Roman Numerals

roman.clj

(ns miner.roman
  (:require [clojure.test :refer :all]))

;; inspired by 
;; http://www.jayway.com/2012/08/04/a-decimal-to-roman-numeral-converter-in-just-a-few-lines/

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

(def roman-bases (sort > (keys roman-map)))

(defn roman-addends [n]
  {:pre [(< 0 n 4000)]}
  (loop [n n bases roman-bases addends []]
    (if (zero? n)
      addends
      (let [base (first bases)]
        (if (>= n base)
          (recur (- n base) bases (conj addends base))
          (recur n (rest bases) addends))))))

(defn roman [n]
  (apply str (map roman-map (roman-addends n))))


;; clojure.pprint/cl-format works but is slow
(defn roman-cl [n]
  (clojure.pprint/cl-format nil "~@R" n))


(deftest roman-4k
  (doseq [n (range 1 4000)]
    (is (= (roman-cl n) (roman n)))))


(def inv-roman-char-map
  {\M 1000 \D 500 \C 100 \L 50 \X 10 \V 5 \I 1})

(defn roman-values-seq [rn]
  (let [vs (rseq (conj (mapv inv-roman-char-map rn) 0))]
    ;; going in reverse order is easier,
    ;; padded zero to simplify prev
    (map (fn [v prev] (if (>= v prev) v (- v))) (rest vs) vs)))

(defn parse-roman [rn]
  (reduce + (roman-values-seq rn)))
    
(deftest parse-roman-test
  (doseq [n (range 1 4000)]
    (is (= n (parse-roman (roman n))))))

here's a faster version:
https://gist.github.com/miner/9ff494e7cd0c9af64d03