Roman to Integer Conversion in DSA Java

Mental Model

Roman numerals are letters that represent values. We add or subtract these values to get the number.

Analogy: Think of reading a price tag where some discounts apply if a smaller number comes before a bigger number, so you subtract instead of add.

R O M A N  N U M E R A L S
I(1) -> V(5) -> X(10) -> L(50) -> C(100) -> D(500) -> M(1000)

Dry Run Walkthrough

Input: Roman numeral: "MCMIV"

Goal: Convert the Roman numeral "MCMIV" to its integer value.

Step 1: Read 'M' (1000), add 1000 to total

total = 1000

Why: Start with the first symbol's value

Step 2: Read 'C' (100), next is 'M' (1000), since 100 < 1000, subtract 100

total = 1000 - 100 = 900

Why: Smaller before bigger means subtract

Step 3: Read 'M' (1000), next is 'I' (1), since 1000 > 1, add 1000

total = 900 + 1000 = 1900

Why: Bigger or equal means add

Step 4: Read 'I' (1), next is 'V' (5), since 1 < 5, subtract 1

total = 1900 - 1 = 1899

Why: Smaller before bigger means subtract

Step 5: Read 'V' (5), no next symbol, add 5

total = 1899 + 5 = 1904

Why: Last symbol always adds

Result:

total = 1904

Annotated Code

DSA Java

import java.util.Map;

public class RomanToInteger {
    private static final Map<Character, Integer> romanMap = Map.of(
        'I', 1,
        'V', 5,
        'X', 10,
        'L', 50,
        'C', 100,
        'D', 500,
        'M', 1000
    );

    public static int romanToInt(String s) {
        int total = 0;
        for (int i = 0; i < s.length(); i++) {
            int currentVal = romanMap.get(s.charAt(i));
            int nextVal = (i + 1 < s.length()) ? romanMap.get(s.charAt(i + 1)) : 0;
            if (currentVal < nextVal) {
                total -= currentVal; // subtract when smaller before bigger
            } else {
                total += currentVal; // add otherwise
            }
        }
        return total;
    }

    public static void main(String[] args) {
        String roman = "MCMIV";
        int result = romanToInt(roman);
        System.out.println(result);
    }
}

int currentVal = romanMap.get(s.charAt(i));

Get value of current Roman symbol

int nextVal = (i + 1 < s.length()) ? romanMap.get(s.charAt(i + 1)) : 0;

Get value of next symbol or 0 if none

if (currentVal < nextVal) {

Check if current is smaller than next to decide subtract

total -= currentVal; // subtract when smaller before bigger

Subtract current value from total

total += currentVal; // add otherwise

Add current value to total

Output

1904

Complexity Analysis

Time: O(n) because we scan each Roman character once

Space: O(1) because the map size is fixed and no extra space grows with input

vs Alternative: This is more efficient than checking all substrings or using repeated subtraction which would be slower

Edge Cases

Empty string

Returns 0 because no symbols to convert

DSA Java

int nextVal = (i + 1 < s.length()) ? romanMap.get(s.charAt(i + 1)) : 0;

Single character like 'V'

Returns value of that single symbol (5)

DSA Java

int nextVal = (i + 1 < s.length()) ? romanMap.get(s.charAt(i + 1)) : 0;

All symbols in descending order like 'MDCLXVI'

All values add up normally

DSA Java

if (currentVal < nextVal) {

When to Use This Pattern

When you see a problem asking to convert Roman numerals to numbers, use the subtract-if-smaller-before-bigger pattern to handle special cases.

Common Mistakes

Mistake: Always adding values without checking the next symbol leads to wrong totals for subtractive cases.
Fix: Compare current and next symbol values; subtract current if smaller than next.

Summary

Converts Roman numeral strings to integer values by adding or subtracting symbol values.

Use when you need to interpret Roman numerals as numbers in code.

Remember to subtract when a smaller value comes before a bigger one, otherwise add.

Practice

1. What is the value of the Roman numeral IX when converted to an integer?

easy

A. 6

B. 11

C. 9

D. 19

Solution

1. Step 1: Understand Roman numeral rules for subtraction

   In Roman numerals, when a smaller numeral appears before a larger one, it is subtracted. Here, I (1) is before X (10), so 1 is subtracted from 10.

2. Step 2: Calculate the integer value

   10 - 1 = 9.

3. Final Answer:

   9 -> Option C

4. Quick Check:

   IX = 9 [OK]

Hint: Subtract when smaller numeral precedes larger one [OK]

Common Mistakes:

• Adding values instead of subtracting
• Confusing IX with XI
• Ignoring subtraction rule

2. Which of the following Java code snippets correctly initializes a map for Roman numeral values?

easy

A. Map map = new HashMap<>(); map.add('I', 1); map.add('V', 5);

B. Map map = Map.of("I", 1, "V", 5, "X", 10);

C. Map map = new Map(); map['I'] = 1; map['V'] = 5;

D. Map map = new HashMap<>(); map.put('I', 1); map.put('V', 5); map.put('X', 10);

Solution

1. Step 1: Check correct Map initialization syntax in Java

   Java requires using a concrete class like HashMap to create a Map instance. Then, use put() method to add key-value pairs.

