0013. 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 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 a roman numeral, convert it to an integer.

Example 1:

Input: s = "III"
Output: 3

Example 2:

Input: s = "IV"
Output: 4

Example 3:

Input: s = "IX"
Output: 9

Example 4:

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

Example 5:

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].

Analysis

for 1 to 9 (one digit): 1: I, 2: II, 3: III, 4: IV, 5: V, 6: VI, 7: VII, 8: VIII, 9: IX.

for 10 to 99 (two digits): 10: X, 20: XX, 30: XXX, 40: XL, 50: L, 60: LX, 70: LXX, 80: LXXX, 90: XC.

for 100 to 999 (three digits): 100: C, 200: CC, 300: CCC, 400: CD, 500: D, 600: DC, 700: DCC, 800: DCCC, 900: CM.

for 1000 to 3999 (four digits): 1000: M, 2000: MM, 3000: MMM

Notice that only 4, 40 and 400 are having the roman character reversed (smaller mapping is in the front the larger mapping), so we only need to handle the special case for that.

Code

class Solution {
public:
    int romanToInt(string s) {
        unordered_map<char, int> hash;
        hash['I'] = 1, hash['V'] = 5;
        hash['X'] = 10, hash['L'] = 50;
        hash['C'] = 100, hash['D'] = 500;
        hash['M'] = 1000;

        int res = 0;
        for (int i = 0; i < s.size(); i ++ ) {
            if (i + 1 < s.size() && hash[s[i]] < hash[s[i + 1]]) // compare neighour character
                res -= hash[s[i]]; // if less then -
            else
                res += hash[s[i]]; // normal case then +
        }

        return res;
    }
};

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Last update: April 1, 2022