Dado un número romano, la tarea es encontrar su valor decimal correspondiente.
Ejemplo :
Input: IX Output: 9 IX is a Roman symbol which represents 9 Input: XL Output: 40 XL is a Roman symbol which represents 40 Input: MCMIV Output: 1904 M is a thousand, CM is nine hundred and IV is four
Los números romanos se basan en los siguientes símbolos.
SYMBOL VALUE I 1 IV 4 V 5 IX 9 X 10 XL 40 L 50 XC 90 C 100 CD 400 D 500 CM 900 M 1000
Enfoque: Un número en números romanos es una string de estos símbolos escritos en orden descendente (por ejemplo, la M primero, seguida de la D, etc.). Sin embargo, en algunos casos específicos, para evitar que cuatro caracteres se repitan en sucesión (como IIII o XXXX), la notación sustractiva se usa a menudo de la siguiente manera:
- Coloqué antes de V o X indica uno menos, entonces cuatro es IV (uno menos que 5) y 9 es IX (uno menos que 10).
- X colocado antes de L o C indica diez menos, por lo que cuarenta es XL (10 menos que 50) y 90 es XC (diez menos que cien).
- C colocada antes de D o M indica cien menos, por lo que cuatrocientos es CD (cien menos que quinientos) y novecientos es CM (cien menos que mil).
Algoritmo para convertir números romanos a números enteros:
- Divida la string de números romanos en símbolos romanos (carácter).
- Convierta cada símbolo de números romanos en el valor que representa.
- Tome el símbolo uno por uno desde el índice 0:
- Si el valor actual del símbolo es mayor o igual que el valor del siguiente símbolo, agregue este valor al total acumulado.
- de lo contrario, reste este valor sumando el valor del siguiente símbolo al total acumulado.
A continuación se muestra la implementación del algoritmo anterior:
C++
// Program to convert Roman
// Numerals to Numbers
#include <bits/stdc++.h>
using namespace std;
// This function returns value
// of a Roman symbol
int value(char r)
{
if (r == 'I')
return 1;
if (r == 'V')
return 5;
if (r == 'X')
return 10;
if (r == 'L')
return 50;
if (r == 'C')
return 100;
if (r == 'D')
return 500;
if (r == 'M')
return 1000;
return -1;
}
// Returns decimal value of
// roman numaral
int romanToDecimal(string& str)
{
// Initialize result
int res = 0;
// Traverse given input
for (int i = 0; i < str.length(); i++) {
// Getting value of symbol s[i]
int s1 = value(str[i]);
if (i + 1 < str.length()) {
// Getting value of symbol s[i+1]
int s2 = value(str[i + 1]);
// Comparing both values
if (s1 >= s2) {
// Value of current symbol
// is greater or equal to
// the next symbol
res = res + s1;
}
else {
// Value of current symbol is
// less than the next symbol
res = res + s2 - s1;
i++;
}
}
else {
res = res + s1;
}
}
return res;
}
// Driver Code
int main()
{
// Considering inputs given are valid
string str = "MCMIV";
cout << "Integer form of Roman Numeral is "
<< romanToDecimal(str) << endl;
return 0;
}
C
// Program to convert Roman
// Numerals to Numbers
#include <stdio.h>
#include <string.h>
// This function returns value
// of a Roman symbol
int value(char r)
{
if (r == 'I')
return 1;
if (r == 'V')
return 5;
if (r == 'X')
return 10;
if (r == 'L')
return 50;
if (r == 'C')
return 100;
if (r == 'D')
return 500;
if (r == 'M')
return 1000;
return -1;
}
// Returns decimal value of
// roman numaral
int romanToDecimal(char str[])
