# LeetCode: 13. Roman to Integer

**The Problem**

Roman numerals are represented by seven different symbols: `I`

, `V`

, `X`

, `L`

, `C`

, `D`

and `M`

.

**Symbol**** Value**I 1 V 5 X 10 L 50 C 100 D 500 M 1000

For example, `2`

is written as `II`

in Roman numeral, just two ones added together. `12`

is written as `XII`

, which is simply `X + II`

. The number `27`

is written as `XXVII`

, which is `XX + V + II`

.

Roman numerals are usually written largest to smallest from left to right. However, the numeral for four is not `IIII`

. Instead, the number four is written as `IV`

. Because the one is before the five we subtract it making four. The same principle applies to the number nine, which is written as `IX`

. There are six instances where subtraction is used:

`I`

can be placed before`V`

(5) and`X`

(10) to make 4 and 9.`X`

can be placed before`L`

(50) and`C`

(100) to make 40 and 90.`C`

can be placed before`D`

(500) and`M`

(1000) to make 400 and 900.

Given a roman numeral, convert it to an integer.

**Examples**

```
Example 1:
Input: s = "III" Output: 3 Explanation: III = 3.
Example 2:
Input: s = "LVIII" Output: 58 Explanation: L = 50, V= 5, III = 3.
Example 3:
Input: s = "MCMXCIV" Output: 1994 Explanation: M = 1000, CM = 900, XC = 90 and IV = 4.
```

**Constraints:**

`1 <= s.length <= 15`

`s`

contains only the characters`('I', 'V', 'X', 'L', 'C', 'D', 'M')`

.- It is
that**guaranteed**`s`

is a valid roman numeral in the range`[1, 3999]`

.

**The Solution**

We opted for a simple approach using a **for** loop, this was the result:

```
unordered_map<char, int> values = {
{'I', 1}, {'V', 5}, {'X', 10}, {'L', 50}, {'C', 100}, {'D', 500}, {'M', 1000}
};
int romanToInt(string s) {
int currentValue, lastValue = values[s.back()];
int ans = lastValue;
for(int i = s.size() - 2; i >= 0; --i) {
currentValue = values[s[i]];
if (currentValue >= lastValue) ans += currentValue;
else ans -= currentValue;
lastValue = currentValue;
}
return ans;
}
```

Let's break down the code step by step:

**unordered_map<char, int> values = {...}:**

- This line declares an unordered map named
`values`

which maps characters (Roman numerals) to their corresponding integer values. - Each key-value pair represents a Roman numeral character and its corresponding integer value.
- For example, 'I' maps to 1, 'V' maps to 5, 'X' maps to 10, and so on.

**int romanToInt(string s):**

- This line defines a function named
`romanToInt`

that takes a string`s`

as input and returns an integer.

**int currentValue, lastValue = values[s.back()];:**

- This line declares two integer variables
`currentValue`

and`lastValue`

. `lastValue`

is initialized with the integer value corresponding to the last character of the input string`s`

.- For instance, if
`s`

is "IX", then`lastValue`

will be initialized with the integer value corresponding to 'X'.

**int ans = lastValue;:**

- This line initializes the variable
`ans`

with the value of`lastValue`

. `ans`

will hold the final result of converting the Roman numeral string to an integer.

**for(int i = s.size() - 2; i >= 0; --i) { ... }:**

- This is a
`for`

loop that iterates over the characters of the input string`s`

in reverse order, starting from the second-to-last character. - The loop continues until it reaches the first character of the string.

**currentValue = values[s[i]];:**

- Inside the loop,
`currentValue`

is assigned the integer value corresponding to the character at index`i`

in the string`s`

. - For example, if
`s[i]`

is 'I', then`currentValue`

will be assigned 1.

**if (currentValue >= lastValue) ans += currentValue; else ans -= currentValue;:**

- This
`if`

statement checks whether the current integer value (`currentValue`

) is greater than or equal to the previous integer value (`lastValue`

). - If
`currentValue`

is greater than or equal to`lastValue`

, it adds`currentValue`

to`ans`

. - Otherwise, it subtracts
`currentValue`

from`ans`

. - This logic is based on the rule of Roman numerals where smaller numerals to the right of larger ones are added, and smaller numerals to the left of larger ones are subtracted.

**lastValue = currentValue;:**

- This line updates
`lastValue`

with the value of`currentValue`

for the next iteration of the loop.

**return ans;:**

- Finally, the function returns the calculated integer value
`ans`

, which represents the conversion of the Roman numeral string`s`

to an integer.