Roman to Integer Conversion in DSA Typescript - Build from Scratch

Roman to Integer Conversion

📖 Scenario: Imagine you are building a simple tool that converts Roman numerals into regular numbers. This is useful in many places like clocks, book chapters, or movie sequels.

🎯 Goal: You will create a program that takes a Roman numeral string and converts it into its integer value step-by-step.

📋 What You'll Learn

Create a dictionary to map Roman numerals to their integer values

Create a variable to hold the total integer value

Use a loop to process each character and apply Roman numeral rules

Print the final integer value

💡 Why This Matters

🌍 Real World

Roman numerals are used in clocks, book chapters, movie titles, and legal documents. Converting them to integers helps computers understand and process these values.

💼 Career

Understanding how to map symbols to values and apply rules is a key skill in programming. This project builds skills in dictionaries, loops, and conditional logic used in many software tasks.

1

Create Roman Numeral Map

Create a dictionary called romanMap that maps these Roman numerals to integers: 'I': 1, 'V': 5, 'X': 10, 'L': 50, 'C': 100, 'D': 500, 'M': 1000.

DSA Typescript

// Your code here

Hint

Use an object with keys as Roman letters and values as numbers.

2

Create Total Variable and Input

Create a variable called total and set it to 0. Also create a variable called roman and set it to the string 'MCMXCIV'.

DSA Typescript

const romanMap: { [key: string]: number } = {
  'I': 1,
  'V': 5,
  'X': 10,
  'L': 50,
  'C': 100,
  'D': 500,
  'M': 1000
};
// Your code here

Hint

Initialize total to zero and set roman to the example Roman numeral.

3

Convert Roman Numeral to Integer

Use a for loop with variable i from 0 to roman.length - 2. Inside the loop, get the current value from romanMap[roman[i]] and the next value from romanMap[roman[i + 1]] if it exists. If the current value is less than the next value, subtract the current value from total. Otherwise, add the current value to total. After the loop, add the value of the last character to total.

DSA Typescript

const romanMap: { [key: string]: number } = {
  'I': 1,
  'V': 5,
  'X': 10,
  'L': 50,
  'C': 100,
  'D': 500,
  'M': 1000
};

let total = 0;
const roman = 'MCMXCIV';

// Your code here

Hint

Remember to check the next character to decide if you add or subtract.

4

Print the Result

Write console.log(total) to display the integer value of the Roman numeral.

DSA Typescript

const romanMap: { [key: string]: number } = {
  'I': 1,
  'V': 5,
  'X': 10,
  'L': 50,
  'C': 100,
  'D': 500,
  'M': 1000
};

let total = 0;
const roman = 'MCMXCIV';

for (let i = 0; i < roman.length - 1; i++) {
  const current = romanMap[roman[i]];
  const next = romanMap[roman[i + 1]];
  if (current < next) {
    total -= current;
  } else {
    total += current;
  }
}
total += romanMap[roman[roman.length - 1]];

// Your code here

Hint

The Roman numeral 'MCMXCIV' equals 1994.

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