{
// Initialize result
int res = 0;
// Traverse given input
for (int i = 0; i < strlen(str); i++)
{
// Getting value of symbol s[i]
int s1 = value(str[i]);
if (i + 1 < strlen(str))
{
// Getting value of symbol s[i+1]
int s2 = value(str[i + 1]);
// Comparing both values
if (s1 >= s2)
{
// Value of current symbol
// is greater or equal to
// the next symbol
res = res + s1;
}
else
{
// Value of current symbol is
// less than the next symbol
res = res + s2 - s1;
i++;
}
}
else {
res = res + s1;
}
}
return res;
}
// Driver Code
int main()
{
// Considering inputs given are valid
char str[10] = "MCMIV";
printf("Integer form of Roman Numeral is %d",romanToDecimal(str));
return 0;
}
Java
// Program to convert Roman
// Numerals to Numbers
import java.util.*;
public class RomanToNumber {
// This function returns
// value of a Roman symbol
int value(char r)
{
if (r == 'I')
return 1;
if (r == 'V')
return 5;
if (r == 'X')
return 10;
if (r == 'L')
return 50;
if (r == 'C')
return 100;
if (r == 'D')
return 500;
if (r == 'M')
return 1000;
return -1;
}
// Finds decimal value of a
// given roman numeral
int romanToDecimal(String str)
{
// Initialize result
int res = 0;
for (int i = 0; i < str.length(); i++) {
// Getting value of symbol s[i]
int s1 = value(str.charAt(i));
// Getting value of symbol s[i+1]
if (i + 1 < str.length()) {
int s2 = value(str.charAt(i + 1));
// Comparing both values
if (s1 >= s2) {
// Value of current symbol
// is greater or equalto
// the next symbol
res = res + s1;
}
else {
// Value of current symbol is
// less than the next symbol
res = res + s2 - s1;
i++;
}
}
else {
res = res + s1;
}
}
return res;
}
// Driver Code
public static void main(String args[])
{
RomanToNumber ob = new RomanToNumber();
// Considering inputs given are valid
String str = "MCMIV";
System.out.println("Integer form of Roman Numeral"
+ " is "
+ ob.romanToDecimal(str));
}
}
Python
# Python program to convert Roman Numerals
# to Numbers
# This function returns value of each Roman symbol
def value(r):
if (r == 'I'):
return 1
if (r == 'V'):
return 5
if (r == 'X'):
return 10
if (r == 'L'):
return 50
if (r == 'C'):
return 100
if (r == 'D'):
return 500
if (r == 'M'):
return 1000
return -1
def romanToDecimal(str):
res = 0
i = 0
while (i < len(str)):
# Getting value of symbol s[i]
s1 = value(str[i])
if (i + 1 < len(str)):
# Getting value of symbol s[i + 1]
s2 = value(str[i + 1])
# Comparing both values
if (s1 >= s2):
# Value of current symbol is greater
# or equal to the next symbol
res = res + s1
i = i + 1
else:
# Value of current symbol is greater
# or equal to the next symbol
res = res + s2 - s1
i = i + 2
else:
res = res + s1
i = i + 1
return res
# Driver code
print("Integer form of Roman Numeral is"),
print(romanToDecimal("MCMIV"))
C#
// C# Program to convert Roman
// Numerals to Numbers
using System;
class GFG {
// This function returns value
// of a Roman symbol
public virtual int value(char r)
{
if (r == 'I')
return 1;
if (r == 'V')
return 5;
if (r == 'X')
return 10;
if (r == 'L')
return 50;
if (r == 'C')
return 100;
if (r == 'D')
return 500;
if (r == 'M')
return 1000;
return -1;
}
// Finds decimal value of a
// given roman numeral
public virtual int romanToDecimal(string str)
{
// Initialize result
