Problem statement
Roman numerals are represented by seven 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 from largest to smallest and 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 beforeV
(5
) andX
(10
) to make4
and9
.X
can be placed beforeL
(50
) andC
(100
) to make40
and90
.C
can be placed beforeD
(500
) andM
(1000
) to make400
and900
.
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: Mapping and summing the values
And to treat the subtraction cases easier, you can iterate the string s
backward.
Code
#include <iostream>
#include <unordered_map>
using namespace std;
int romanToInt(string s) {
unordered_map<char, int> value = {
{'I', 1},
{'V', 5},
{'X', 10},
{'L', 50},
{'C', 100},
{'D', 500},
{'M', 1000}
};
int i = s.length() - 1;
int result = value[s[i--]];
while (i >= 0) {
if (value[s[i]] < value[s[i+1]]) {
result -= value[s[i--]];
} else {
result += value[s[i--]];
}
}
return result;
}
int main() {
cout << romanToInt("III") << endl;
cout << romanToInt("LVIII") << endl;
cout << romanToInt("MCMXCIV") << endl;
}
Output:
3
58
1994
Complexity
Runtime:
O(N)
whereN = s.length
.Extra space:
O(1)
(the mapvalue
is very small).
Conclusion
The problem is about encoding/decoding between a string and an integer, you could use an unordered_map here.
This is a very interesting problem since it is about history and mathematics. You can read more about it on Wikipedia.
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