> ## Documentation Index
> Fetch the complete documentation index at: https://leetcode-py.wisl.dev/llms.txt
> Use this file to discover all available pages before exploring further.

> ## Agent Instructions
> leetcode-py is a Python LeetCode practice environment generator with one CLI: lcpy. It is not a service or platform.
> Each problem is a directory under leetcode/ with README.md, solution.py, test_solution.py, helpers.py, and playground.ipynb. lcpy gen creates them from JSON templates bundled with the package.
> Examples are backed by tests; copy them verbatim.

# Rotate Function Python Solution with Tests

> Tested Python solution for LeetCode 396 with 22 pytest cases. Generate a practice environment with lcpy.

LeetCode 396, [Medium](/catalog/medium). Topics: [Array](/catalog/topics/array), [Math](/catalog/topics/math), [Dynamic Programming](/catalog/topics/dynamic-programming). [View on LeetCode](https://leetcode.com/problems/rotate-function/description/).

Generate this problem as a practice environment: tested reference solution, 22 [parametrized pytest cases](/practice/testing), and a playground notebook:

```bash theme={"theme":{"light":"github-light","dark":"github-dark"}}
lcpy gen -n 396   # by problem number
lcpy gen -s rotate_function   # by problem name
```

## Problem

You are given an integer array `nums` of length `n`.

Assume `arrk` to be an array obtained by rotating `nums` by `k` positions clock-wise. We define the **rotation function** `F` on `nums` as follow:

* `F(k) = 0 * arrk[0] + 1 * arrk[1] + ... + (n - 1) * arrk[n - 1].`

Return *the maximum value of* `F(0), F(1), ..., F(n-1)`.

The test cases are generated so that the answer fits in a **32-bit** integer.

### Examples

```
Input: nums = [4,3,2,6]
Output: 26
```

**Explanation:**
F(0) = (0 \* 4) + (1 \* 3) + (2 \* 2) + (3 \* 6) = 0 + 3 + 4 + 18 = 25
F(1) = (0 \* 6) + (1 \* 4) + (2 \* 3) + (3 \* 2) = 0 + 4 + 6 + 6 = 16
F(2) = (0 \* 2) + (1 \* 6) + (2 \* 4) + (3 \* 3) = 0 + 6 + 8 + 9 = 23
F(3) = (0 \* 3) + (1 \* 2) + (2 \* 6) + (3 \* 4) = 0 + 2 + 12 + 12 = 26
So the maximum value of F(0), F(1), F(2), F(3) is F(3) = 26.

```
Input: nums = [100]
Output: 0
```

### Constraints

* n == nums.length
* 1 \<= n \<= 10^5
* -100 \<= nums\[i] \<= 100

## Solution

Reference implementation from [solution.py on GitHub](https://github.com/wislertt/leetcode-py/blob/main/leetcode/rotate_function/solution.py), full suite in [test\_solution.py](https://github.com/wislertt/leetcode-py/blob/main/leetcode/rotate_function/test_solution.py):

```python theme={"theme":{"light":"github-light","dark":"github-dark"}}
class Solution:
    # Time: O(n)
    # Space: O(1)
    def max_rotate_function(self, nums: list[int]) -> int:
        total = sum(nums)
        cur = sum(i * v for i, v in enumerate(nums))
        best = cur
        for k in range(1, len(nums)):
            # rotating clockwise by k moves the last element of arr_(k-1) to index 0
            # and adds total to every other index: F(k) = F(k-1) + total - n * nums[n - k]
            cur += total - len(nums) * nums[-k]
            best = max(best, cur)
        return best
```

## Complexity

| Time | Space |
| - | - |
| O(n) | O(1) |

## Tags


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