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

Recall & Review

beginner

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

The Roman numeral 'X' represents the value 10.

beginner

How do you handle subtractive notation in Roman numerals (e.g., IV, IX)?

If a smaller numeral appears before a larger one, subtract the smaller from the larger (e.g., IV = 5 - 1 = 4).

beginner

What is the first step in converting a Roman numeral string to an integer?

Map each Roman numeral character to its integer value for easy lookup during conversion.

intermediate

Why do we compare the current Roman numeral value with the next one during conversion?

To decide whether to add or subtract the current value based on whether it is less than the next value.

intermediate

What is the output integer for the Roman numeral 'MCMXCIV'?

The Roman numeral 'MCMXCIV' converts to 1994.

What integer does the Roman numeral 'L' represent?

A 100

B 500

C 50

D 10

'L' represents 50 in Roman numerals.

In Roman numerals, what does 'IX' equal?

A 11

B 4

C 6

D 9

'IX' means 10 - 1 = 9 using subtractive notation.

When converting Roman numerals, if the current numeral is smaller than the next, what should you do?

A Add the current numeral's value

B Subtract the current numeral's value

C Ignore the current numeral

D Multiply the current numeral's value

If the current numeral is smaller than the next, subtract its value.

What is the integer value of 'D' in Roman numerals?

A 500

B 100

C 1000

D 50

'D' represents 500.

Which of these is NOT a valid Roman numeral?

A IC

B XVII

C XL

D MCM

'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 you decide to add or subtract each numeral.

Describe how subtractive notation works in Roman numerals and give two examples.

Look for cases where a smaller letter comes before a bigger one.

Practice

1. What is the main rule to convert Roman numerals to integers?

easy

A. Subtract all values from the largest symbol

B. Add values of symbols, subtract if a smaller symbol is before a larger one

C. Add values only if symbols are the same

D. Multiply values of symbols in order

Solution

1. Step 1: Understand Roman numeral rules

   Roman numerals are added normally, but if a smaller numeral appears before a larger one, it is subtracted.

2. Step 2: Apply addition and subtraction rules

   For example, IV is 5 - 1 = 4, while VI is 5 + 1 = 6.

3. Final Answer:

   Add values of symbols, subtract if a smaller symbol is before a larger one -> Option B

4. Quick Check:

   Roman numeral rules = Add and subtract [OK]

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

Common Mistakes:

• Always adding without subtraction
• Multiplying values incorrectly
• Ignoring order of symbols

2. Which of the following is the correct JavaScript syntax to get the integer value of a Roman numeral character from a map object named romanMap?

easy

A. romanMap['V']

B. romanMap.get('V')

C. romanMap.V

D. romanMap('V')

Solution

1. Step 1: Identify the data structure type

   If romanMap is a plain JavaScript object, access values using square brackets with the key as a string.

2. Step 2: Choose correct syntax for object property access

   Using romanMap['V'] correctly accesses the value for key 'V'. romanMap.get('V') is for Map objects, not plain objects.

3. Final Answer:

   romanMap['V'] -> Option A

4. Quick Check:

   Object property access = romanMap['V'] [OK]

Hint: Use square brackets for object keys as strings [OK]

Common Mistakes:

• Using .get() on plain objects
• Using dot notation with string keys
• Calling object like a function

3. What will be the output of the following JavaScript code?

function romanToInt(s) {
  const map = {I:1, V:5, X:10, L:50, C:100, D:500, M:1000};
  let total = 0;
  for(let i = 0; i < s.length; i++) {
    const current = map[s[i]];
    const next = map[s[i+1]] || 0;
    if(current < next) {
      total -= current;
    } else {
      total += current;
    }
  }
  return total;
}
console.log(romanToInt('IX'));

medium

A. 9

B. 11

C. 1

D. Error

Solution

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

   For 'I' (1), next is 'X' (10), since 1 < 10, subtract 1 (total = -1). For 'X' (10), next is undefined (0), so add 10 (total = 9).

2. Step 2: Calculate final total

   Total after loop is 9, which is the integer value of 'IX'.

3. Final Answer:

   9 -> Option A

4. Quick Check:

   'IX' = 9 [OK]

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

Common Mistakes:

• Adding all values without subtraction
• Ignoring next character check
• Off-by-one errors in loop

4. Find the error in this JavaScript function for Roman to Integer conversion:

function romanToInt(s) {
  const map = {I:1, V:5, X:10, L:50, C:100, D:500, M:1000};
  let total = 0;
  for(let i = 0; i <= s.length; i++) {
    const current = map[s[i]];
    const next = map[s[i+1]] || 0;
    if(current < next) {
      total -= current;
    } else {
      total += current;
    }
  }
  return total;
}

medium

A. Use '==' instead of '<' in if condition

B. map object keys should be lowercase

C. total should be initialized to 1

D. Loop condition should be i < s.length, not i <= s.length

Solution

1. Step 1: Analyze loop boundary

   The loop runs from i = 0 to i <= s.length, which means it accesses s[s.length], an undefined index causing current to be undefined.

2. Step 2: Correct loop condition

   Changing loop condition to i < s.length prevents accessing out-of-bound index and avoids errors.

3. Final Answer:

   Loop condition should be i < s.length, not i <= s.length -> Option D

4. Quick Check:

   Loop boundary off-by-one error fixed [OK]

Hint: Use i < length to avoid out-of-bound errors [OK]

Common Mistakes:

• Using <= instead of < in loops
• Wrong case for map keys
• Incorrect comparison operators

5. Given the Roman numeral string 'MCMXCIV', what integer should the conversion function return?

hard

A. 2004

B. 1904

C. 1994

D. 1094

Solution

1. Step 1: Break down the Roman numeral 'MCMXCIV'

   M = 1000, CM = 900 (1000 - 100), XC = 90 (100 - 10), IV = 4 (5 - 1).

2. Step 2: Add all parts

   1000 + 900 + 90 + 4 = 1994 total.

3. Final Answer:

   1994 -> Option C

4. Quick Check:

   'MCMXCIV' = 1994 [OK]

Hint: Identify subtractive pairs and sum all values [OK]

Common Mistakes:

• Adding all numerals without subtraction
• Misreading subtractive pairs
• Confusing similar numerals