13. Roman to Integer

Problem

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 simply X + 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) 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. Input is guaranteed to be within the range from 1 to 3999.

Example 1:

Input: "III"
Output: 3

Example 2:

Input: "IV"
Output: 4

Example 3:

Input: "IX"
Output: 9

Example 4:

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

Example 5:

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

Problem Summary

Roman numerals contain the following seven characters: I， V， X， L，C，D and M。

Character          Value
I             1
V             5
X             10
L             50
C             100
D             500
M             1000

For example， Roman numeral 2 is written as II ，which is two adjacent 1。12 is written as XII ，which is X + II 。 27 is written as  XXVII, which is XX + V + II 。

Under normal circumstances，smaller numbers in Roman numerals are on the right of larger numbers。But there are also special cases，for example 4 is not written as IIII，but as IV。The number 1 is on the left of the number 5，the represented number equals the value 4 obtained by subtracting the smaller number 1 from the larger number 5 。Similarly，the number 9 is represented as IX。This special rule only applies to the following six cases：

• I can be placed to the left of V (5) and X (10)，to represent 4 and 9。
• X can be placed to the left of L (50) and C (100)，to represent 40 and 90。 
• C can be placed to the left of D (500) and M (1000)，to represent 400 and 900。

Given a Roman numeral，convert it to an integer。The input is guaranteed to be within the range from 1 to 3999。

Solution Approach

• Given a Roman numeral，convert it to an integer。The input is guaranteed to be within the range from 1 to 3999。
• Simple problem。According to the character values of Roman numerals in the problem，just calculate the decimal number corresponding to the Roman numeral。

Code

package leetcode

var roman = map[string]int{
	"I": 1,
	"V": 5,
	"X": 10,
	"L": 50,
	"C": 100,
	"D": 500,
	"M": 1000,
}

func romanToInt(s string) int {
	if s == "" {
		return 0
	}
	num, lastint, total := 0, 0, 0
	for i := 0; i < len(s); i++ {
		char := s[len(s)-(i+1) : len(s)-i]
		num = roman[char]
		if num < lastint {
			total = total - num
		} else {
			total = total + num
		}
		lastint = num
	}
	return total
}