将阿拉伯数字转换成罗马数字 Integer to Roman

最新推荐文章于 2023-03-12 20:27:03 发布

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最新推荐文章于 2023-03-12 20:27:03 发布

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分类专栏： LeetCode 我爱算法

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本文介绍了一种将阿拉伯数字转换为罗马数字的方法。利用数组存储罗马数字对应的字符，通过简单的数学运算实现转换。代码示例使用C++实现。

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题目源自于leetcode。

题目：将一个int型的阿拉伯数字转换为string型的罗马数字。

方法：首先要知道罗马数字的表示法。

个位、十位、百位、千位都是特点的字幕作为权值，每一个位的10个数字的表示方法也类似，都会在5有另一个中间的字母。

				M=1000		D = 500

I	1	XXXII	32	LXIII	63	XCIV	94
II	2	XXXIII	33	LXIV	64	XCV	95
III	3	XXXIV	34	LXV	65	XCVI	96
IV	4	XXXV	35	LXVI	66	XCVII	97
V	5	XXXVI	36	LXVII	67	XCVIII	98
VI	6	XXXVII	37	LXVIII	68	XCIX	99
VII	7	XXXVIII	38	LXIX	69	C	100
VIII	8	XXXIX	39	LXX	70
IX	9	XL	40	LXXI	71	EX.
X	10	XLI	41	LXXII	72	DI	501
XI	11	XLII	42	LXXIII	73	DL	550
XII	12	XLIII	43	LXXIV	74	DXXX	530
XIII	13	XLIV	44	LXXV	75	DCCVII	707
XIV	14	XLV	45	LXXVI	76	DCCCXC	890
XV	15	XLVI	46	LXXVII	77	MD	1500
XVI	16	XLVII	47	LXXVIII	78	MDCCC	1800
XVII	17	XLVIII	48	LXXIX	79	CM	900
XVIII	18	XLIX	49	LXXX	80
XIX	19	L	50	LXXXI	81
XX	20	LI	51	LXXXII	82
XXI	21	LII	52	LXXXIII	83
XXII	22	LIII	53	LXXXIV	84
XXIII	23	LIV	54	LXXXV	85
XXIV	24	LV	55	LXXXVI	86
XXV	25	LVI	56	LXXXVII	87
XXVI	26	LVII	57	LXXXVIII	88
XXVII	27	LVIII	58	LXXXIX	89
XXVIII	28	LIX	59	XC	90
XXIX	29	LX	60	XCI	91
XXX	30	LXI	61	XCII	92
XXXI	31	LXII	62	XCIII	93

既然各个位的表示方法固定，并且位与位之间并不影响，所以用数组将他们罗列出来。转换是从低位到高位。

string cost[][10] = {{"","I","II","III","IV","V","VI","VII","VIII","IX"},
{"","X","XX","XXX","XL","L","LX","LXX","LXXX","XC"},
{"","C","CC","CCC","CD","D","DC","DCC","DCCC","CM"},
{"","M","MM","MMM",""}};

代码：

class Solution {
public:
    string intToRoman(int num) {
        string cost[][10] = {{"","I","II","III","IV","V","VI","VII","VIII","IX"},
                             {"","X","XX","XXX","XL","L","LX","LXX","LXXX","XC"},
                             {"","C","CC","CCC","CD","D","DC","DCC","DCCC","CM"},
                             {"","M","MM","MMM",""}};
        int n;
        int idx = 0;
        string roman = "", tmp = "";
        while(num!=0)
        {
            n = num%10;
            num /= 10;
            tmp = cost[idx][n];
            roman = tmp + roman;
            idx++;
        }
        return roman;
    }
};

注意：借助二维数组来对应不同位的不同权值字母。