## 396. Rotate Function

Given an array of integers `A` and let n to be its length.

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

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

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

Note:
n is 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.
```

## Rust Solution

``````struct Solution;

impl Solution {
fn max_rotate_function(a: Vec<i32>) -> i32 {
let n = a.len();
if n == 0 {
return 0;
}
let sum: i32 = a.iter().sum();
let mut f = 0;
for i in 0..n {
f += i as i32 * a[i];
}
let mut res = f;
for i in (1..n).rev() {
f = f + sum - n as i32 * a[i];
res = res.max(f);
}
res
}
}

#[test]
fn test() {
let a = vec![4, 3, 2, 6];
let res = 26;
assert_eq!(Solution::max_rotate_function(a), res);
}
``````

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