Largest Roman Numeral possible by rearranging characters of a given string
Given a string S of length N, the task is to print the highest roman number possible by rearranging the characters of the given string, if the given string is a valid roman number. If found to be not possible, then print “Invalid”.
Examples:
Input: S = “MCMIV”
Output: MMCVI
Explanation: The given string S is valid Roman numeral. Rearranging characters to obtain the string “MMCVI” generates the highest roman numeral possible using given set of characters.Input: S = “XCYVM”
Output: Invalid
Approach: The idea is to use the sorting by the second element. Follow the steps below to solve the problem:
- Iterate over the characters of the string.
- Check if the string contains any character other than { ‘I’, ‘V’, ‘X’, ‘L’, ‘C’, ‘D’, ‘M’ } or not. If found to be true, then print “Invalid”.
- Otherwise, sort the string in descending order with respect to the decimal value of the characters of the string.
- Now convert the roman value to equivalent decimal and store it in a variable, say X.
- Now find the equivalent roman value of the decimal number X and store it in a variable, say Y.
- Now print the string S if S is found to be equal to Y. Otherwise print “Invalid”.
Below is the implementation of the above approach:
C++
// C++ implementation of the above approach#include <bits/stdc++.h>using namespace std;// Function to find decimal// value of a roman characterint charVal(char c){ if (c == 'I') return 1; if (c == 'V') return 5; if (c == 'X') return 10; if (c == 'L') return 50; if (c == 'C') return 100; if (c == 'D') return 500; if (c == 'M') return 1000; return -1;}// Function to convert string representing// roman number to equivalent decimal valueint romanToDec(string S){ // Stores the decimal value // of the string S int res = 0; // Stores the size of the S int n = S.size(); // Update res res = charVal(S[n - 1]); // Traverse the string for (int i = n - 2; i >= 0; i--) { if (charVal(S[i]) < charVal(S[i + 1])) res -= charVal(S[i]); else res += charVal(S[i]); } // Return res return res;}// Function to convert decimal// to equivalent roman numeralstring DecToRoman(int number){ // Stores the string string res = ""; // Stores all the digit values of a roman digit int num[] = { 1, 4, 5, 9, 10, 40, 50, 90, 100, 400, 500, 900, 1000 }; string sym[] = { "I", "IV", "V", "IX", "X", "XL", "L", "XC", "C", "CD", "D", "CM", "M" }; int i = 12; // Iterate while number // is greater than 0 while (number > 0) { int div = number / num[i]; number = number % num[i]; while (div--) { res += sym[i]; } i--; } // Return res return res;}// Function to sort the string// in descending order of values// assigned to charactersbool compare(char x, char y){ // Return character with // highest decimal value int val_x = charVal(x); int val_y = charVal(y); return (val_x > val_y);}// Function to find largest roman// value possible by rearranging// the characters of the stringstring findLargest(string S){ // Stores all roman characters set<char> st = { 'I', 'V', 'X', 'L', 'C', 'D', 'M' }; // Traverse the string for (auto x : S) { // If X is not found if (st.find(x) == st.end()) return "Invalid"; } sort(S.begin(), S.end(), compare); // Stores the decimal value // of the roman number int N = romanToDec(S); // Find the roman value equivalent // to the decimal value of N string R = DecToRoman(N); if (S != R) return "Invalid"; // Return result return S;}// Driver Codeint main(){ string S = "MCMIV"; cout << findLargest(S);} |
Java
// Java program for the above approachimport java.io.*;import java.lang.*;import java.util.*;class GFG{// Function to find decimal// value of a roman characterstatic int charVal(char c){ if (c == 'I') return 1; if (c == 'V') return 5; if (c == 'X') return 10; if (c == 'L') return 50; if (c == 'C') return 100; if (c == 'D') return 500; if (c == 'M') return 1000; return -1;}// Function to convert string representing// roman number to equivalent decimal valuestatic int romanToDec(String S){ // Stores the decimal value // of the string S int res = 0; // Stores the size of the S int n = S.length(); // Update res res = charVal(S.charAt(n - 1)); // Traverse the string for(int i = n - 2; i >= 0; i--) { if (charVal(S.charAt(i)) < charVal(S.charAt(i + 1))) res -= charVal(S.charAt(i)); else res += charVal(S.charAt(i)); } // Return res return res;}// Function to convert decimal// to equivalent roman numeralstatic String DecToRoman(int number){ // Stores the string String res = ""; // Stores all the digit values of a roman digit int num[] = { 1, 4, 5, 9, 10, 40, 50, 90, 100, 400, 500, 900, 1000 }; String sym[] = { "I", "IV", "V", "IX", "X", "XL", "L", "XC", "C", "CD", "D", "CM", "M" }; int i = 12; // Iterate while number // is greater than 0 while (number > 0) { int div = number / num[i]; number = number % num[i]; while (div-- > 0) { res += sym[i]; } i--; } // Return res return res;}// Function to find largest roman// value possible by rearranging// the characters of the stringstatic String findLargest(String S){ char arr[] = { 'I', 'V', 'X', 'L', 'C', 'D', 'M' }; // Stores all roman characters Set<Character> st = new HashSet<>(); for(char x : arr) st.add(x); Character s[] = new Character[S.length()]; for(int i = 0; i < S.length(); i++) s[i] = S.charAt(i); // Traverse the string for(char x : s) { // If X is not found if (!st.contains(x)) return "Invalid"; } Arrays.sort(s, new Comparator<Character>() { @Override public int compare(Character x, Character y) { return charVal(y) - charVal(x); } }); String ss = ""; for(char ch : s) ss += ch; // Stores the decimal value // of the roman number int N = romanToDec(ss); // Find the roman value equivalent // to the decimal value of N String R = DecToRoman(N); if (!ss.equals(R)) return "Invalid"; // Return result return ss;}// Driver Codepublic static void main(String[] args){ // Input String S = "MCMIV"; int N = S.length(); System.out.println(findLargest(S));}}// This code is contributed by Kingash |
Output:
MMCVI
Time Complexity: O(N*log(N))
Auxiliary Space: O(1)
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