Roman to Integer Conversion in DSA Java - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the value of the Roman numeral 'IV'?

'IV' represents 4 because 'I' (1) is before 'V' (5), so we subtract 1 from 5.

beginner

What does the Roman numeral 'X' stand for?

'X' stands for 10 in Roman numerals.

intermediate

How do you convert Roman numerals to integers using subtraction?

If a smaller numeral comes before a larger one, subtract the smaller from the larger; otherwise, add the values.

intermediate

In Roman to Integer conversion, what is the integer value of 'MCMXCIV'?

'MCMXCIV' equals 1994. Breakdown: M(1000) + CM(900) + XC(90) + IV(4).

intermediate

Why do we check the next Roman numeral when converting to integer?

Checking the next numeral helps decide if we add or subtract the current numeral's value.

What is the integer value of the Roman numeral 'IX'?

A 6

B 11

C 19

D 9

'IX' means 10 - 1 = 9 because 'I' is before 'X'.

Which Roman numeral represents 50?

A X

B C

C L

D D

'L' stands for 50 in Roman numerals.

In Roman to Integer conversion, when do you subtract the value of a numeral?

A When the current numeral is larger than the next numeral

B When the current numeral is smaller than the next numeral

C Always subtract

D Never subtract

Subtract when a smaller numeral comes before a larger one.

What is the integer value of 'XL'?

A 40

B 60

C 90

D 30

'XL' means 50 - 10 = 40.

Which of these is NOT a valid Roman numeral?

A IC

B VI

C XII

D MM

'IC' is invalid because 'I' cannot be subtracted from 'C' directly.

Explain the process of converting a Roman numeral string to an integer step-by-step.

Think about how subtraction works when a smaller numeral comes before a larger one.

Describe why the Roman numeral 'IV' equals 4 and not 6.

Focus on the order and value comparison of numerals.

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