13. Roman to Integer

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 ones 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 a roman numeral, convert it to an integer.

Example 1:

Input: s = "III"
Output: 3
Explanation: III = 3.

Example 2:

Input: s = "LVIII"
Output: 58
Explanation: L = 50, V= 5, III = 3.

Example 3:

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

Constraints:

• 1 <= s.length <= 15
• s contains only the characters ('I', 'V', 'X', 'L', 'C', 'D', 'M').
• It is guaranteed that s is a valid roman numeral in the range [1, 3999].

Solution:

本题的难点在于处理六种特殊规则，但这六种特殊规则其实可以统一起来：

设 x=s[i−1], y=s[i]，这是两个相邻的罗马数字。 如果 x 的数值小于 y 的数值，那么 x 的数值要取相反数。例如 IV 中的 I 相当于 −1，CM 中的 C 相当于 −100。 把所有数值相加，即为答案。

代码实现时，可以创建一个哈希表（或者数组），把字符作为 key，对应的数值作为 value，从而避免写一堆 if-else.

class Solution {
    public int romanToInt(String s) {
        Map<Character, Integer> map = new HashMap<>();
        map.put('I', 1);
        map.put('V', 5);
        map.put('X', 10);
        map.put('L', 50);
        map.put('C', 100);
        map.put('D', 500);
        map.put('M', 1000);

        char[] sArray = s.toCharArray();
        int n = s.length();
        int result = 0;

        for (int i = 1; i < n; i++){
            int x = map.get(sArray[i - 1]);
            int y = map.get(sArray[i]);
            if (x < y){
                x = -x;
            }

            result = result + x;
        }

        return result + map.get(sArray[n - 1]);


    }
}
// TC: O(n)
// SC: O(n)

class Solution {
    public int romanToInt(String s) {
        Map<Character, Integer> map = new HashMap<>();
        map.put('I', 1);
        map.put('V', 5);
        map.put('X', 10);
        map.put('L', 50);
        map.put('C', 100);
        map.put('D', 500);
        map.put('M', 1000);

        int n  = s.length();

        int result = 0;
        int i = 1;
        char[] sArray = s.toCharArray();
        while(i < n){
            char first = sArray[i - 1];
            char second = sArray[i];
            int firstVal = map.get(first);
            int secondVal = map.get(second);

            if (firstVal < secondVal){
                int cur = secondVal - firstVal;
                result = result + cur;
                i = i + 2;
            }else{
                result = result + firstVal;
                i = i + 1;
            }
        }

        if (i == n){
            result = result + map.get(sArray[n-1]);
        }
        return result;
    }
}

// TC: O(n)
// SC: O(n)

class Solution {
    public int romanToInt(String s) {
        Map<String, Integer> map = new HashMap<>();
        map.put("I", 1);
        map.put("IV", 4);
        map.put("V", 5);
        map.put("IX", 9);
        map.put("X", 10);
        map.put("XL", 40);
        map.put("L", 50);
        map.put("XC", 90);
        map.put("C", 100);
        map.put("CD", 400);
        map.put("D", 500);
        map.put("CM", 900);
        map.put("M", 1000);

        int result = 0;
        int i = 1;
        int n = s.length();
        //  0123456
        // "MCMXCIV"
        //       i 
        //  
        while(i < n){
            String curTwo = s.substring(i - 1, i + 1); // MC // CM // XC // CI
            // III // I
            //   i 
            if (map.containsKey(curTwo)){
                result = result + map.get(curTwo);// 900
                i = i + 2; // 
            }else{
                result = result + map.get(s.substring(i - 1, i)); // M // C
                // X 1900 + 10 + 100   // 1 
                i = i + 1; // 
            }
        }

        if (i == n){
            result = result + map.get(s.substring(i - 1, i));
        }

        // 1900

        return result;
    }
}

// TC: O(n)
// SC: O(n)