# [LeetCode]--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.

public int maxRotateFunction(int[] A) {
int len = A.length;
int max = 0, sum = 0, presum = 0;
for (int i = 0; i < len; i++) {
sum += A[i];
presum += A[i] * i;
}
max = presum;
for (int i = len - 1; i >= 0; i--) {
presum += sum - len * A[i];
max = Math.max(max, presum);
}
return max;
}

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