Roman to Integer Conversion in DSA Go - 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 convert a Roman numeral to an integer?

You convert by adding values of symbols from left to right, but if a smaller value precedes a larger one, subtract the smaller from the larger.

beginner

Why do we subtract in Roman numeral conversion when a smaller numeral comes before a larger one?

Because in Roman numerals, placing a smaller numeral before a larger one means subtraction, like IV means 5 - 1 = 4.

beginner

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

'IX' equals 9 because I (1) is before X (10), so 10 - 1 = 9.

beginner

What is the first step in the Roman to Integer conversion algorithm?

The first step is to map each Roman numeral character to its integer value.

What integer does the Roman numeral 'L' represent?

A 100

B 500

C 50

D 10

'L' represents 50 in Roman numerals.

In Roman numeral conversion, what do you do when a smaller numeral is before a larger numeral?

A Subtract the smaller numeral

B Ignore the smaller numeral

C Add the smaller numeral

D Multiply the numerals

When a smaller numeral comes before a larger one, subtract the smaller from the larger.

What is the integer value of 'XV'?

A 15

B 14

C 5

D 20

'X' is 10 and 'V' is 5, so 10 + 5 = 15.

Which Roman numeral represents 100?

A L

B D

C M

D C

'C' represents 100 in Roman numerals.

What is the result of converting 'IV' to an integer?

A 6

B 4

C 9

D 11

'IV' means 5 - 1 = 4.

Explain the rule for subtracting values in Roman numeral to integer conversion.

Think about when a smaller symbol comes before a bigger one.

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

Imagine reading the Roman numeral from left to right.

Practice

1. What is the value of the Roman numeral IX when converted to an integer?

easy

A. 6

B. 11

C. 19

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 integer value

   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 Go code snippets correctly initializes a map for Roman numeral values?

easy

A. romanMap := map[string]int{"I" = 1, "V" = 5, "X" = 10}

B. romanMap := map[int]string{1: "I", 5: "V", 10: "X"}

C. romanMap := map[string]int{"I": 1, "V": 5, "X": 10}

D. romanMap := map[string]int{I: 1, V: 5, X: 10}

Solution

1. Step 1: Check map key and value types

   The map should have string keys (Roman numerals) and int values (their integer equivalents). romanMap := map[string]int{"I": 1, "V": 5, "X": 10} uses map[string]int correctly.

2. Step 2: Verify syntax correctness

   romanMap := map[string]int{"I": 1, "V": 5, "X": 10} uses correct Go syntax with colon ':' to assign values. Options A and C have syntax errors, and B reverses key-value types.

3. Final Answer:

   romanMap := map[string]int{"I": 1, "V": 5, "X": 10} -> Option C

4. Quick Check:

   Correct map syntax uses colons and proper types [OK]

Hint: Use colon ':' for map key-value pairs in Go [OK]

Common Mistakes:

• Using '=' instead of ':' in map initialization
• Swapping key and value types
• Omitting quotes around string keys

3. What will be the output of the following Go code snippet?

func romanToInt(s string) int {
    romanMap := map[byte]int{'I': 1, 'V': 5, 'X': 10}
    total := 0
    for i := 0; i < len(s); i++ {
        if i+1 < len(s) && romanMap[s[i]] < romanMap[s[i+1]] {
            total -= romanMap[s[i]]
        } else {
            total += romanMap[s[i]]
        }
    }
    return total
}

fmt.Println(romanToInt("IV"))

medium

A. 6

B. 4

C. 9

D. Error

Solution

1. Step 1: Analyze the loop and subtraction logic

   The code subtracts the value if the current numeral is less than the next one, else adds it. For "IV", 'I' (1) < 'V' (5), so subtract 1, then add 5.

2. Step 2: Calculate total value

   Total = -1 + 5 = 4.

3. Final Answer:

   4 -> Option B

4. Quick Check:

   IV = 4 using subtraction rule [OK]

Hint: Subtract when current < next numeral [OK]

Common Mistakes:

• Adding all values without subtraction
• Index out of range errors
• Confusing byte and string keys in map

4. The following Go function is intended to convert Roman numerals to integers. What is the bug?

func romanToInt(s string) int {
    romanMap := map[byte]int{'I': 1, 'V': 5, 'X': 10}
    total := 0
    for i := 0; i < len(s); i++ {
        if romanMap[s[i]] < romanMap[s[i+1]] {
            total -= romanMap[s[i]]
        } else {
            total += romanMap[s[i]]
        }
    }
    return total
}

medium

A. Missing check for i+1 < len(s) causing index out of range

B. Using map with byte keys instead of string keys

C. Incorrect subtraction logic for Roman numerals

D. Returning total before loop ends

Solution

1. Step 1: Identify loop boundary issue

   The code accesses s[i+1] without checking if i+1 is within string length, causing possible index out of range error.

2. Step 2: Explain fix

   Adding condition 'i+1 < len(s)' before accessing s[i+1] prevents runtime error.

3. Final Answer:

   Missing check for i+1 < len(s) causing index out of range -> Option A

4. Quick Check:

   Always check bounds before accessing next element [OK]

Hint: Check i+1 < len(s) before accessing s[i+1] [OK]

Common Mistakes:

• Ignoring string length check for next index
• Confusing byte and string keys (not a bug here)
• Incorrect subtraction logic (logic is correct)

5. Given the Roman numeral MCMXCIV, what integer does it convert to using the standard Roman to Integer rules?

hard

A. 1994

B. 1984

C. 2004

D. 1949

Solution

1. Step 1: Break down the numeral into parts

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

2. Step 2: Sum all parts

   1000 + 900 + 90 + 4 = 1994.

3. Final Answer:

   1994 -> Option A

4. Quick Check:

   MCMXCIV = 1994 by adding and subtracting parts [OK]

Hint: Add values, subtract when smaller before larger [OK]

Common Mistakes:

• Adding all numerals without subtraction
• Misreading CM as 1100 instead of 900
• Ignoring subtraction pairs