Roman to Integer problem and solution in Java and Python

Let’s cover both directions — Roman → Integer and Integer → Roman — with full intuition, Java + Python code, and visual understanding.

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🧩 1️⃣ Problem: Roman to Integer

Question

Given a string representing a Roman numeral, convert it to an integer.

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Roman Numeral Basics

Symbol	Value
I	1
V	5
X	10
L	50
C	100
D	500
M	1000

But there are subtractive cases:

• IV = 4 (not 6) → because I before V means 5−1
• IX = 9
• XL = 40
• XC = 90
• CD = 400
• CM = 900

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Example

Input: "MCMXCIV"
Output: 1994
Explanation:
M (1000) + CM (900) + XC (90) + IV (4)
= 1994

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✅ Approach

• Start from left to right.
• If current numeral < next numeral → subtract
• Otherwise → add

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Java Solution

import java.util.*;

class Solution {
    public int romanToInt(String s) {
        Map<Character, Integer> map = new HashMap<>();
        map.put('I', 1);
        map.put('V', 5);
        map.put('X', 10);
        map.put('L', 50);
        map.put('C', 100);
        map.put('D', 500);
        map.put('M', 1000);

        int result = 0;

        for (int i = 0; i < s.length(); i++) {
            int value = map.get(s.charAt(i));
            if (i + 1 < s.length() && value < map.get(s.charAt(i + 1))) {
                result -= value;
            } else {
                result += value;
            }
        }
        return result;
    }
}

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Python Solution

def romanToInt(s: str) -> int:
    roman = {'I': 1, 'V': 5, 'X': 10, 'L': 50,
             'C': 100, 'D': 500, 'M': 1000}
    total = 0

    for i in range(len(s)):
        if i + 1 < len(s) and roman[s[i]] < roman[s[i + 1]]:
            total -= roman[s[i]]
        else:
            total += roman[s[i]]
    return total

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🧠 To Explain to a Kid

Think of Roman numbers as stickers with values. If a smaller sticker (I) comes before a bigger one (V), you’re taking away one sticker’s value — that’s why IV = 4.

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⚙️ Complexity

Type	Time	Space
Roman → Integer	O(n)	O(1)

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🧩 2️⃣ Problem: Integer to Roman

Question

Given an integer (1 ≤ num ≤ 3999), convert it to a Roman numeral.

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Idea

We can map integer values to Roman numerals from largest to smallest, and greedily subtract.

Value	Symbol
1000	M
900	CM
500	D
400	CD
100	C
90	XC
50	L
40	XL
10	X
9	IX
5	V
4	IV
1	I

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Example

Input: 1994
Output: "MCMXCIV"
Explanation:
1000 (M) + 900 (CM) + 90 (XC) + 4 (IV)

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Java Solution

class Solution {
    public String intToRoman(int num) {
        int[] values = {1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1};
        String[] symbols = {"M", "CM", "D", "CD", "C", "XC", "L", "XL", "X", "IX", "V", "IV", "I"};
        
        StringBuilder sb = new StringBuilder();

        for (int i = 0; i < values.length; i++) {
            while (num >= values[i]) {
                num -= values[i];
                sb.append(symbols[i]);
            }
        }
        return sb.toString();
    }
}

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Python Solution

def intToRoman(num: int) -> str:
    val = [1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1]
    syms = ["M", "CM", "D", "CD", "C", "XC", "L", "XL", "X", "IX", "V", "IV", "I"]
    
    roman = []
    for i in range(len(val)):
        while num >= val[i]:
            num -= val[i]
            roman.append(syms[i])
    return ''.join(roman)

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🧠 To Explain to a Kid

Imagine you’re making change for money. You always give the largest coin first — just like you write M (1000) before C (100), etc.

So for 1994:

• Start with M (1000) → left with 994
• Then CM (900) → left with 94
• Then XC (90) → left with 4
• Then IV (4) → done ✅ → “MCMXCIV”

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⚙️ Complexity

Type	Time	Space
Integer → Roman	O(1)	O(1)
Because Roman numerals have a fixed set of symbols, and the loop runs a constant number of times.

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🌍 Real-World Use

Roman numerals are still used in:

• Clocks and watches (XII for 12)
• Movie release years (MMXXV = 2025)
• Monarch names (Queen Elizabeth II)
• Outlines (I, II, III, IV in documents)

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