2. Step 2: Verify each option

   Map map = new HashMap<>(); map.put('I', 1); map.put('V', 5); map.put('X', 10); correctly uses new HashMap<>(), then map.put() calls. B uses Map.of with string keys ("I", etc.) causing type mismatch for Map<Character, Integer>. Options C and D use invalid syntax.

3. Final Answer:

   Map map = new HashMap<>(); map.put('I', 1); map.put('V', 5); map.put('X', 10); -> Option D

4. Quick Check:

   Use HashMap and put() for map initialization [OK]

Hint: Use HashMap and put() to add entries [OK]

Common Mistakes:

• Using invalid Map constructor
• Using map.add() instead of map.put()
• Trying to assign values with brackets

3. What is the output of the following Java code snippet?

String s = "MCMXCIV";
int result = 0;
Map map = Map.of('I',1,'V',5,'X',10,'L',50,'C',100,'D',500,'M',1000);
for (int i = 0; i < s.length(); i++) {
    int value = map.get(s.charAt(i));
    if (i + 1 < s.length() && value < map.get(s.charAt(i + 1))) {
        result -= value;
    } else {
        result += value;
    }
}
System.out.println(result);

medium

A. 1904

B. 1994

C. 1094

D. 1949

Solution

1. Step 1: Understand the Roman numeral string and map values

   The string "MCMXCIV" represents a Roman numeral. Map assigns values: M=1000, C=100, X=10, I=1, V=5.

2. Step 2: Trace the loop and calculate result

   Loop through each character:
   - M(1000), next C(100): 1000 > 100, add 1000
   - C(100), next M(1000): 100 < 1000, subtract 100
   - M(1000), next X(10): 1000 > 10, add 1000
   - X(10), next C(100): 10 < 100, subtract 10
   - C(100), next I(1): 100 > 1, add 100
   - I(1), next V(5): 1 < 5, subtract 1
   - V(5), no next, add 5
   Sum = 1000 - 100 + 1000 - 10 + 100 - 1 + 5 = 1994.

3. Final Answer:

   1994 -> Option B

4. Quick Check:

   MCMXCIV = 1994 [OK]

Hint: Subtract if current < next, else add [OK]

Common Mistakes:

• Adding all values without subtraction
• Incorrectly subtracting when not needed
• Misreading character order

4. The following Java method aims to convert a Roman numeral string to an integer but has a bug. What is the bug?

public int romanToInt(String s) {
    Map map = Map.of('I',1,'V',5,'X',10,'L',50,'C',100,'D',500,'M',1000);
    int result = 0;
    for (int i = 0; i < s.length(); i++) {
        int value = map.get(s.charAt(i));
        if (i + 1 < s.length() && value > map.get(s.charAt(i + 1))) {
            result -= value;
        } else {
            result += value;
        }
    }
    return result;
}

medium

A. The comparison operator should be '<' instead of '>' in the if condition.

B. The map initialization is incorrect and causes runtime error.

C. The loop should start from 1 instead of 0.

D. The method does not handle lowercase Roman numerals.

Solution

1. Step 1: Analyze the if condition logic

   The code subtracts value when current value is greater than next. But Roman numerals subtract when current is less than next.

2. Step 2: Identify the correct comparison operator

   The condition should be value < map.get(next char) to subtract, not value > next value.

3. Final Answer:

   The comparison operator should be '<' instead of '>' in the if condition. -> Option A

4. Quick Check:

   Subtract when current < next [OK]

Hint: Subtract if current numeral is smaller than next [OK]

Common Mistakes:

• Using wrong comparison operator
• Ignoring subtraction rule
• Assuming map initialization error

5. You want to convert a list of Roman numerals ["XL", "IX", "MMXX"] to their integer values using Java. Which approach correctly handles this with minimal code duplication?

hard

A. Write a separate method to convert one Roman numeral to integer, then loop over the list calling this method for each element.

B. Manually convert each Roman numeral in the list with separate code blocks for each string.

C. Use a single loop over the list and convert each character individually without a helper method.

D. Convert only the first Roman numeral and reuse the result for all elements.

Solution

1. Step 1: Identify the need for reusable code

   Converting Roman numerals requires the same logic for each string. Writing a helper method avoids repeating code.

2. Step 2: Use a loop to process the list

   Loop through the list and call the helper method for each Roman numeral string to get its integer value.

3. Final Answer:

   Write a separate method to convert one Roman numeral to integer, then loop over the list calling this method for each element. -> Option A

4. Quick Check:

   Use helper method + loop for clean code [OK]

Hint: Use helper method and loop to avoid repetition [OK]

Common Mistakes:

• Repeating conversion code for each string
• Ignoring code reuse principles
• Using incorrect logic for all elements