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

Recall & Review

beginner

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

The value of 'IV' is 4. It is 5 (V) minus 1 (I) because a smaller numeral before a larger numeral means subtraction.

beginner

What does the Roman numeral 'X' represent?

'X' represents the number 10 in Roman numerals.

intermediate

Why do we subtract when a smaller Roman numeral appears before a larger one?

Because in Roman numerals, placing a smaller numeral before a larger numeral means you subtract the smaller from the larger to get the correct value.

intermediate

In Roman to Integer conversion, what is the purpose of checking the next numeral during iteration?

Checking the next numeral helps decide if we should add or subtract the current numeral's value. If the next numeral is larger, we subtract; otherwise, we add.

advanced

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

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

What integer does the Roman numeral 'IX' represent?

A 9

B 11

C 6

D 4

'IX' means 10 (X) minus 1 (I), which equals 9.

In Roman numerals, when should you subtract the value of a numeral?

A When the current numeral is smaller than the next numeral

B When the current numeral is larger than the next numeral

C Always add values

D When the current numeral is equal to the next numeral

You subtract when the current numeral is smaller than the next numeral.

What is the value of 'XL' in Roman numerals?

A 90

B 60

C 40

D 50

'XL' means 50 (L) minus 10 (X), which equals 40.

Which Roman numeral represents 1000?

A L

B D

C C

D M

'M' represents 1000 in Roman numerals.

What is the integer value of 'LVIII'?

A 38

B 58

C 68

D 48

'LVIII' is 50 (L) + 5 (V) + 3 (III) = 58.

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

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

Describe how the subtraction rule affects the conversion of Roman numerals like 'IV' and 'IX'.

Focus on the position of smaller numerals relative to larger ones.

Practice

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

easy

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

B. Multiply all symbol values together

C. Add values only if symbols are the same

D. Subtract all symbol values from 1000

Solution

1. Step 1: Understand Roman numeral rules

   Roman numerals are converted by adding values of symbols, but if a smaller value comes before a larger one, it is subtracted.

2. Step 2: Apply the rule to conversion

   For example, IV is 5 - 1 = 4, not 1 + 5 = 6.

3. Final Answer:

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

4. Quick Check:

   Roman to integer = add/subtract values [OK]

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

Common Mistakes:

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

2. Which TypeScript syntax correctly defines a function to convert Roman numerals to integers?

easy

A. def romanToInt(s): return 0

B. function romanToInt(s: string): number { return 0; }

C. func romanToInt(s string) int { return 0 }

D. romanToInt = (s) => { return '0'; }

Solution

1. Step 1: Identify TypeScript function syntax

   TypeScript functions use the syntax: function name(params): returnType { body }

2. Step 2: Match correct syntax

   function romanToInt(s: string): number { return 0; } matches TypeScript syntax with parameter type and return type specified.

3. Final Answer:

   function romanToInt(s: string): number { return 0; } -> Option B

4. Quick Check:

   TypeScript function syntax = function romanToInt(s: string): number { return 0; } [OK]

Hint: Use 'function name(params: type): returnType' in TypeScript [OK]

Common Mistakes:

• Using Python or Go syntax in TypeScript
• Returning string instead of number
• Missing type annotations

3. What is the output of this TypeScript code?

function romanToInt(s: string): number {
  const map: {[key: string]: number} = {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. 11

B. 4

C. 9

D. Error

Solution

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

   For 'I' (1) and next 'X' (10), since 1 < 10, subtract 1. For 'X' (10), no next, add 10.

2. Step 2: Calculate total

   Total = -1 + 10 = 9.

3. Final Answer:

   9 -> Option C

4. Quick Check:

   'IX' = 9 [OK]

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

Common Mistakes:

• Adding all values without subtraction
• Off-by-one error in loop
• Not handling last character correctly

4. Find the bug in this TypeScript code for Roman to Integer conversion:

function romanToInt(s: string): number {
  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. Return type should be string, not number

B. map object keys should be lowercase

C. Use 'var' instead of 'let' for i

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

Solution

1. Step 1: Check loop boundary

   The loop runs from i = 0 to i <= s.length, which causes s[i] to be undefined at last iteration.

2. Step 2: Correct loop condition

   Change to i < s.length to avoid accessing undefined index.

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-bounds access [OK]

Common Mistakes:

• Using <= instead of < in loops
• Wrong case for map keys
• Incorrect return type

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

function romanToInt(s: string): number {
  const map: {[key: string]: number} = {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('MCMXCIV'));

hard

A. 1994

B. 1904

C. 2004

D. 1494

Solution

1. Step 1: Break down 'MCMXCIV'

   M=1000, C=100, M=1000, X=10, C=100, I=1, V=5. Apply subtraction where smaller precedes larger.

2. Step 2: Calculate total step-by-step

   1000 (M) + (100 < 1000, subtract 100) + 1000 + (10 < 100, subtract 10) + 100 + (1 < 5, subtract 1) + 5 = 1000 - 100 + 1000 - 10 + 100 - 1 + 5 = 1994.

3. Final Answer:

   1994 -> Option A

4. Quick Check:

   'MCMXCIV' = 1994 [OK]

Hint: Subtract smaller before larger, else add [OK]

Common Mistakes:

• Adding all values without subtraction
• Misreading symbol order
• Skipping last character