Understanding the Problem
We are given a string that represents a Roman numeral. Our task is to convert this Roman numeral into its integer equivalent.
To solve this, we need to understand two key things:
- Each Roman character maps to a fixed integer value (like
I = 1
, V = 5
, X = 10
, etc.).
- Sometimes, Roman numerals use a subtractive rule: a smaller numeral placed before a larger one means subtraction instead of addition (e.g.,
IV = 4
).
Step-by-Step Solution with Example
Step 1: Map Roman characters to values
We define a dictionary that maps each Roman numeral to its integer value:
const romanMap = {
'I': 1, 'V': 5, 'X': 10,
'L': 50, 'C': 100,
'D': 500, 'M': 1000
};
Step 2: Process characters from left to right
We initialize a variable total
to store the final result. We look at one character at a time and compare its value to the next one.
Step 3: Apply subtraction rule if needed
If the current character’s value is less than the next one, we subtract it. Otherwise, we add it.
Step 4: Walk through the example "MCMXCIV"
Let's break this down step-by-step for clarity:
M = 1000 → Add → total = 1000
C = 100, M = 1000 → C < M → Subtract → total = 1000 - 100 = 900
M = 1000 → Already processed with previous → skip
X = 10, C = 100 → X < C → Subtract → total = 900 - 10 = 890
C = 100 → Already processed with previous → skip
I = 1, V = 5 → I < V → Subtract → total = 890 - 1 = 889
V = 5 → Already processed with previous → skip
Add all remaining values: 1000 + 900 + 90 + 4 = 1994
Step 5: Return the final total
After looping through the string, return the total computed value.
Edge Cases
- Empty string: Return
0
. There's nothing to process.
- Single character: Just return its mapped value directly. E.g.,
"V"
→ 5
- Invalid characters: Ideally, these should be caught and handled (e.g., with an error or by skipping them).
- Incorrect ordering: If subtractive notation is used incorrectly (like
IC
), you may choose to return an error or ignore it depending on requirements.
Finally
This approach is easy to implement and intuitive once we understand how Roman numerals work. By processing the string from left to right and applying the subtractive rule carefully, we can accurately convert the numeral to its integer form in linear time, O(n).
It’s a perfect example of combining simple logic with careful attention to character relationships for accurate results.
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