# 12. Integer to Roman

## LeetCode [12. Integer to Roman](https://leetcode-cn.com/problems/integer-to-roman/)

### Description

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 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 = 4
Output: "IV"
```

**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`

### Tags

Math, String, Greedy

### Solution

首先整理所有的基础的数字对应罗马字母的情况，然后由大到小检查这些数字，用`num`减去刚好小于等于它的数字，并把相应的罗马字母添加到结果之后，直至`num == 0`，最后返回结果字符串。

Collate all base-mapping from value to symbol first. Then check these values in decending order, and find a value which is just smaller than or equal to `num`. Subtract that value from `num` and append the corresponding symbol to the `ans` string. Repeat until `num == 0`.

### Complexity

* Time complexity: $$O(1)$$
* Space complexity: $$O(1)$$

### Code

```go
func intToRoman(num int) string {
	var ans string
	for num > 0 {
		switch {
		case num >= 1000:
			num -= 1000
			ans += "M"
		case num >= 900:
			num -= 900
			ans += "CM"
		case num >= 500:
			num -= 500
			ans += "D"
		case num >= 400:
			num -= 400
			ans += "CD"
		case num >= 100:
			num -= 100
			ans += "C"
		case num >= 90:
			num -= 90
			ans += "XC"
		case num >= 50:
			num -= 50
			ans += "L"
		case num >= 40:
			num -= 40
			ans += "XL"
		case num >= 10:
			num -= 10
			ans += "X"
		case num >= 9:
			num -= 9
			ans += "IX"
		case num >= 5:
			num -= 5
			ans += "V"
		case num >= 4:
			num -= 4
			ans += "IV"
		case num >= 1:
			num -= 1
			ans += "I"
		}
	}
	return ans
}
```

## Reference

1. [整数转罗马数字](https://leetcode-cn.com/problems/integer-to-roman/solution/zheng-shu-zhuan-luo-ma-shu-zi-by-leetcode/)