Capgemini Stavanger code dojo 2012-02-7: Integer to roman numeral in Clojure

roman.clj

(ns roman)

(declare test-integer-to-roman)

(def roman-numerals
  ["I" 1,
   "IV" 4,
   "V" 5,
   "IX" 9,
   "X" 10,
   "XL" 40
   "L" 50,
   "XC" 90,
   "C" 100,
   "CD" 400,
   "D" 500,
   "CM" 900
   "M" 1000])

(def roman-numerals-index
  ;Vector of [r d nidx] where r is a roman numeral, d is the decimal value of r and
  ;nidx is the index of the largest numeral that is smaller than r.
  (let [even-count (/ (count roman-numerals) 2)]
    (vec
      (for [[even-idx nidx] (take even-count (map vector (iterate #(+ 2 %1) 0) (iterate inc -1)))]
        [(roman-numerals even-idx) (roman-numerals (inc even-idx)) nidx]))))

(defn- next-roman [[r d nidx]]
  (if (< nidx 0)
    nil
    (roman-numerals-index nidx)))

(defn- roman [n [r d nidx :as indexed-roman] ^StringBuilder acc]
  "n decimal number to convert,
   [r d nidx] entry from roman-numerals-index,
   acc accumulated value of the conversion."
  (let [rcount (int (/ n d)) ; The number of times the roman literal r occurs in n
        unconverted (- n (* rcount d))] ; Remaining unconverted part of n
    (dotimes [_ rcount] (.append acc r))
    (if (= unconverted 0)
      acc
      (recur unconverted (next-roman indexed-roman) acc))))

(defn
  #^{:test #'test-integer-to-roman}
  integer-to-roman [n]
  {:pre [(> n 0) (< n 4000)]}
  "Convert the integer n to roman numerals."
    (str (roman n (last roman-numerals-index) (StringBuilder.))))


(defn- test-integer-to-roman []
  ;; The symbols
  (assert (= "I" (integer-to-roman 1)))
  (assert (= "IV" (integer-to-roman 4)))
  (assert (= "V" (integer-to-roman 5)))
  (assert (= "IX" (integer-to-roman 9)))
  (assert (= "X" (integer-to-roman 10)))
  (assert (= "XL" (integer-to-roman 40)))
  (assert (= "L" (integer-to-roman 50)))
  (assert (= "XC" (integer-to-roman 90)))
  (assert (= "C" (integer-to-roman 100)))
  (assert (= "CD" (integer-to-roman 400)))
  (assert (= "D" (integer-to-roman 500)))
  (assert (= "CM" (integer-to-roman 900)))
  (assert (= "M" (integer-to-roman 1000)))
  ;; Multiple occurances
  (assert (= "II" (integer-to-roman 2)))
  (assert (= "III" (integer-to-roman 3)))
  ;; Other rules
  (assert (= "XXX" (integer-to-roman 30)))
  (assert (= "XIX" (integer-to-roman 19)))
  (assert (= "XLIX" (integer-to-roman 49)))
  (assert (= "XCIX" (integer-to-roman 99)))
  (assert (= "XCV" (integer-to-roman 95)))
  (assert (= "CMXCIX" (integer-to-roman 999)))
  (assert (= "MCDL" (integer-to-roman 1450)))
  (assert (= "MDCCXVII" (integer-to-roman 1717)))
  (assert (= "MCMXCIX" (integer-to-roman 1999)))
  (assert (= "MMMCMXCIX" (integer-to-roman 3999))))