> For the complete documentation index, see [llms.txt](https://maksimdan.gitbook.io/interview-practice-problems/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://maksimdan.gitbook.io/interview-practice-problems/leetcode_sessions/396-rotate-function.md).

# 396 Rotate Function

Given an array of integers`A`and letnto be its length.

Assume`Bk`to be an array obtained by rotating the array`A`kpositions clock-wise, we define a "rotation function"`F`on`A`as follow:

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

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

**Note:**\
nis guaranteed to be less than 105.

**Example:**

```
A = [4, 3, 2, 6]

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.
```

**Brute Force:** (time limit exceeded)

```python
def maxRotateFunction(self, A):
    """
    :type A: List[int]
    :rtype: int
    """

    if not any(A): return 0
    my_max = float('-inf')
    adder = 0
    for i in range(0, len(A)):
        my_max = max(my_max, sum(A[(mult + adder) % len(A)] * mult for mult in range(0, len(A))))
        adder += len(A) - 1

    return my_max
```


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