Integer to Roman

class Solution {
public:
    std::string integerToRoman(int value) {
        std::vector<std::string> M = {"", "M", "MM", "MMM"};
        std::vector<std::string> C = {"",  "C",  "CC",  "CCC",  "CD",
                                             "D", "DC", "DCC", "DCCC", "CM"};
        std::vector<std::string> X = {"",  "X",  "XX",  "XXX",  "XL",
                                         "L", "LX", "LXX", "LXXX", "XC"};
        std::vector<std::string> I = {"",  "I",  "II",  "III",  "IV",
                                         "V", "VI", "VII", "VIII", "IX"};
        return M[value / 1000] + C[value % 1000 / 100] +
               X[value % 100 / 10] + I[value % 10];
    }
};

The provided C++ class, named Solution, implements a function integerToRoman that converts an integer to a Roman numeral. This function elegantly maps integers to their corresponding Roman numeral strings using vectorized indices, providing an efficient way to break down the number into thousands, hundreds, tens, and ones. Each position (M, C, X, I) corresponds to a specific range of Roman numerals:

• The M vector is meant for the thousands place and includes representations for values 0-3000 (i.e., "", "M", "MM", "MMM").
• The C vector deals with hundreds ranging from 0 to 900.
• The X array handles tens, and it's filled with Roman numeral equivalents from 0 to 90.
• The I vector encapsulates units up to 9.

To form the Roman numeral:

• Start by obtaining the contribution of thousands by dividing the number by 1000.
• Get the hundreds by computing the remainder when dividing by 1000, then divide that result by 100.
• Tens are found by taking the remainder when dividing by 100 and dividing the result by 10.
• Units are simply the remainder of the number when divided by 10.

These indices are used directly to access values from their respective vectors, which are then concatenated to form the full Roman numeral string.

class RomanConverter {
    private static final String[] thousandsLevel = { "", "M", "MM", "MMM" };
    private static final String[] hundredsLevel = {
        "",
        "C",
        "CC",
        "CCC",
        "CD",
        "D",
        "DC",
        "DCC",
        "DCCC",
        "CM",
    };
    private static final String[] tensLevel = {
        "",
        "X",
        "XX",
        "XXX",
        "XL",
        "L",
        "LX",
        "LXX",
        "LXXX",
        "XC",
    };
    private static final String[] onesLevel = {
        "",
        "I",
        "II",
        "III",
        "IV",
        "V",
        "VI",
        "VII",
        "VIII",
        "IX",
    };

    public String convertToRoman(int number) {
        return (
            thousandsLevel[number / 1000] +
            hundredsLevel[(number % 1000) / 100] +
            tensLevel[(number % 100) / 10] +
            onesLevel[number % 10]
        );
    }
}

Convert an integer to its Roman numeral representation using the provided Java class RomanConverter. This class utilizes four static arrays to map specific segments of numbers—thousands, hundreds, tens, and ones—to their corresponding Roman numerals.

• Each segment of the integer (thousands, hundreds, tens, ones) is processed by dividing and taking the modulus of the number.
• It then fetches the appropriate Roman numeral from the pre-defined arrays using these calculated values.
• The Roman numerals for each segment are then concatenated in the order of thousands to ones to form the final Roman numeral string.

Ensure you input an integer within the range this converter can process, which based on the arrays, should be between 1 and 3999. Usage involves creating an instance of the RomanConverter class and calling the convertToRoman method with the integer you wish to convert. This approach offers a straightforward and effective method for integer-to-Roman numeral conversion, leveraging indexed based retrieval, which ensures efficient and quick conversion.

char *convertToRoman(int value) {
    const char *m[] = {"", "M", "MM", "MMM"};
    const char *c[] = {"", "C", "CC", "CCC", "CD", "D", "DC", "DCC", "DCCC", "CM"};
    const char *x[] = {"", "X", "XX", "XXX", "XL", "L", "LX", "LXX", "LXXX", "XC"};
    const char *i[] = {"", "I", "II", "III", "IV", "V", "VI", "VII", "VIII", "IX"};

    char *roman = (char *)malloc(16 * sizeof(char));
    roman[0] = '\0';

    strcat(roman, m[value / 1000]);
    strcat(roman, c[value % 1000 / 100]);
    strcat(roman, x[value % 100 / 10]);
    strcat(roman, i[value % 10]);

    return roman;
}

The provided C function convertToRoman transforms an integer into its equivalent Roman numeral representation. It achieves this conversion utilizing predefined string arrays corresponding to Roman numeral values for thousands, hundreds, tens, and units. Importantly, the function dynamically allocates memory for the resultant Roman numeral string, ensuring that enough space is secured.