int res = 0;
for (int i = 0; i < str.Length; i++) {
// Getting value of symbol s[i]
int s1 = value(str[i]);
// Getting value of symbol s[i+1]
if (i + 1 < str.Length) {
int s2 = value(str[i + 1]);
// Comparing both values
if (s1 >= s2) {
// Value of current symbol is greater
// or equalto the next symbol
res = res + s1;
}
else {
res = res + s2 - s1;
i++; // Value of current symbol is
// less than the next symbol
}
}
else {
res = res + s1;
i++;
}
}
return res;
}
// Driver Code
public static void Main(string[] args)
{
GFG ob = new GFG();
// Considering inputs given are valid
string str = "MCMIV";
Console.WriteLine("Integer form of Roman Numeral"
+ " is "
+ ob.romanToDecimal(str));
}
}
// This code is contributed by Shrikant13
PHP
<?php
// Program to convert Roman
// Numerals to Numbers
// This function returns
// value of a Roman symbol
function value($r)
{
if ($r == 'I')
return 1;
if ($r == 'V')
return 5;
if ($r == 'X')
return 10;
if ($r == 'L')
return 50;
if ($r == 'C')
return 100;
if ($r == 'D')
return 500;
if ($r == 'M')
return 1000;
return -1;
}
// Returns decimal value
// of roman numeral
function romanToDecimal(&$str)
{
// Initialize result
$res = 0;
// Traverse given input
for ($i = 0; $i < strlen($str); $i++)
{
// Getting value of
// symbol s[i]
$s1 = value($str[$i]);
if ($i+1 < strlen($str))
{
// Getting value of
// symbol s[i+1]
$s2 = value($str[$i + 1]);
// Comparing both values
if ($s1 >= $s2)
{
// Value of current symbol
// is greater or equal to
// the next symbol
$res = $res + $s1;
}
else
{
$res = $res + $s2 - $s1;
$i++; // Value of current symbol is
// less than the next symbol
}
}
else
{
$res = $res + $s1;
$i++;
}
}
return $res;
}
// Driver Code
// Considering inputs
// given are valid
$str ="MCMIV";
echo "Integer form of Roman Numeral is ",
romanToDecimal($str), "\n";
// This code is contributed by ajit
?>
Javascript
<script>
// Program to convert Roman
// Numerals to Numberspublic
// This function returns
// value of a Roman symbol
function value(r) {
if (r == 'I')
return 1;
if (r == 'V')
return 5;
if (r == 'X')
return 10;
if (r == 'L')
return 50;
if (r == 'C')
return 100;
if (r == 'D')
return 500;
if (r == 'M')
return 1000;
return -1;
}
// Finds decimal value of a
// given roman numeral
function romanToDecimal( str)
{
// Initialize result
var res = 0;
for (i = 0; i < str.length; i++)
{
// Getting value of symbol s[i]
var s1 = value(str.charAt(i));
// Getting value of symbol s[i+1]
if (i + 1 < str.length) {
var s2 = value(str.charAt(i + 1));
// Comparing both values
if (s1 >= s2) {
// Value of current symbol
// is greater or equalto
// the next symbol
res = res + s1;
}
else
{
// Value of current symbol is
// less than the next symbol
res = res + s2 - s1;
i++;
}
} else {
res = res + s1;
}
}
return res;
}
// Driver Code
// Considering inputs given are valid
var str = "MCMIV";
document.write("Integer form of Roman Numeral"
+ " is " + romanToDecimal(str));
// This code is contributed by umadevi9616
</script>
Producción
Integer form of Roman Numeral is 1904
Análisis de Complejidad:
- Complejidad de tiempo: O(n), donde n es la longitud de la string.
Solo se requiere un recorrido de la string. - Complejidad espacial: O(1).
Como no se requiere espacio adicional.
