How to check the entered Roman number for the correct notation?

Question

Algorithms

I'm trying to check a roman number. Specifically, the problem arose when considering the case that the user enters a smaller number before a larger one. Such a number, the program, when translated into Arabic, will add up the numbers. For example "DM", "LXC" , "CDCM"...

#include <iostream>
#include <string>

using namespace std;

const int size_num = 13;
char Roman_nums[][3] = { "I","IV","V","IX","X","XL","L","XC","C","CD","D","CM","M" };
int num[] = { 1, 4, 5, 9, 10, 40, 50, 90, 100, 400, 500, 900, 1000 };

bool isValidRomanNumeral(string roman) {
  for (int i = 0; i < roman.length(); i++) {//Проверка на использование допустимых символов
    int check = 0;
    for (int j = 0; j < size_num; j += 2) {
      if (roman.substr(i, 1) == Roman_nums[j]){
        check++;
        break;
      }
    }
    if (check == 0)
      return false;
  }
  
  for (int i = 11; i > 0; i -= 2) {//Проверка на отсутствие повторяющихся чисел размерностью 2
    int counter = 0;
    for (int j = 0; j < roman.length(); j++) {
      if (roman.substr(j, 2) == Roman_nums[i]) {
        ++counter;
        if (counter > 1)
          return false;
      }
    }
  }

  for (int i = 12; i >= 0; i -= 2) {//Проверка на отсутствие повтора больше 3х раз подряд чисел 
    int counter = 0;
    for (int j = 1; j < roman.length(); j++) {
      if (roman.substr(j, 1) == Roman_nums[i] && roman.substr(j - 1, 1) == Roman_nums[i]) {
        ++counter;
        if (counter > 3)
          return false;
      }
    }
  }

  return true;
}

int main() {
  string number;

  do {
    cout << "Enter the Rom number\n";
    cin >> number;
  } while (isValidRomanNumeral(number) == false);

  return 0;

Answer 1

Too lazy to remember C, keep the variant of the state machine for checking Roman numerals in JS.

// Матрица переходов конечного автомата
// -1 - допустимое конечное состояние
// null - недопустимое состояние
const dka = [
  [-1, 1, 5, 4, 10, 9, 15, 14], // 0
  [-1, 2, 5, 4, 10, 9, 15, 14], // 1
  [-1, 3, 5, 4, 10, 9, 15, 14], // 2
  [-1, null, 5, 4, 10, 9, 15, 14], // 3
  [-1, 8, 8, 7, null, null, null, null], // 4
  [-1, null, null, 6, 10, 9, 15, 14], // 5
  [-1, null, null, 7, 10, 9, 15, 14], // 6
  [-1, null, null, 8, 10, 9, 15, 14], // 7
  [-1, null, null, null, 10, 9, 15, 14], // 8
  [-1, null, null, 13, 13, 12, null, null], // 9
  [-1, null, null, null, null, 11, 15, 14], // 10
  [-1, null, null, null, null, 12, 15, 14], // 11
  [-1, null, null, null, null, 13, 15, 14], // 12
  [-1, null, null, null, null, null, 15, 14], // 13
  [-1, null, null, null, null, 18, 18, 17], // 14
  [-1, null, null, null, null, null, null, 16], // 15
  [-1, null, null, null, null, null, null, 17], // 16
  [-1, null, null, null, null, null, null, 18], // 17
  [-1, null, null, null, null, null, null, null], // 18
];

// Алфавит
const alphabet = 'MDCLXVI';

// Разбивает строку на лексемы
// (номера символов в алфавите, начиная с 1)
// для отсутствующих символов возвращает 0
const lexer = (str) => str.split('').map((l) => alphabet.indexOf(l) + 1);

// Проверяет корректность числа в римской записи
const check = (str) => {
  const lexems = lexer(str);
  let state = 0;
  let idx = 0;
  while (true) {
    const lex = lexems[idx] ?? 0;
    state = dka[state][lex];
    if (state === null) {
      return false;
    }
    if (state === -1) {
      return  idx === str.length;
    }
    idx += 1;
  }
}

Answer 2

Just make a function to convert Roman numeral to regular numeral (int32). An error (i.e. an exception) during the operation of this function will mean the conversion is impossible. The algorithm is the same.
In other words, use the roman to arabic translation algorithm. Some new ideas are not needed, since the algorithm is known (and if not, then Google will help). There is no problem. It is only necessary to translate the algorithm into a programming language. Jun's task. By the way, there are probably already implementations for different PLs, and you just need to google it correctly.