# 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.
``````

F(0) = 0A + 1B + 2C +3D

F(1) = 0D + 1A + 2B +3C

F(2) = 0C + 1D + 2A +3B

F(3) = 0B + 1C + 2D +3A

sum = 1A + 1B + 1C + 1D

F(1) = F(0) + sum - 4D

F(2) = F(1) + sum - 4C

F(3) = F(2) + sum - 4B

``````class Solution {
public:
int maxRotateFunction(vector<int>& A) {
int t = 0, sum = 0, n = A.size();
for (int i = 0; i < n; ++i) {
sum += A[i];
t += i * A[i];
}
int res = t;
for (int i = 1; i < n; ++i) {
t = t + sum - n * A[n - i];
res = max(res, t);
}
return res;
}
};
``````

https://leetcode.com/problems/rotate-function/

https://leetcode.com/problems/rotate-function/discuss/87853/Java-O(n)-solution-with-explanation

https://leetcode.com/problems/rotate-function/discuss/87842/Java-Solution-O(n)-with-non-mathametical-explaination

LeetCode All in One 题目讲解汇总(持续更新中…)

 微信打赏 Venmo 打赏
（欢迎加入博主的知识星球，博主将及时答疑解惑，并分享刷题经验与总结，试运营期间前五十位可享受半价优惠～）

×

Help us with donation