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[0] + 1 * Bk[1] + ... + (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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