012 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, two is written as II in Roman numeral, just two one's added together. Twelve is written as, XII, which is simplyX + II. The number twenty seven 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) andX (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. Input is guaranteed to be within the range from 1 to 3999.

Example：

Input: 3
Output: "III"

Input: 4
Output: "IV"

Input: 9
Output: "IX"

Input: 58
Output: "LVIII"
Explanation: C = 100, L = 50, XXX = 30 and III = 3.

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

解释下题目：

就是给定一个数字，把它转成罗马数字，注意给定的数字是从1开始到3999

1. 分解的方法

实际耗时：48ms

public String intToRoman(int num) {
        StringBuilder result = new StringBuilder();
        if (num < 10) {
            //只有一位数的时候，注意题设说了从1开始
            return oneNumberToRoman(num);
        } else if (num < 100) {
            //两位数的时候
            return twoNumberToRoman(num);
        } else if (num < 1000) {
            //三位数的时候
            return threeNumberToRoman(num);
        } else {
            //四位数的时候
            return fourNumberToRoman(num);
        }
    }

    public static String oneNumberToRoman(int num) {
        if (1 == num) {
            return "I";
        }
        if (2 == num) {
            return "II";
        }
        if (3 == num) {
            return "III";
        }
        if (4 == num) {
            return "IV";
        }
        if (5 == num) {
            return "V";
        }
        if (6 == num) {
            return "VI";
        }
        if (7 == num) {
            return "VII";
        }
        if (8 == num) {
            return "VIII";
        }
        if (9 == num) {
            return "IX";
        }
        return "";
    }

    public static String twoNumberToRoman(int num) {
        //x是十位数
        int x = num / 10;
        String result = "";
        if (1 == x) {
            result = "X";
        }
        if (2 == x) {
            result = "XX";
        }
        if (3 == x) {
            result = "XXX";
        }
        if (4 == x) {
            result = "XL";
        }
        if (5 == x) {
            result = "L";
        }
        if (6 == x) {
            result = "LX";
        }
        if (7 == x) {
            result = "LXX";
        }
        if (8 == x) {
            result = "LXXX";
        }
        if (9 == x) {
            result = "XC";
        }

        return result + oneNumberToRoman(num % 10);

    }

    public static String threeNumberToRoman(int num) {
        //c是百位数
        int c = num / 100;
        String result = "";
        if (1 == c) {
            result = "C";
        }
        if (2 == c) {
            result = "CC";
        }
        if (3 == c) {
            result = "CCC";
        }
        if (4 == c) {
            result = "CD";
        }
        if (5 == c) {
            result = "D";
        }
        if (6 == c) {
            result = "DC";
        }
        if (7 == c) {
            result = "DCC";
        }
        if (8 == c) {
            result = "DCCC";
        }
        if (9 == c) {
            result = "CM";
        }

        return result + twoNumberToRoman(num % 100);

    }

    public static String fourNumberToRoman(int num) {
        //m是千位数
        int m = num / 1000;
        String result = "";
        if (1 == m) {
            result = "M";
        }
        if (2 == m) {
            result = "MM";
        }
        if (3 == m) {
            result = "MMM";
        }
        return result + threeNumberToRoman(num % 1000);

    }

  如果想知道1444这个数字是怎么转成罗马字的，我需要首先知道1000和444是怎么转成罗马字的；如果想知道444这个数字是怎么转成罗马字的，我需要知道400和44是怎么转成罗马字的，以此类推。

时间复杂度O(1)

空间复杂度O(1)

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2. 直接用数组来做，原解法点这里

实际耗时：53ms

public static String intToRoman2(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 % 1000) / 100] + X[(num % 100) / 10] + I[num % 10];
    }

  代码简单了很多，但是思路是一样的。

时间复杂度O(1)

空间复杂度O(1)

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