Integer to Roman using C++
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Explanation
-
Symbols and Values:
vector<string> symbols: Contains the Roman numeral symbols in descending order of their values.vector<int> values: Corresponding integer values for the Roman numeral symbols.
-
Conversion Loop:
- Loop through each value-symbol pair.
- Subtract the value from
numand add the corresponding symbol to the result string untilnumis less than the current value.
Example for num = 3749
- Start with
num = 3749. - Check the first value
1000:3749 >= 1000: Subtract1000from3749, addMto result.2749 >= 1000: Subtract1000from2749, addMto result.1749 >= 1000: Subtract1000from1749, addMto result.
- Move to the next value
900:749 >= 900: Skip.
- Move to the next value
500:749 >= 500: Subtract500from749, addDto result.
- Continue with the remaining values in a similar manner.
The final result is "MMMDCCXLIX", representing the integer 3749.
#include <vector>
#include <string>
#include <iostream>
using namespace std;
string intToRoman(int num) {
// Define Roman symbols and their values
vector<string> symbols = {
"M", "CM", "D", "CD", "C", "XC", "L", "XL", "X", "IX", "V", "IV", "I"
};
vector<int> values = {
1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1
};
string result = "";
for (int i = 0; i < values.size() && num > 0; ++i) {
while (num >= values[i]) {
num -= values[i]; // Subtract the current value from num
result += symbols[i]; // Append the corresponding symbol to result
}
}
return result;
}
int main() {
int num = 3749;
string result = intToRoman(num);
cout << result << " "; // Output: "MMMDCCXLIX"
return 0;
}
Detailed Explanation of num -= values[i]; and result += symbols[i];
The two lines inside the loop are responsible for building the Roman numeral string by repeatedly subtracting the appropriate value from num and adding the corresponding Roman numeral symbol to the result string.
while (num >= values[i]) {
num -= values[i];
result += symbols[i];
}
-
Condition:
while (num >= values[i])- Check if
numis greater than or equal to the current value. - If true, proceed to subtract the value from
num.
- Check if
-
Subtraction:
num -= values[i];- Subtract the current value from
num. - This reduces
numby the largest possible value that can still be subtracted without makingnumnegative.
- Subtract the current value from
-
Appending Symbol:
result += symbols[i];- Add the corresponding Roman numeral symbol to the
resultstring. - This constructs the Roman numeral representation incrementally.
- Add the corresponding Roman numeral symbol to the
Step-by-Step Execution
First Iteration (i = 0):
num = 3749
values[0] = 1000, symbols[0] = "M"
3749 >= 1000: True
Subtract 1000 from 3749 -> num = 2749
Append "M" to result -> result = "M"
2749 >= 1000: True
Subtract 1000 from 2749 -> num = 1749
Append "M" to result -> result = "MM"
1749 >= 1000: True
Subtract 1000 from 1749 -> num = 749
Append "M" to result -> result = "MMM"
749 >= 1000: False (move to next value)
Second Iteration (i = 1):
num = 749
values[1] = 900, symbols[1] = "CM"
749 >= 900: False (move to next value)
Third Iteration (i = 2):
num = 749
values[2] = 500, symbols[2] = "D"
749 >= 500: True
Subtract 500 from 749 -> num = 249
Append "D" to result -> result = "MMMD"
249 >= 500: False (move to next value)
Continue this process for the remaining values until num becomes 0.
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