**12. Integer to Roman**

- Hardness: \(\color{orange}\textsf{Medium}\)
- Ralated Topics:
`Hash Table`

、`Math`

、`String`

### 一、題目

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

, `V`

, `X`

, `L`

, `C`

, `D`

, and `M`

.

\(\boxed{\begin{array}{ll}
\textbf{Symbol}&\textbf{Value}\\
\texttt{I}&1\\
\texttt{V}&5\\
\texttt{X}&10\\
\texttt{L}&50\\
\texttt{C}&100\\
\texttt{D}&500\\
\texttt{M}&1000\\
\end{array}}\)

For example, `2`

is written as `II`

in Roman numeral, just two one’s 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 an integer, convert it to a roman numeral.

**Example 1:**

**Input:**num = 3**Output:**“III”**Explanation**: 3 is represented as 3 ones.

**Example 2:**

**Input:**num = 58**Output:**“LVIII”**Explanation**: L = 50, V = 5, III = 3.

**Example 3:**

**Input:**num = 1994**Output:**“MCMXCIV”**Explanation:**M = 1000, CM = 900, XC = 90 and IV = 4.

**Constraints:**

`1 <= num <= 3999`

### 二、分析

- 既然
`num`

的範圍不大，我們可以利用其轉換的規律，直接用`Array`

去定義。

### 三、解題

#### 1. Math

- Time complexity: \(O(1)\)
- Space complexity: \(O(1)\)

```
string intToRoman(int num) {
string M[] = {"", "M", "MM", "MMM"};
string C[] = {"", "C", "CC", "CCC", "CD", "D", "DC", "DCC", "DCCC", "CM"};
string X[] = {"", "X", "XX", "XXX", "XL", "L", "LX", "LXX", "LXXX", "XC"};
string I[] = {"", "I", "II", "III", "IV", "V", "VI", "VII", "VIII", "IX"};
return M[num/1000] + C[(num%1000)/100] + X[(num%100)/10] + I[num%10];
}
```