Otra solución –
C++
// Program to convert Roman
// Numerals to Numbers
#include <bits/stdc++.h>
using namespace std;
// This function returns value
// of a Roman symbol
int romanToDecimal(string& str)
{
map<char, int> m;
m.insert({ 'I', 1 });
m.insert({ 'V', 5 });
m.insert({ 'X', 10 });
m.insert({ 'L', 50 });
m.insert({ 'C', 100 });
m.insert({ 'D', 500 });
m.insert({ 'M', 1000 });
int sum = 0;
for (int i = 0; i < str.length(); i++)
{
/*If present value is less than next value,
subtract present from next value and add the
resultant to the sum variable.*/
if (m[str[i]] < m[str[i + 1]])
{
sum+=m[str[i+1]]-m[str[i]];
i++;
continue;
}
sum += m[str[i]];
}
return sum;
}
// Driver Code
int main()
{
// Considering inputs given are valid
string str = "MCMIV";
cout << "Integer form of Roman Numeral is "
<< romanToDecimal(str) << endl;
return 0;
}
Java
// Program to convert Roman
// Numerals to Numbers
import java.util.Map;
import java.util.HashMap;
class GFG{
private static final Map<Character,
Integer> roman = new HashMap<Character,
Integer>()
{{
put('I', 1);
put('V', 5);
put('X', 10);
put('L', 50);
put('C', 100);
put('D', 500);
put('M', 1000);
}};
// This function returns value
// of a Roman symbol
private static int romanToInt(String s)
{
int sum = 0;
int n = s.length();
for(int i = 0; i < n; i++)
{
// If present value is less than next value,
// subtract present from next value and add the
// resultant to the sum variable.
if (i != n - 1 && roman.get(s.charAt(i)) <
roman.get(s.charAt(i + 1)))
{
sum += roman.get(s.charAt(i + 1)) -
roman.get(s.charAt(i));
i++;
}
else
{
sum += roman.get(s.charAt(i));
}
}
return sum;
}
// Driver Code
public static void main(String[] args)
{
// Considering inputs given are valid
String input = "MCMIV";
System.out.print("Integer form of Roman Numeral is " +
romanToInt(input));
}
}
// This code is contributed by rahuldevgarg
Python3
# Program to convert Roman
# Numerals to Numbers
roman = {}
roman['I'] = 1
roman['V'] = 5
roman['X'] = 10
roman['L'] = 50
roman['C'] = 100
roman['D'] = 500
roman['M'] = 1000
# This function returns value
# of a Roman symbol
def romanToInt(s):
sum = 0
n = len(s)
i = 0
while i < n :
# If present value is less than next value,
# subtract present from next value and add the
# resultant to the sum variable.
# print(roman[s[i]],roman[s[i+1]])
if (i != n - 1 and roman[s[i]] < roman[s[i + 1]]):
sum += roman[s[i + 1]] - roman[s[i]]
i += 2
continue
else:
sum += roman[s[i]]
i += 1
return sum
# Driver Code
# Considering inputs given are valid
input = "MCMIV"
print(f"Integer form of Roman Numeral is {romanToInt(input)}")
# This code is contributed by shinjanpatra
C#
// Program to convert Roman
// Numerals to Numbers
using System;
using System.Collections.Generic;
public class GFG {
static Dictionary<char, int> roman = new Dictionary<char, int>();
// This function returns value
// of a Roman symbol
public static int romanToInt(String s) {
int sum = 0;
int n = s.Length;
for (int i = 0; i < n; i++) {
// If present value is less than next value,
// subtract present from next value and add the
// resultant to the sum variable.
if (i != n - 1 && roman[s[i]] < roman[s[i + 1]]) {
sum += roman[s[i + 1]] - roman[s[i]];
i++;
} else {
sum += roman[s[i]];
}
}
return sum;
}
// Driver Code
public static void Main(String[] args) {
roman['I'] = 1;
roman['V'] =5;
roman['X'] =10;
roman['L'] =50;
roman['C'] =100;
roman['D'] =500;
roman['M'] =1000;
// Considering inputs given are valid
String input = "MCMIV";
Console.Write("int form of Roman Numeral is " + romanToInt(input));
}
}
// This code is contributed by Rajput-Ji
Javascript
<script>
// Program to convert Roman
// Numerals to Numbers
var roman = new Map() ;
roman.set('I', 1);
roman.set('V', 5);
roman.set('X', 10);
roman.set('L', 50);
roman.set('C', 100);
roman.set('D', 500);
roman.set('M', 1000);
// This function returns value
// of a Roman symbol
function romanToInt( s) {
var sum = 0;
var n = s.length;
for (i = 0; i < n; i++) {
// If present value is less than next value,
// subtract present from next value and add the
// resultant to the sum variable.
