## Description

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

, `V`

, `X`

, `L`

, `C`

, `D`

and `M`

.

SymbolValueI 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:3Output:"III"

**Example 2:**

Input:4Output:"IV"

**Example 3:**

Input:9Output:"IX"

**Example 4:**

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

**Example 5:**

Input:1994Output:"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(); } }