# 553. Optimal Division

## Approach 1: I don't whether its fair to call it stupid or not

```python
class Solution(object):
    def optimalDivision(self, nums):
        """
        https://leetcode.com/problems/optimal-division/description/
        :type nums: List[int]
        :rtype: str
        """
        A = map(str, nums)
        if len(A) <= 2: return '/'.join(A)
        return A[0] + '/(' + '/'.join(A[1:]) + ')'
```

The first number definitely has to be in the numerator of the final division. Moreover all the numbers are greater than 2, which means division of one number by the other will always result in a smaller number.

So the naiive approach is to simply maximize numerator while minimizing denominator. Since the first number is the only one in the numerator at first we don't want to reduce it further by dividing it with any other number.&#x20;

Our best approach would be to just divide the first number by the result of division of all the other numbers.&#x20;

i.e. in a list of \[2,4,5,7,8,9] our best answer would inevitably be: 2/(4/5/6/7/8/9) since this way the numerator is maximized \[we're not dividing it by anything] and denominator is minimized.

> **Time Complexity:** O(n)
>
> **Space Complexity:** O(n)


---

# 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://programming.arora-aditya.com/leetcode/math/553.-optimal-division.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.