Decimal to Roman Numeral Algorithm
The manner of denoting numbers in the decimal system is often referred to as decimal notation."Decimal" may also refer specifically to the digits after the decimal separator, such as in" 3.14 is the estimation of π to two decimals". The Egyptian hieratic numerals, the Greek alphabet numerals, the Hebrew alphabet numerals, the Roman numerals, the Chinese numerals and early Indian Brahmi numerals are all non-positional decimal systems, and need large numbers of symbols. Egyptian hieroglyphs, in evidence since around 3000 BCE, used a purely decimal system, as make the Cretan hieroglyphs (c. 1625−1500 BCE) of the Minoans whose numerals are closely based on the Egyptian model. Some non-mathematical ancient texts like the Vedas, dating back to 1900–1700 BCE make purpose of decimals and mathematical decimal fractions.
//This Programme Converts a given decimal number in the range [0,4000)
//to both Lower case and Upper case Roman Numeral
#include <cmath>
#include <cstdio>
#include <string>
#include <iostream>
using namespace std;
//This functions fills a string with character c, n times and returns it
string fill(char c, int n)
{
string s = "";
while (n--)
s += c;
return s;
}
//to convert to lowercase Roman Numeral
// the function works recursively
string tolowerRoman(int n)
{
if (n < 4)
return fill('i', n);
if (n < 6)
return fill('i', 5 - n) + "v";
if (n < 9)
return string("v") + fill('i', n - 5);
if (n < 11)
return fill('i', 10 - n) + "x";
if (n < 40)
return fill('x', n / 10) + tolowerRoman(n % 10);
if (n < 60)
return fill('x', 5 - n / 10) + 'l' + tolowerRoman(n % 10);
if (n < 90)
return string("l") + fill('x', n / 10 - 5) + tolowerRoman(n % 10);
if (n < 110)
return fill('x', 10 - n / 10) + "c" + tolowerRoman(n % 10);
if (n < 400)
return fill('c', n / 100) + tolowerRoman(n % 100);
if (n < 600)
return fill('c', 5 - n / 100) + 'd' + tolowerRoman(n % 100);
if (n < 900)
return string("d") + fill('c', n / 100 - 5) + tolowerRoman(n % 100);
if (n < 1100)
return fill('c', 10 - n / 100) + "m" + tolowerRoman(n % 100);
if (n < 4000)
return fill('m', n / 1000) + tolowerRoman(n % 1000);
return "?";
}
//to convert to uppercase Roman Numeral
// the function works recursively
string toupperRoman(int n)
{
if (n < 4)
return fill('I', n);
if (n < 6)
return fill('I', 5 - n) + "V";
if (n < 9)
return string("V") + fill('I', n - 5);
if (n < 11)
return fill('I', 10 - n) + "X";
if (n < 40)
return fill('X', n / 10) + toupperRoman(n % 10);
if (n < 60)
return fill('X', 5 - n / 10) + 'L' + toupperRoman(n % 10);
if (n < 90)
return string("L") + fill('X', n / 10 - 5) + toupperRoman(n % 10);
if (n < 110)
return fill('X', 10 - n / 10) + "C" + toupperRoman(n % 10);
if (n < 400)
return fill('C', n / 100) + toupperRoman(n % 100);
if (n < 600)
return fill('C', 5 - n / 100) + 'D' + toupperRoman(n % 100);
if (n < 900)
return string("D") + fill('C', n / 100 - 5) + toupperRoman(n % 100);
if (n < 1100)
return fill('C', 10 - n / 100) + "M" + toupperRoman(n % 100);
if (n < 4000)
return fill('M', n / 1000) + toupperRoman(n % 1000);
return "?";
}
//main function
int main()
{
int n;
cout << "\t\tRoman numbers converter\n\n";
cout << "Type in decimal number between 0 up to 4000 (exclusive): ";
cin >> n;
cout << n << " in Upper Roman Numerals is " << toupperRoman(n) << "\n";
cout << n << " in Lower Roman Numerals is " << tolowerRoman(n) << "\n";
return 0;
}
