12. Integer to Roman

最新推荐文章于 2022-10-20 18:00:00 发布
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本文介绍了一种将整数转换为罗马数字的算法实现，输入范围限制在1到3999之间。通过定义不同数量级的罗马数字表示方式，该算法能够快速准确地完成转换。

Given an integer, convert it to a roman numeral.

Input is guaranteed to be within the range from 1 to 3999.

class Solution {
public:
    string intToRoman(int num) {
        string M[] = {"", "M", "MM", "MMM"};
        string C[] = {"", "C", "CC", "CCC", "CD", "D", "DC", "DCC", "DCCC", "CM"};
        string X[] = {"", "X", "XX", "XXX", "XL", "L", "LX", "LXX", "LXXX", "XC"};
        string I[] = {"", "I", "II", "III", "IV", "V", "VI", "VII", "VIII", "IX"};
        return M[num/1000] + C[(num/100)%10] + X[(num/10)%10] + I[num%10];
        
    }
};


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''' 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 CM ...........900 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. '''
最新发布
07-05
### Convert an Integer to a Roman Numeral with Subtractive Rules To convert an integer to a Roman numeral, especially accounting for subtractive combinations like IV (4), IX (9), XL (40), and so on, you can follow a structured approach using predefined mappings of integers to Roman numerals. This method ensures that the subtractive notation is applied correctly. The core idea is to use two arrays: one for the integer values and another for their corresponding Roman numeral representations. These arrays are ordered from the largest to the smallest values, including the special subtractive cases. The algorithm iterates through these values, subtracting them from the input number while appending the corresponding Roman numeral symbols to the result string. Here’s how this can be implemented in Python: ```python def int_to_roman(num): # Define the mapping of integers to Roman numerals, including subtractive cases val = [1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1] syms = ["M", "CM", "D", "CD", "C", "XC", "L", "XL", "X", "IX", "V", "IV", "I"] roman_numeral = "" i = 0 while num > 0: while num >= val[i]: roman_numeral += syms[i] num -= val[i] i += 1 return roman_numeral ``` This function works by repeatedly subtracting the largest possible value from the given number and appending the corresponding Roman numeral symbol(s) to the result string. For example, when converting the number 1994, the function first subtracts 1000 (M), then 900 (CM), followed by 90 (XC), and finally 4 (IV), resulting in the Roman numeral "MCMXCIV" [^2]. ### Explanation of Subtractive Notation Handling Subtractive notation is used in specific cases where a smaller numeral precedes a larger one, indicating subtraction rather than addition. These cases include: - IV for 4 (5 - 1) - IX for 9 (10 - 1) - XL for 40 (50 - 10) - XC for 90 (100 - 10) - CD for 400 (500 - 100) - CM for 900 (1000 - 100) By including these subtractive combinations in the `val` and `syms` arrays, the function ensures that the correct Roman numeral representation is generated without requiring additional logic to handle these cases separately [^3]. ### Example Usage For instance, if you call `int_to_roman(1994)`, the function will return `"MCMXCIV"`, which accurately represents the year 1994 in Roman numerals [^2]. Similarly, calling `int_to_roman(58)` will return `"LVIII"`, representing 58 as L (50), V (5), and III (3).
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