# Integer to Roman

Roman numerals are represented by seven different symbols: IVXLCD and M.

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.

### Solution

#include <iostream>
#include <string>
#include <vector>
#include <sstream>

using namespace std;

string intToRoman(int num) {
// all possible basic blocks
std::vector<int> entry = {1, 4, 5, 9, 10, 40, 50, 90, 100, 400, 500, 900, 1000};
// and their corresponding Roman numbers
std::vector<string> roman = {"I", "IV", "V", "IX", "X", "XL", "L", "XC", "C", "CD", "D", "CM", "M"};

// build result string
std::ostringstream result;
// iterate reversely
unsigned long index = entry.size() - 1;
// number remained to be translate
int remain = num;
// translate to Roman numbers until remaining value gets 0
while (remain != 0) {
// calculate number of repeats of current Roman number
int repeat = remain / entry[index];
// repeat current Roman number / translation
for (int i = 0;i < repeat;i++) {
result << roman[index];
}
// substract value represented in this round
remain -= repeat * entry[index];
// move to next Roman number
index--;
}

return result.str();
}
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