Integer to Roman

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 = 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

Solution:

def intToRoman(self, num: int) -> str:
        symbols = ['I', 'V', 'X', 'L', 'C', 'D', 'M']
        level = 0
        roman_num = ''
        while num:
            remainder = num % 10
            num = num // 10
            
            if remainder == 0:
                pass
            elif remainder in [1,2,3]:
                roman_num = symbols[level] * remainder + roman_num
            elif remainder == 4:
                roman_num = symbols[level] + symbols[level+1] + roman_num
            elif remainder in [5,6,7,8]:
                roman_num = symbols[level+1] + (remainder-5) * symbols[level] + roman_num
            elif remainder == 9:
                roman_num = symbols[level] + symbols[level+2] + roman_num
            
            level += 2
        
        return roman_num

Solution 2:

class Solution:
    def intToRoman(self, num: int) -> str:
        Dict={1:'I',4:'IV',5:'V', 9:'IX',10:'X',40:'XL',50:'L',90:'XC',100:'C',400:'CD',500:'D',900:'CM',1000:'M'}
        output=''
        while num:
            keys=list(Dict.keys())
            l=bisect.bisect_right(keys,num)
            output=output+Dict[keys[l-1]]
            num=num-keys[l-1]
        return output

Solution 3 – Recursion:

class Solution:
    def __init__(self):
        self.symbol_table = [('M',1000),('CM',900),('D',500),('CD',400),('C',100),('XC',90),('L',50),('XL',40),('X',10),('IX',9),('V',5),('IV',4),('I',1)]
        
    def intToRoman(self, num: int) -> str:
        
        if num == 0:
            return ""
        
        for index,symbol in enumerate(self.symbol_table) :
            #If modulo by the roman symbol is zero its bigger than num, try next symbol
            if num%symbol[1] == num :
                continue
            #This is the biggest symbol which divides num into at least one part
            if num%symbol[1] < num :
                #How many symbols do we need?
                factor = num // symbol[1]
                #Index of this symbol in symbol table
                x=index
                break
        
        roman=self.symbol_table[x][0]
        roman_int_val=self.symbol_table[x][1]
        
        return roman*factor + self.intToRoman(num - factor*roman_int_val)