freeCodeCamp/guide/english/certifications/javascript-algorithms-and-data-structures/javascript-algorithms-and-data-structures-projects/roman-numeral-converter/index.md

title

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Roman Numeral Converter

Roman Numeral Converter

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Problem Explanation

You will create a program that converts an integer to a Roman Numeral.

Relevant Links

• Roman Numerals
• Array.splice()
• Array.indexOf()
• Array.join()

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Hints

Hint 1

Creating two arrays, one with the Roman Numerals and one with the decimal equivalent for the new forms will be very helpful.

Hint 2

If you add the numbers to the arrays that go before the new letter is introduced, like values for 4, 9, and 40, it will save you plenty of code.

Hint 3

You can't have more than three consecutive Roman numerals together.

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Solutions

Solution 1 (Click to Show/Hide)

var convertToRoman = function(num) {
  var decimalValue = [1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1];
  var romanNumeral = [
    "M",
    "CM",
    "D",
    "CD",
    "C",
    "XC",
    "L",
    "XL",
    "X",
    "IX",
    "V",
    "IV",
    "I"
  ];

  var romanized = "";

  for (var index = 0; index < decimalValue.length; index++) {
    while (decimalValue[index] <= num) {
      romanized += romanNumeral[index];
      num -= decimalValue[index];
    }
  }

  return romanized;
};

// test here
convertToRoman(36);

Code Explanation

• We start off by creating two arrays with default conversion with matching indices. These are called decimalValue and romanNumeral. We also create an empty string variable, romanized, which will house the final roman number.
• Using a for loop, we loop through the indicies of the decimalValue array. We continue to loop until while the value at the current index will fit into num.
• Next, we add the roman numeral and decrease num by the decimal equivalent.
• Finally, we return the value of romanized.

Relevant Links

• For Loops
• While Loops

Solution 2 (Click to Show/Hide)

function convertToRoman(num) {
  var romans = ["I", "V", "X", "L", "C", "D", "M"],
    ints = [],
    romanNumber = [],
    numeral = "";
  while (num) {
    ints.push(num % 10);
    num = Math.floor(num / 10);
  }
  for (i = 0; i < ints.length; i++) {
    units(ints[i]);
  }
  function units() {
    numeral = romans[i * 2];
    switch (ints[i]) {
      case 1:
        romanNumber.push(numeral);
        break;
      case 2:
        romanNumber.push(numeral.concat(numeral));
        break;
      case 3:
        romanNumber.push(numeral.concat(numeral).concat(numeral));
        break;
      case 4:
        romanNumber.push(numeral.concat(romans[i * 2 + 1]));
        break;
      case 5:
        romanNumber.push(romans[i * 2 + 1]);
        break;
      case 6:
        romanNumber.push(romans[i * 2 + 1].concat(numeral));
        break;
      case 7:
        romanNumber.push(romans[i * 2 + 1].concat(numeral).concat(numeral));
        break;
      case 8:
        romanNumber.push(
          romans[i * 2 + 1]
            .concat(numeral)
            .concat(numeral)
            .concat(numeral)
        );
        break;
      case 9:
        romanNumber.push(romans[i * 2].concat(romans[i * 2 + 2]));
    }
  }
  return romanNumber
    .reverse()
    .join("")
    .toString();
}

// test here
convertToRoman(97);

Code Explanation

• Create an array of Roman Numerals (romans).
• Use a for loop to create an array of the digits (ints) in the number.
• Loop through the array of digits (base 10) and as you do, increment the Roman Numeral (base 5) index by 2 (numeral = romans[i*2]).
• Within the loop, use Switch Case to push the proper Roman Numerals (backwards) onto that array.
• Reverse the Roman Numerals array and turn it into a string.

Relevant Links

• For Loops
• While Loops
• Math

Solution 3 (Click to Show/Hide)

function convertToRoman(num) {
  var romans = [
      // 10^i 10^i*5
      ["I", "V"], // 10^0
      ["X", "L"], // 10^1
      ["C", "D"], // 10^2
      ["M"] // 10^3
    ],
    digits = num
      .toString()
      .split("")
      .reverse()
      .map(function(item, index) {
        return parseInt(item);
      }),
    numeral = "";

  // Loop through each digit, starting with the ones place
  for (var i = 0; i < digits.length; i++) {
    // Make a Roman numeral that ignores 5-multiples and shortening rules
    numeral = romans[i][0].repeat(digits[i]) + numeral;
    // Check for a Roman numeral 5-multiple version
    if (romans[i][1]) {
      numeral = numeral
        // Change occurrences of 5 * 10^i to the corresponding 5-multiple Roman numeral
        .replace(romans[i][0].repeat(5), romans[i][1])
        // Shorten occurrences of 9 * 10^i
        .replace(
          romans[i][1] + romans[i][0].repeat(4),
          romans[i][0] + romans[i + 1][0]
        )
        // Shorten occurrences of 4 * 10^i
        .replace(romans[i][0].repeat(4), romans[i][0] + romans[i][1]);
    }
  }

  return numeral;
}

// test here
convertToRoman(36);

Code Explanation

• Use an array (romans) to create a matrix containing the Roman numeral for a given power of 10 and, if available, the Roman numeral for that power of 10 times 5.
• Convert the input number (num) to a reversed array of digits (digits) so that we can loop through those digits starting with the ones position and going up.
• Loop through each digit, starting with the ones place, and create a Roman numeral string by adding each higher-power Roman numeral to the start of the numeral string a number of times equal to digit. This initial string ignores the Roman numerals that are a power of 10 times 5 and also ignores shortening rules.
• If the relevant power of 10 has a 5-multiple Roman numeral, in numeral, replace 5-in-a-row occurrences with the relevant 5-multiple Roman numeral (i.e., V, L, or D) and shorten occurrences of 9 * 10^i (e.g., VIIII to VIX) and 4 * 10^i (e.g., XXXX to XL). Order is important here!
• Finally, return numeral.

Relevant Links

• For Loops
• .split()
• .reverse()
• .map()
• .toString()
• parseInt()
• .replace()
• .repeat()