if (i != n - 1 && roman.get(s.charAt(i)) < roman.get(s.charAt(i + 1))) {
sum += roman.get(s.charAt(i + 1)) - roman.get(s.charAt(i));
i++;
} else {
sum += roman.get(s.charAt(i));
}
}
return sum;
}
// Driver Code
// Considering inputs given are valid
var input = "MCMIV";
document.write("Integer form of Roman Numeral is " + romanToInt(input));
// This code is contributed by Rajput-Ji
</script>
Producción
Integer form of Roman Numeral is 1904
Complejidad temporal – O(N)
Espacio auxiliar – O(1)
Otra solución: código más corto usando python
Java
// Java Program to convert Roman
// Numerals to Numbers
import java.io.*;
import java.util.*;
class GFG
{
public static void romanToInt(String s)
{
Map<Character,Integer> translations=new HashMap<Character,Integer>();
//Adding elements to map
translations.put('I',1);
translations.put('V',5);
translations.put('X',10);
translations.put('L',50);
translations.put('C',100);
translations.put('D',500);
translations.put('M',1000);
s = s.replace("IV","IIII");
s = s.replace("IX","VIIII");
s = s.replace("XL","XXXX");
s = s.replace("XC","LXXXX");
s = s.replace("CD","CCCC");
s = s.replace("CM","DCCCC");
int number = 0;
for (int i = 0; i < s.length(); i++)
{
number = number + (translations.get(s.charAt(i)));
}
System.out.println(number);
}
public static void main (String[] args)
{
romanToInt("MCMIV");
}
}
// This code is contributed by kothavvsaakash
C#
// C# Program to convert Roman
// Numerals to Numbers
using System;
using System.Collections.Generic;
using System.Collections;
public class GFG {
public static void romanToInt(String s)
{
var translations = new Dictionary<char, int>();
// Adding elements to map
translations['I'] = 1;
translations['V'] = 5;
translations['X'] = 10;
translations['L'] = 50;
translations['C'] = 100;
translations['D'] = 500;
translations['M'] = 1000;
s = s.Replace("IV", "IIII");
s = s.Replace("IX", "VIIII");
s = s.Replace("XL", "XXXX");
s = s.Replace("XC", "LXXXX");
s = s.Replace("CD", "CCCC");
s = s.Replace("CM", "DCCCC");
var number = 0;
for (int i = 0; i < s.Length; i++) {
number = number + (translations[s[i]]);
}
Console.WriteLine(number);
}
public static void Main(String[] args)
{
romanToInt("MCMIV");
}
}
// This code is contributed by Aarti_Rathi
Python3
def romanToInt(s):
translations = {
"I": 1,
"V": 5,
"X": 10,
"L": 50,
"C": 100,
"D": 500,
"M": 1000
}
number = 0
s = s.replace("IV", "IIII").replace("IX", "VIIII")
s = s.replace("XL", "XXXX").replace("XC", "LXXXX")
s = s.replace("CD", "CCCC").replace("CM", "DCCCC")
for char in s:
number += translations[char]
print(number)
romanToInt('MCMIV')
Javascript
<script>
function romanToInt(s){
let translations = new Map()
translations.set("I",1)
translations.set("V",5)
translations.set("X",10)
translations.set("L",50)
translations.set("C",100)
translations.set("D",500)
translations.set("M",1000)
let number = 0
s = s.replace("IV", "IIII").replace("IX", "VIIII")
s = s.replace("XL", "XXXX").replace("XC", "LXXXX")
s = s.replace("CD", "CCCC").replace("CM", "DCCCC")
for(let char of s)
number += translations.get(char)
document.write(number)
}
romanToInt('MCMIV')
// code is contributed by shinjanpatra
</script>
Producción
1904
Complejidad temporal – O(N)
Espacio auxiliar – O(1)
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Publicación traducida automáticamente
Artículo escrito por GeeksforGeeks-1 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA