Roman to Integer Conversion in DSA Python - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Roman to Integer Conversion Function

What is the output of the following code when converting the Roman numeral 'MCMXCIV' to an integer?

DSA Python

def roman_to_int(s):
    roman_map = {'I': 1, 'V': 5, 'X': 10, 'L': 50, 'C': 100, 'D': 500, 'M': 1000}
    total = 0
    prev_value = 0
    for char in reversed(s):
        value = roman_map[char]
        if value < prev_value:
            total -= value
        else:
            total += value
        prev_value = value
    return total

print(roman_to_int('MCMXCIV'))

A 1904

B None (KeyError)

C 2094

D 1994

💡 Hint

Remember that when a smaller value appears before a larger value, it should be subtracted.

The Roman numeral 'MCMXCIV' breaks down as M (1000) + CM (900) + XC (90) + IV (4), totaling 1994.

🧠 Conceptual

intermediate

Understanding Subtraction Rule in Roman Numerals

Which of the following Roman numeral pairs correctly demonstrates the subtraction rule used in Roman to Integer conversion?

A MM (2000), CC (200)

B VI (6), XI (11)

C IV (4), IX (9)

D XV (15), LX (60)

💡 Hint

Look for pairs where a smaller numeral comes before a larger numeral.

The subtraction rule applies when a smaller numeral precedes a larger one, such as IV (4) and IX (9). Other options show addition.

🔧 Debug

advanced

Identify the Error in Roman to Integer Code

What error will the following code produce when run with input 'XLII'?

DSA Python

def roman_to_int(s):
    roman_map = {'I': 1, 'V': 5, 'X': 10, 'L': 50, 'C': 100, 'D': 500, 'M': 1000}
    total = 0
    prev_value = 0
    for char in s:
        value = roman_map[char]
        if value > prev_value:
            total += value - 2 * prev_value
        else:
            total += value
        prev_value = value
    return total

print(roman_to_int('XLII'))

A KeyError

B 42

C Incorrect output: 52

D SyntaxError

💡 Hint

Check how subtraction is handled when the current value is greater than the previous.

The code correctly implements the subtraction rule by subtracting twice the previous value when the current value is greater. For 'XLII', it returns 42.

❓ Predict Output

advanced

Output of Incorrect Roman to Integer Implementation

What is the output of this code when converting 'IX' to an integer?

DSA Python

def roman_to_int(s):
    roman_map = {'I': 1, 'V': 5, 'X': 10}
    total = 0
    for i in range(len(s)):
        value = roman_map[s[i]]
        if i + 1 < len(s) and roman_map[s[i+1]] > value:
            total -= value
        else:
            total += value
    return total

print(roman_to_int('IX'))

A 9

B 11

C 1

D KeyError

💡 Hint

Check how the code subtracts the value when the next numeral is larger.

The code subtracts 1 for 'I' because 'X' is larger, then adds 10 for 'X', resulting in 9.

🚀 Application

expert

Number of Valid Roman Numerals of Length 3

How many valid Roman numerals of length exactly 3 characters exist using the symbols I, V, X, L, C, D, M following standard Roman numeral rules?

A 64

B 100

C 49

D 75

💡 Hint

Consider valid combinations and subtraction rules for 3-character numerals.

Counting all valid 3-character Roman numerals respecting subtraction and repetition rules results in 64 valid numerals.