📌Problem

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"

Example 2:

Input: num = 4
Output: "IV"

Example 3:

Input: num = 9
Output: "IX"

Example 4:

Input: num = 58
Output: "LVIII"

Explanation: L = 50, V = 5, III = 3.

Example 5:

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

Constraints:

• 1 <= num <= 3999

leetcode 에서 풀기

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📝Solution

class Solution:
    def intToRoman(self, num: int) -> str:
        
        value2roman={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'}
            
        roman=''
        while num!=0:
            for value in value2roman:
                if num-value >=0:
                    roman+=value2roman[value]
                    num=num-value
                    break
        
        return roman
                
                

• Time complexity : $O(N*13)=O(N)$

• value2roman 은 변환이 가능한 값에 대한 정보를 가지고 있다.

• value2roman 에서 가장 큰 것부터 순차적으로 num 에서 뺀 후 non-negative 이고 value2roman에 값이 존재한다면 변환하고, num ,roman 을 업데이트 한다.

• 위의 과정을 num==0 이 될 때까지 반복한다.

  num	value	num-value	conversion
  253	100	153	'C'
  153	100	53	'CC'
  53	50	3	'CCL'
  3	1	2	'CCLI'
  2	1	1	'CCLII'
  1	1	0	'CCLII'