Problem Description
Given an integer, convert it to a Roman numeral. Roman numerals are represented by seven different symbols with specific values, and the conversion follows certain rules regarding their combination.
Key Insights
- Roman numerals use a combination of symbols that represent values.
- Subtractive forms are used for specific values (e.g., 4 is represented as IV, 9 as IX).
- Symbols representing values can only be used consecutively a certain number of times (e.g., I, X, C, and M can be repeated up to three times).
- The algorithm must efficiently map integer values to their corresponding Roman numeral representations.
Space and Time Complexity
Time Complexity: O(1) - The algorithm processes a fixed set of symbols regardless of the input size. Space Complexity: O(1) - Only a constant amount of space is used for the output string and variables.
Solution
To convert an integer to a Roman numeral, we can use a greedy algorithm that iterates over predefined values and symbols in descending order. For each value, we append the corresponding symbol to the result while subtracting that value from the integer until the integer is reduced to zero. This approach efficiently builds the Roman numeral representation.