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.

Practice

1. What is the integer value of the Roman numeral IX?

easy

A. 11

B. 19

C. 6

D. 9

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 value of IX

   10 - 1 = 9.

3. Final Answer:

   9 -> Option D

4. Quick Check:

   IX = 9 [OK]

Hint: Subtract when smaller numeral is before larger one [OK]

Common Mistakes:

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

2. Which of the following Python code snippets correctly initializes a dictionary mapping Roman numerals to integers?

easy

A. roman_map = {'I': 1, 'V': 5, 'X': 10, 'L': 50}

B. roman_map = ['I': 1, 'V': 5, 'X': 10, 'L': 50]

C. roman_map = ('I' = 1, 'V' = 5, 'X' = 10, 'L' = 50)

D. roman_map = {I: 1, V: 5, X: 10, L: 50}

Solution

1. Step 1: Identify correct dictionary syntax in Python

   Python dictionaries use curly braces with key:value pairs, keys as strings must be quoted.

2. Step 2: Check each option

   roman_map = {'I': 1, 'V': 5, 'X': 10, 'L': 50} uses correct syntax with quotes and curly braces. Options A, B, and D use invalid syntax. roman_map = {I: 1, V: 5, X: 10, L: 50} uses unquoted keys which causes NameError.

3. Final Answer:

   roman_map = {'I': 1, 'V': 5, 'X': 10, 'L': 50} -> Option A

4. Quick Check:

   Correct dictionary syntax = roman_map = {'I': 1, 'V': 5, 'X': 10, 'L': 50} [OK]

Hint: Use curly braces and quote keys for dictionaries [OK]

Common Mistakes:

• Using square brackets instead of curly braces
• Not quoting string keys
• Using assignment '=' inside dictionary

3. What is the output of the following Python code?

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

print(roman_to_int('XIV'))

medium

A. 14

B. 16

C. 9

D. 11

Solution

1. Step 1: Trace the loop for input 'XIV'

   Characters: X(10), I(1), V(5). Loop index i from 0 to 2.
   i=0: X(10) < I(1)? No, add 10.
   i=1: I(1) < V(5)? Yes, subtract 1.
   i=2: V(5), no next char, add 5.

2. Step 2: Calculate total

   Total = 10 - 1 + 5 = 14.

3. Final Answer:

   14 -> Option A

4. Quick Check:

   X(10) + IV(4) = 14 [OK]

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

Common Mistakes:

• Adding all values without subtraction
• Off-by-one errors in loop
• Ignoring last character addition

4. The following code is intended to convert a Roman numeral string to an integer. What is the error?

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

print(roman_to_int('IX'))

medium

A. SyntaxError due to missing colon

B. KeyError because 'IX' is not in roman_map

C. IndexError due to accessing s[i + 1] without boundary check

D. Returns incorrect value 11 instead of 9

Solution

1. Step 1: Identify loop and index usage

   The loop runs from i=0 to len(s)-1. At last index i, accessing s[i+1] causes IndexError.

2. Step 2: Explain why error occurs

   For input 'IX' (length 2), when i=1, s[i+1] is s[2], which is out of range.

3. Final Answer:

   IndexError due to accessing s[i + 1] without boundary check -> Option C

4. Quick Check:

   Check index bounds before s[i+1] access [OK]

Hint: Always check index before accessing s[i+1] [OK]

Common Mistakes:

• Not checking index bounds in loops
• Assuming s[i+1] always exists
• Ignoring runtime errors

5. Given the Roman numeral string 'MCMXCIV', what integer does the following code return?

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'))

hard

A. 1494

B. 1994

C. 1949

D. 2094

Solution

1. Step 1: Understand reversed traversal and subtraction logic

   The code processes characters from right to left, subtracting if current value is less than previous.

2. Step 2: Trace values for 'MCMXCIV'

   Characters reversed: V(5), I(1), C(100), X(10), M(1000), C(100), M(1000)
   Calculate total:
   V=5 (add 5)
   I=1 < 5 subtract 1 (total=4)
   C=100 > 1 add 100 (total=104)
   X=10 < 100 subtract 10 (total=94)
   M=1000 > 10 add 1000 (total=1094)
   C=100 < 1000 subtract 100 (total=994)
   M=1000 > 100 add 1000 (total=1994)

3. Final Answer:

   1994 -> Option B

4. Quick Check:

   MCMXCIV = 1994 [OK]

Hint: Traverse right to left, subtract if smaller than previous [OK]

Common Mistakes:

• Processing left to right without subtraction logic
• Confusing numeral values
• Missing reversed traversal step