# 018 Integer to Roman

### 12. Integer to Roman 🔢

**Difficulty**: `Medium` - **Tags**: `Math`, `Greedy`

[LeetCode Problem Link](https://leetcode.com/problems/integer-to-roman/description/)

#### Description

Roman numerals are represented by seven different symbols:

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

Given an integer, convert it to a Roman numeral by breaking the integer into its decimal components and mapping them to corresponding Roman symbols.

#### Examples

**Example 1:**

Input:

```java
num = 3749
```

Output:

```
"MMMDCCXLIX"
```

Explanation:

* 3000 = MMM (M + M + M)
* 700 = DCC (D + C + C)
* 40 = XL (X less than L)
* 9 = IX (I less than X)

**Example 2:**

Input:

```java
num = 58
```

Output:

```
"LVIII"
```

Explanation:

* 50 = L
* 8 = VIII

**Example 3:**

Input:

```java
num = 1994
```

Output:

```
"MCMXCIV"
```

Explanation:

* 1000 = M
* 900 = CM
* 90 = XC
* 4 = IV

#### Constraints

* The input `num` is in the range \[1, 3999].

### 12. Integer to Roman Conversion 🔢

**Difficulty**: `Medium` - **Tags**: `Math`, `Greedy`

[LeetCode Problem Link](https://leetcode.com/problems/integer-to-roman/description/)

#### Description

Roman numerals are represented by seven different symbols:

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

Given an integer, convert it to a Roman numeral by breaking the integer into its decimal components and mapping them to corresponding Roman symbols.

#### Examples

**Example 1:**

Input:

```java
num = 3749
```

Output:

```
"MMMDCCXLIX"
```

Explanation:

* 3000 = MMM (M + M + M)
* 700 = DCC (D + C + C)
* 40 = XL (X less than L)
* 9 = IX (I less than X)

**Example 2:**

Input:

```java
num = 58
```

Output:

```
"LVIII"
```

Explanation:

* 50 = L
* 8 = VIII

**Example 3:**

Input:

```java
num = 1994
```

Output:

```
"MCMXCIV"
```

Explanation:

* 1000 = M
* 900 = CM
* 90 = XC
* 4 = IV

#### Constraints

* The input `num` is in the range \[1, 3999].

#### Solution 💡

To convert an integer to Roman numerals, we use a list of symbols representing each Roman numeral and their corresponding values. We subtract from the input number in descending order, appending the corresponding symbol to the result string each time.

**Java**

```java
class Solution {
    public String intToRoman(int num) {
        String[] symbols = {"M", "CM", "D", "CD", "C", "XC", "L", "XL", "X", "IX", "V", "IV", "I"};
        int[] values = {1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1};
        
        StringBuilder romanNumeral = new StringBuilder();
        
        int i = 0;
        while (num > 0) {
            if (num >= values[i]) {
                romanNumeral.append(symbols[i]);
                num -= values[i];
            } else {
                i++;
            }
        }
        
        return romanNumeral.toString();
    }
}
```

**Time Complexity ⏳**

* **O(1)**: The time complexity is constant since the number of Roman symbols is fixed.

**Space Complexity 💾**

* **O(1)**: The space complexity is constant as we only use a few variables and a fixed-size array.

You can find the full solution [here](https://github.com/ChunhThanhDe/Leetcode-Top-Interview/blob/main/Topic%201%20Array%20-%20String/018%20Integer%20to%20Roman/Solution.java).


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://chunhthanhde.gitbook.io/leetcode-top-interview/topic-1-array-string/018-integer-to-roman.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.