Today we will learn about a famous interview question **Roman Numerals to Integer**. The question is simple but still requires one of those “Aha” moments to solve.

### Problem Statement

Given a roman numeral, convert it to an integer.

Input is guaranteed to be within the range from 1 to 3999.

**Example :**

Input : “XIV”

Output : 14

Input : “XX”

Output : 20

Now I know most of you are familiar with Roman Numerals. But we are still going to go over them briefly. Also keep in mind we will base all of our assumptions for the input range **1-3999** as given in the question.

### Roman Numerals

Roman Numerals are numbers formed by combining symbols. These are based on seven symbols. Other symbols are produces by combining two or more of the basic symbols.

Symbol |
Value |
---|---|

I | 1 |

IV | 4 |

V | 5 |

IX | 9 |

X | 10 |

XL | 40 |

L | 50 |

XC | 90 |

C | 100 |

CD | 400 |

D | 500 |

CM | 900 |

M | 1000 |

So Two assumptions can be derived from our knowledge of Roman Numerals –

- The symbol at
*i*is always greater than all the symbols following it. - Two symbols can be combined to formed one symbol.

### Algorithm

sum := 0 i := 0 // Iterate over each symbol in Roman string Repeat while i < len(string) do: current_symbol := symbol(i) // If the symbol is smaller than the succeeding symbol // Then combine both symbols as one if value(symbol(i)) < value(symbol(i+1)) do: current_symbol := symbol(i) + symbol(i+1) increment i end // Add the corresponding symbol value from table to sum sum := sum + value(current_symbol) increment i end

### Testing

Now that we have worked out the algorithm, Let’s test it before moving on to the coding part.

input := XXIV

output := 24

That’s what we wanted. So the Algorithm works.

Implementation in C++ is available at GitHub