Here's an overview of the operational strategy:

1. Initialize predefined arrays for different value segments (m for thousands, c for hundreds, x for tens, and i for units).
2. Allocate memory for a character array roman to store the resulting Roman numeral.
3. Use the strcat function to concatenate appropriate values from these arrays into the roman based on the input integer's decomposition (extracting thousands, hundreds, tens, and units).
4. The resultant string roman is returned, representing the complete Roman numeral.

This function is efficient both in terms of memory, due to dynamic allocation preventing wastage, and computational effort, as it uses direct index lookups which are constant in time complexity. Ensure proper memory management when integrating this function to avoid leaks.

var numberToRoman = function (value) {
    let m = ["", "M", "MM", "MMM"];
    let c = ["", "C", "CC", "CCC", "CD", "D", "DC", "DCC", "DCCC", "CM"];
    let x = ["", "X", "XX", "XXX", "XL", "L", "LX", "LXX", "LXXX", "XC"];
    let i = ["", "I", "II", "III", "IV", "V", "VI", "VII", "VIII", "IX"];

    return (
        m[Math.floor(value / 1000)] +
        c[Math.floor((value % 1000) / 100)] +
        x[Math.floor((value % 100) / 10)] +
        i[value % 10]
    );
};

This solution presents a JavaScript function numberToRoman that converts an integer (value) into its equivalent Roman numeral representation. The function utilizes arrays to map integers to their corresponding Roman numeral strings for thousands, hundreds, tens, and units.

• The arrays m, c, x, and i represent Roman numerals for thousands, hundreds, tens, and units respectively.
• Each index of these arrays corresponds to how many times that Roman numeral is counted. For example, m[1] is "M", c[2] is "CC", and so forth.
• The function divides the input number using division and modulus operations to isolate each digit:
  • Thousands digit is extracted by Math.floor(value / 1000).
  • Hundreds digit is determined by Math.floor((value % 1000) / 100).
  • Tens digit is obtained by Math.floor((value % 100) / 10).
  • Units digit is directly accessed by value % 10.
• The Roman numeral string is constructed by concatenating the strings from the respective arrays based on the digits calculated.
• The resulting string is returned, representing the Roman numeral version of the input integer.

By utilizing simple mathematical operations and array indexing, this function effectively transforms an integer into its Roman numeral counterpart, leveraging a clear and structured approach to handle the conversion.

class RomanConverter:
    def numberToRoman(self, value: int) -> str:
        m = ["", "M", "MM", "MMM"]
        c = ["", "C", "CC", "CCC", "CD", "D", "DC", "DCC", "DCCC", "CM"]
        x = ["", "X", "XX", "XXX", "XL", "L", "LX", "LXX", "LXXX", "XC"]
        i = ["", "I", "II", "III", "IV", "V", "VI", "VII", "VIII", "IX"]
        return (
            m[value // 1000]
            + c[value % 1000 // 100]
            + x[value % 100 // 10]
            + i[value % 10]
        )

The provided Python3 solution involves converting an integer to its Roman numeral representation using a class named RomanConverter. This class contains one method numberToRoman, which takes an integer value and returns a string representing its Roman numeral format.

The method uses four arrays (m, c, x, i) containing string values representing the Roman numerals for the thousands, hundreds, tens, and units places, respectively. The Roman numeral is constructed by selecting the appropriate segments from these arrays based on the input integer's place values. The selection is done through integer division and modulus operations, which extract each digit from the thousand down to the unit place. The resulting Roman numeral components are then concatenated in order to form the final string.

This approach allows for efficient mapping from the integer values to their corresponding Roman numeral representations without looping or recursion. It ensures quick conversions, suitable for values ranging up to 3999, which is a common limit for Roman numeral systems in programming challenges.