://projecteuler.net/index.php?section=problems&id=138
(use 'clojure.contrib.math)

(defn height [base leg]
  (sqrt (- (expt leg 2) (expt (/ base 2) 2))))

(defn base [leg height]
  (* 2 (sqrt (- (expt leg 2) (expt height 2)))))

(defn valid? [triangle]
  (let [l (triangle :leg) b (triangle :base) h (triangle :height)]
  (and
    (= (int l) l)
    (or
      (= h (dec b))
      (= h (inc b))))))

(defn leg [base height]
  (sqrt (+ (expt (/ base 2) 2) (expt height 2))))

(defn whole-factors [x]
  (map
    (fn [n] [n (/ x n)])
    (filter #(zero? (rem x %)) (range 1 (inc x)))))

(defn make-triangle [b-h]
  (let [base (first b-h)
        height (last b-h)]
    {:base base :height height :leg (leg base height)}))

(defn make-triangles [size]
  (filter valid?  (map make-triangle (whole-factors (* 2 size)))))

(defn sum-legs [triangles]
  (reduce + (map :leg triangles)))

(println (sum-legs (take 12 (reduce (fn [xs y] (into xs (make-triangles y))) [] (iterate inc 1)))))