Conversion Techniques
Fundamental Conversion Strategies
Roman numeral conversion involves two primary approaches:
- Integer to Roman Numeral
- Roman Numeral to Integer
graph TD
A[Conversion Techniques] --> B[Integer to Roman]
A --> C[Roman to Integer]
B --> D[Greedy Algorithm]
B --> E[Mapping Technique]
C --> F[Symbol Parsing]
C --> G[Value Accumulation]
Integer to Roman Conversion Methods
Greedy Approach
The greedy method systematically breaks down integers into largest possible Roman symbols:
Decimal Range |
Roman Strategy |
1000-3999 |
Use M repeatedly |
900-999 |
CM + Remaining |
500-899 |
D + Remaining |
400-499 |
CD + Remaining |
Mapping Technique
Implement conversion using predefined value-symbol mappings:
def int_to_roman(num):
values = [1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1]
symbols = ["M", "CM", "D", "CD", "C", "XC", "L", "XL", "X", "IX", "V", "IV", "I"]
roman = ''
for i, value in enumerate(values):
while num >= value:
roman += symbols[i]
num -= value
return roman
Roman to Integer Conversion Methods
Symbol Parsing Strategy
Analyze Roman numerals by comparing adjacent symbols:
def roman_to_int(s):
roman_values = {
'I': 1, 'V': 5, 'X': 10,
'L': 50, 'C': 100, 'D': 500, 'M': 1000
}
total = 0
prev_value = 0
for char in reversed(s):
current_value = roman_values[char]
if current_value >= prev_value:
total += current_value
else:
total -= current_value
prev_value = current_value
return total
Advanced Conversion Considerations
Edge Case Handling
- Validate input ranges
- Handle invalid Roman numeral sequences
- Manage zero and negative numbers
- Use lookup tables
- Implement efficient algorithms
- Minimize computational complexity
Practical Implementation Tips
- Choose appropriate conversion method based on use case
- Implement robust error checking
- Consider performance requirements
- Test with diverse input scenarios
By mastering these conversion techniques, developers can efficiently transform between integer and Roman numeral representations in Python, leveraging LabEx's programming expertise.