Roman to Integer Conversion in DSA C# - 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

Why do we sometimes subtract values in Roman numerals, like 'IV' for 4?

In Roman numerals, when a smaller numeral appears before a larger one, it means subtraction. For example, 'IV' means 5 - 1 = 4.

intermediate

What is the main approach to convert a Roman numeral string to an integer?

We scan the Roman numeral from left to right, adding values. If a smaller numeral comes before a larger one, we subtract the smaller instead of adding.

beginner

In C#, how can you store Roman numeral values for quick lookup during conversion?

Use a Dictionary to map Roman characters like 'I', 'V', 'X' to their integer values.

intermediate

What is the time complexity of converting a Roman numeral string to an integer?

The time complexity is O(n), where n is the length of the Roman numeral string, because we process each character once.

What does the Roman numeral 'IX' represent?

A 9

B 11

C 6

D 4

'IX' means 10 - 1 = 9.

Which data structure is best to store Roman numeral values for conversion in C#?

A Stack<int>

B Dictionary<char, int>

C Queue<char>

D List<int>

Dictionary allows quick lookup of integer values by Roman numeral characters.

If a smaller Roman numeral appears after a larger one, what do you do during conversion?

A Subtract the smaller value

B Ignore the smaller value

C Add the smaller value

D Multiply the values

When a smaller numeral is after a larger one, we add its value.

What is the integer value of 'MCMXCIV'?

A 1994

B 1984

C 2004

D 1949

'M' = 1000, 'CM' = 900, 'XC' = 90, 'IV' = 4; total 1994.

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

A Multiply values

B Reverse the string

C Sort the characters

D Create a map of Roman numerals to integers

We first create a map to know the integer value of each Roman numeral.

Explain how to convert the Roman numeral 'XLII' to an integer step-by-step.

Look for smaller numeral before larger to subtract, then add the rest.

Describe how a Dictionary helps in converting Roman numerals to integers in C#.

Think about how to quickly find the value of each Roman character.

Practice

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

easy

A. Subtract all values from the largest symbol

B. Multiply values of all symbols

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

D. Add values only if symbols are in alphabetical order

Solution

1. Step 1: Understand Roman numeral rules

   Roman numerals add values unless a smaller symbol is before a larger one, then subtract.

2. Step 2: Apply rule to conversion

   When converting, add values normally but subtract when a smaller symbol precedes a larger one.

3. Final Answer:

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

4. Quick Check:

   Roman numeral conversion rule = Add values of symbols, subtract if a smaller symbol is before a larger one [OK]

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

Common Mistakes:

• Multiplying values instead of adding/subtracting
• Ignoring subtraction rule
• Adding all values without checking order

2. Which C# code snippet correctly initializes a dictionary for Roman numeral values?

easy

A. var map = new Dictionary { {'I', 1}, {'V', 5} };

B. var map = new Dictionary { {1, 'I'}, {5, 'V'} };

C. var map = new Dictionary { {'I', 1}, {'V', 5} };

D. var map = new Dictionary { {'I', "1"}, {'V', "5"} };

Solution

1. Step 1: Identify correct dictionary types

   Roman numerals are characters mapped to integer values, so Dictionary is correct.

2. Step 2: Check initialization syntax

   Initialization with curly braces and pairs like {'I', 1} is correct syntax in C#.

3. Final Answer:

   var map = new Dictionary { {'I', 1}, {'V', 5} }; -> Option A

4. Quick Check:

   Dictionary with correct pairs = var map = new Dictionary { {'I', 1}, {'V', 5} }; [OK]

Hint: Use Dictionary for Roman numeral mapping [OK]

Common Mistakes:

• Swapping key and value types
• Using string keys instead of char
• Incorrect initialization syntax

3. What is the output of this C# code snippet?

string s = "IX";
var map = new Dictionary { {'I', 1}, {'V', 5}, {'X', 10} };
int result = 0;
for (int i = 0; i < s.Length; i++) {
  if (i + 1 < s.Length && map[s[i]] < map[s[i + 1]]) {
    result -= map[s[i]];
  } else {
    result += map[s[i]];
  }
}
Console.WriteLine(result);

medium

A. 9

B. 11

C. 6

D. 1

Solution

1. Step 1: Analyze loop and conditions

   For 'IX', at i=0: 'I' < 'X' so subtract 1; at i=1: add 10.

2. Step 2: Calculate result

   result = -1 + 10 = 9.

3. Final Answer:

   9 -> Option A

4. Quick Check:

   IX = 9 [OK]

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

Common Mistakes:

• Adding all values without subtraction
• Off-by-one errors in loop
• Incorrect dictionary values

4. Find the error in this C# code for Roman to integer conversion:

var map = new Dictionary { {'I', 1}, {'V', 5}, {'X', 10} };
int result = 0;
for (int i = 0; i < s.Length - 1; i++) {
  if (map[s[i]] < map[s[i + 1]]) {
    result -= map[s[i]];
  } else {
    result += map[s[i]];
  }
}
result += map[s[s.Length - 1]];
Console.WriteLine(result);

medium

A. No error, code works correctly

B. Missing initialization of string s

C. Loop should run till i < s.Length, not s.Length - 1

D. Dictionary keys should be strings, not chars

Solution

1. Step 1: Check variable declarations

   The variable 's' is used but not declared or initialized, causing a compile error.

2. Step 2: Verify loop and dictionary usage

   Loop and dictionary usage are correct; only 's' is missing.

3. Final Answer:

   Missing initialization of string s -> Option B

4. Quick Check:

   Undefined variable s causes error = Missing initialization of string s [OK]

Hint: Always declare and initialize variables before use [OK]

Common Mistakes:

• Forgetting to declare input string
• Incorrect loop range causing index errors
• Wrong dictionary key types

5. Given the Roman numeral string "MCMXCIV", what integer does the following C# code output?

string s = "MCMXCIV";
var map = new Dictionary {
  {'I', 1}, {'V', 5}, {'X', 10}, {'L', 50}, {'C', 100}, {'D', 500}, {'M', 1000}
};
int result = 0;
for (int i = 0; i < s.Length; i++) {
  if (i + 1 < s.Length && map[s[i]] < map[s[i + 1]]) {
    result -= map[s[i]];
  } else {
    result += map[s[i]];
  }
}
Console.WriteLine(result);

hard

A. 1494

B. 1904

C. 2000

D. 1994

Solution

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

   M=1000, CM=900, XC=90, IV=4; sum = 1000 + 900 + 90 + 4.

2. Step 2: Calculate total value using code logic

   Code subtracts smaller before larger and adds others: 1000 - 100 + 1000 - 10 + 100 - 1 + 5 = 1994.

3. Final Answer:

   1994 -> Option D

4. Quick Check:

   MCMXCIV = 1994 [OK]

Hint: Sum values, subtract when smaller precedes larger [OK]

Common Mistakes:

• Adding all values without subtraction
• Misreading compound numerals like CM or XC
• Incorrect dictionary values