Asked in: DOCUSIGN
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All Testcases Passed ✔
Solution
def solve(num):
roman_dict = {1: "I",
5: "V",
4: "IV",10: "X",
// ... rest of solution available after purchaseExplanation
```
To solve the problem of converting integers into their Roman numeral equivalents, it’s important to first understand the structure and rules of Roman numerals, and then devise a systematic way to map integers into the Roman numeral system.
1. **Understanding Roman Numerals:**
Roman numerals are a numeral system originating from ancient Rome, using combinations of letters from the Latin alphabet to represent values. The primary Roman numeral symbols and their values are as follows:
- I = 1
- V = 5
- X = 10
- L = 50
- C = 100
- D = 500
- M = 1000
Additionally, there are certain combinations used to express numbers that would otherwise require repeating symbols more than three times:
- IV = 4 (one less than 5)
- IX = 9 (one less than 10)
- XL = 40 (ten less than 50)
- XC = 90 (ten less than 100)
- CD = 400 (one hundred less than 500)
- CM = 900 (one hundred less than 1000)
Roman numerals are typically written from largest to smallest from left to right, and the values are added, except in the cases above where a smaller numeral precedes a larger one to indicate subtraction.
2. **Decomposition of the Integer:**
When converting an integer into a Roman numeral, the key is to break down the number into parts corresponding to these Roman numeral values, starting from the largest possible and working downward.
For example, to convert 49:
- The largest Roman numeral less than or equal to 49 is 40, which is "XL".
- Subtract 40 from 49 → remainder is 9.
- The largest Roman numeral less than or equal to 9 is 9 itself, represented as "IX".
- So, 49 → "XL" + "IX" = "XLIX".
Similarly, for 23:
- Largest numeral ≤ 23 is 10 → "X"
- Subtract 10 → remainder 13
- Largest numeral ≤ 13 is 10 → "X"
- Subtract 10 → remainder 3
- Largest numeral ≤ 3 is 1 → "I" repeated three times → "III"
- Final result → "XXIII"
3. **Approach to Conversion:**
A systematic approach to convert a number to a Roman numeral is:
- Maintain a list or ordered structure of Roman numeral values paired with their integer equivalents, sorted from largest to smallest. For example:
(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").
- For each number to convert, iterate over the list from the highest value downwards.
- For each pair, while the current number is greater than or equal to the value:
- Append the corresponding Roman numeral symbol(s) to the output string.
- Decrease the number by that value.
- Continue this process until the number is reduced to zero.
This greedy approach ensures you always take the largest possible Roman numeral chunk at each step.
4. **Handling Multiple Numbers:**
Since the input is an array of numbers, the conversion needs to be applied to each integer individually using the approach above.
- Initialize an output array to store the Roman numerals corresponding to each number.
- Loop through each number in the input list.
- Apply the conversion procedure described.
- Append the Roman numeral string to the output list.
- Return the list after processing all numbers.
5. **Considerations and Edge Cases:**
- The problem constraints specify numbers will be between 1 and 1000 inclusive. Since Roman numerals for these ranges are well-defined, the approach works without special cases.
- For number 1000 exactly, it corresponds to "M".
- For numbers less than 4, just repeat "I" as many times as needed (1 → "I", 3 → "III").
- Avoid repeated addition beyond three times by using subtractive notation (like IV for 4, IX for 9).
6. **Efficiency:**
- The approach runs efficiently since for each number, you iterate through a fixed set of Roman numeral mappings (about 13 pairs).
- Since n can be up to 1000, this method is fast enough for all inputs.
- The complexity is approximately O(n * m), where n is number of integers, and m is the number of Roman numeral pairs, which is constant.
7. **Summary:**
- Store a list of Roman numeral pairs ordered by descending value.
- For each integer, subtract the largest possible Roman numeral value repeatedly and build the Roman numeral string.
- Repeat for all integers.
- Return the resulting list of Roman numeral strings.
This approach leverages the structured Roman numeral system and applies a simple greedy algorithm to break down each integer into its Roman numeral components systematically and efficiently.
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