12. Integer to Roman

Description

Seven different symbols represent Roman numerals with the following values:

Symbol	Value
I	1
V	5
X	10
L	50
C	100
D	500
M	1000

Roman numerals are formed by appending the conversions of decimal place values from highest to lowest. Converting a decimal place value into a Roman numeral has the following rules:

• If the value does not start with 4 or 9, select the symbol of the maximal value that can be subtracted from the input, append that symbol to the result, subtract its value, and convert the remainder to a Roman numeral.
• If the value starts with 4 or 9 use the subtractive form representing one symbol subtracted from the following symbol, for example, 4 is 1 (I) less than 5 (V): IV and 9 is 1 (I) less than 10 (X): IX. Only the following subtractive forms are used: 4 (IV), 9 (IX), 40 (XL), 90 (XC), 400 (CD) and 900 (CM).
• Only powers of 10 (I, X, C, M) can be appended consecutively at most 3 times to represent multiples of 10. You cannot append 5 (V), 50 (L), or 500 (D) multiple times. If you need to append a symbol 4 times use the subtractive form.

Given an integer, convert it to a Roman numeral.

Example 1:

• Input: num = 3749
• Output: “MMMDCCXLIX”
• Explanation:

    3000 = MMM as 1000 (M) + 1000 (M) + 1000 (M)
     700 = DCC as 500 (D) + 100 (C) + 100 (C)
      40 = XL as 10 (X) less of 50 (L)
       9 = IX as 1 (I) less of 10 (X)
    

  Note: 49 is not 1 (I) less of 50 (L) because the conversion is based on decimal places

Example 2:

• Input: num = 58
• Output: “LVIII”
• Explanation:

    50 = L
     8 = VIII
    

Example 3:

• Input: num = 1994
• Output: “MCMXCIV”
• Explanation:

    1000 = M
     900 = CM
      90 = XC
       4 = IV
    

Constraints:

• 1 <= num <= 3999

Submitted Code

class Solution:
    def intToRoman(self, num: int) -> str:
        res = []
        vals = [
            (1000, "M"), (900, "CM"),
            (500, "D"), (400, "CD"),
            (100, "C"), (90, "XC"),
            (50, "L"), (40, "XL"),
            (10, "X"), (9, "IX"),
            (5, "V"), (4, "IV"),
            (1, "I")
        ]

        for val, rom in vals:
            while num >= val:
                num -= val
                res.append(rom)

        return "".join(res)

Runtime: 1 ms | Beats 85.85%
Memory: 19.18 MB | Beats 97.90%

큰 값부터 빼면서 로마자를 붙이는 방법을 사용했다.

Other Solutions

1st

class Solution:
    def intToRoman(self, num: int) -> str:
        M = ['', 'M', 'MM', 'MMM'] # 0, 1000, 2000, 3000
        C = ['', 'C', 'CC', 'CCC', 'CD', 'D', 'DC', 'DCC', 'DCCC', 'CM'] # 0, 100, 200...900
        X = ['', 'X', 'XX', 'XXX', 'XL', 'L', 'LX', 'LXX', 'LXXX', 'XC'] # 0, 10, 20...90
        I = ['', 'I', 'II', 'III', 'IV', 'V', 'VI', 'VII', 'VIII', 'IX'] # 0, 1, 2...9
        
        return M[num // 1000] + C[num % 1000 // 100] + X[num % 100 // 10] + I[num % 10]      

time complexity: 𝑂(1)
space complexity: 𝑂(1)

각 자리수별로 가능한 모든 조합을 저장하면 바로 해당하는 로마자를 찾을 수 있다.