12. Integer to Roman #

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, 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 an integer, convert it to a roman numeral.

Example 1:

Input: num = 3
Output: "III"

Example 2:

Input: num = 4
Output: "IV"

Example 3:

Input: num = 9
Output: "IX"

Example 4:

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

Example 5:

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

Constraints:

• 1 <= num <= 3999

Problem Summary #

Normally, in Roman numerals, smaller numbers are placed to the right of larger numbers. However, there are special cases; for example, 4 is not written as IIII, but as IV. The number 1 is on the left of the number 5, so the represented value is equal to the larger number 5 minus the smaller number 1, resulting in 4. Similarly, the number 9 is represented as IX. This special rule applies only 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 an integer, convert it to a Roman numeral. The input is guaranteed to be within the range from 1 to 3999.

Solution Approach #

• According to the problem statement, larger numbers should be chosen first, so the solution uses a greedy algorithm. Put the Roman numerals within the range 1-3999 into an array from largest to smallest, then choose from beginning to end to convert the integer into a Roman numeral.

Code #

package leetcode

func intToRoman(num int) string {
	values := []int{1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1}
	symbols := []string{"M", "CM", "D", "CD", "C", "XC", "L", "XL", "X", "IX", "V", "IV", "I"}
	res, i := "", 0
	for num != 0 {
		for values[i] > num {
			i++
		}
		num -= values[i]
		res += symbols[i]
	}
	return res
}