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## 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, two is written as `II` in Roman numeral, just two one’s added together. Twelve is written as, `XII`, which is simply `X` + `II`. The number twenty seven 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. Input is guaranteed to be within the range from 1 to 3999.

Example 1:

```Input: 3
Output: "III"```

Example 2:

```Input: 4
Output: "IV"```

Example 3:

```Input: 9
Output: "IX"```

Example 4:

```Input: 58
Output: "LVIII"
Explanation: L = 50, V = 5, III = 3.
```

Example 5:

```Input: 1994
Output: "MCMXCIV"
Explanation: M = 1000, CM = 900, XC = 90 and IV = 4.```

## Submission

A straight forward solution is to traverse the mapping table from in descending order and subtract the largest smaller factor of s given num iteratively.

```class Solution {
public String intToRoman(int num) {
HashMap<Integer, String> map = new HashMap();
map.put(1, "I");
map.put(5, "V");
map.put(10, "X");
map.put(50, "L");
map.put(100, "C");
map.put(500, "D");
map.put(1000, "M");
map.put(4, "IV");
map.put(9, "IX");
map.put(40, "XL");
map.put(90, "XC");
map.put(400, "CD");
map.put(900, "CM");

StringBuilder sb = new StringBuilder();

TreeSet sortedKeys = new TreeSet(map.keySet());
TreeSet descendingKeys = (TreeSet)sortedKeys.descendingSet();
for(Object key: descendingKeys) {
int i = (int)key;
while(num >= i) {
sb.append(map.get(i));
num -= i;
}
}
return sb.toString();
}
}```