Clojure Kata #3 – Roman Numerals

April 29th, 2014

I’m still in the process of trying to wrap my head around Clojure. I’ve been practicing several different katas like Fizz Buzz and the Bowling Game. Another one I’ve been doing a lot lately is the Roman Numerals kata. This exercise combines both my fascination for Ancient Rome and learning a programming language.

Here is the code of my latest stab at this problem:

(ns roman_numbers.core
    (:require [clojure.math.numeric-tower :as math])
    (:require [clojure.string :as str]))

(def symbols (sorted-map-by > 1000 "M" 500 "D" 100 "C" 50 "L" 10 "X" 5 "V", 1 "I"))

(defn orderOfMagnitude [number]
    (math/expt 10 (count (str number))))

(defn determineApplicableSymbols [number]
    (let [magnitude (orderOfMagnitude number)]
        (if(<= magnitude 1000)
            (take 3 (filter (fn[x] (>= magnitude (first x))) symbols))
            { -1 "-" -2 "-" 1000 "M" } )

(defn selectSymbol [number unitSymbol fiveSymbol tenSymbol]
    (let [unitSymbolValue (key unitSymbol)
          unitNumber (quot number unitSymbolValue)
          total (* unitNumber unitSymbolValue)]

            (< unitNumber 4)
                (first { total (apply str (repeat unitNumber (val unitSymbol))) })

            (< unitNumber 9)
                (first { total 
                            (repeat (- 5 unitNumber) (val unitSymbol))
                            (val fiveSymbol)
                            (repeat (- unitNumber 5) (val unitSymbol)))

            (= unitNumber 9)
                (first { total (apply str (val unitSymbol) (val tenSymbol)) })

(defn convert [number]
    (loop [currentNumber number
           result ""]
        (if (zero? currentNumber)
            (let [applicableSymbols (determineApplicableSymbols currentNumber)
                  unitSymbol (last applicableSymbols)
                  fiveSymbol (second applicableSymbols)
                  tenSymbol (first applicableSymbols)
                  matchingSymbol (selectSymbol currentNumber unitSymbol 
                                    fiveSymbol tenSymbol)]
                (recur (- currentNumber (key matchingSymbol)) 
                       (str result (val matchingSymbol)))

This might seem a bit overwhelming, but don’t let that scare you. Let me explain the gist of this piece of code. When the convert function is called with a particular number, let’s say 14, first thing the applicable symbols are determined by calling the function determineApplicableSymbols. These are taken from the symbols map depending on the size of the specified number. For this first iteration, the applicable symbols are returned in a sequence containing [100 C] [50 L] [10 X].

The actual meat of the conversion functionality is contained by the selectSymbol function. Calling this function returns a matching symbol, which in this case returns [10 X]. The number 10 is subtracted from our initial number and the symbol X is added to the result. Then the recursion starts again, but now currentNumber is assigned to the number 4 and result contains the string “X”.

For the second iteration, the applicable symbols are [10 X] [5 V] [1 I] where the selectSymbol function converts the number 4 into “IV” which is added to the result.

In the third and final iteration, the currentNumber is 0 which breaks out of the loop and returns the result, which is “XIV”.

For completeness sake, here are the unit tests:

(ns roman_numbers.t-core
  (:use midje.sweet)
  (:use [roman_numbers.core]))

(facts "When converting an Arabic number to a Roman Number"
    (fact "it returns I for the number 1"
        (convert 1) => "I")

    (fact "it returns II for the number 2"
        (convert 2) => "II")

    (fact "it returns III for the number 3"
        (convert 3) => "III")

    (fact "it returns IV for the number 4"
        (convert 4) => "IV")

    (fact "it returns V for the number 5"
        (convert 5) => "V")

    (fact "it returns VIII for the number 8"
        (convert 8) => "VIII")

    (fact "it returns IX for the number 9"
        (convert 9) => "IX")

    (fact "it returns X for the number 10"
        (convert 10) => "X")

    (fact "it returns XIV for the number 14"
        (convert 14) => "XIV")

    (fact "it returns XXXIX for the number 39"
        (convert 39) => "XXXIX")

    (fact "it returns XLIX for the number 49"
        (convert 49) => "XLIX")

    (fact "it returns CCLXXVIII for the number 278"
        (convert 278) => "CCLXXVIII")

    (fact "it returns CML for the number 950"
        (convert 950) => "CML")

    (fact "it returns MDCCCXLV for the number 1845"
         (convert 1845) => "MDCCCXLV")

    (fact "it returns MMCCCLXXVIII for the number 2378"
         (convert 2378) => "MMCCCLXXVIII")

There are probably better and more idiomatic solutions to solve this problem in Clojure or other programming languages. I would love to see some other solutions as well.

Until next time.

  • asdasd


  • Erik Assum

    With the algorithm from

    (def nums {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”})

    (defn roman [n i]
    (if (> i 0)
    (let [val (first n)
    m (if (= 1 (count n))
    (rest n))]
    (if ( (keys nums)) 1992))

    ;; => “MCMXCII”

    • JanVanRyswyck

      Nice one. I’ve been toying with a similar solution. The reason I wanted to try the solution that I posted is that I didn’t want to include IV, IX, XC, … into the list of symbols as they are made up of base symbols (just for the sake of the exercise).