Roman to Integer Conversion in DSA Java - Time & Space Complexity

Time Complexity: Roman to Integer Conversion

O(n)

Understanding Time Complexity

We want to know how the time to convert Roman numerals to integers grows as the input gets longer.

How does the number of steps change when the Roman numeral string gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

public int romanToInt(String s) {
    int result = 0;
    for (int i = 0; i < s.length(); i++) {
        int value = valueOfRoman(s.charAt(i));
        if (i + 1 < s.length() && value < valueOfRoman(s.charAt(i + 1))) {
            result -= value;
        } else {
            result += value;
        }
    }
    return result;
}

private int valueOfRoman(char c) {
    switch(c) {
        case 'I': return 1;
        case 'V': return 5;
        case 'X': return 10;
        case 'L': return 50;
        case 'C': return 100;
        case 'D': return 500;
        case 'M': return 1000;
        default: return 0;
    }
}

This code converts a Roman numeral string to its integer value by checking each character and deciding whether to add or subtract its value.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: A single loop that goes through each character of the input string once.
• How many times: Exactly once for each character in the string, so as many times as the string length.

How Execution Grows With Input

As the Roman numeral string gets longer, the number of steps grows directly with its length.

Input Size (n)	Approx. Operations
10	About 10 checks and additions/subtractions
100	About 100 checks and additions/subtractions
1000	About 1000 checks and additions/subtractions

Pattern observation: The work grows in a straight line with input size; doubling the input doubles the work.

Final Time Complexity

Time Complexity: O(n)

This means the time to convert grows directly with the length of the Roman numeral string.

Common Mistake

[X] Wrong: "Because of the subtraction rule, the code might need to look ahead multiple characters, making it slower than linear."

[OK] Correct: The code only looks one character ahead at a time, so it still processes each character once, keeping the time linear.

Interview Connect

Understanding this time complexity helps you explain how your solution scales and shows you can analyze simple loops well, a key skill in many coding problems.

Self-Check

"What if the code used recursion to process the string instead of a loop? How would the time complexity change?"

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