396. Rotate Function

• Difficulty: Medium

• Topics: Math

• Similar Questions:

Problem:

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. </pre> </p>

Solutions:

class Solution {
public:
    int maxRotateFunction(vector<int>& A) {
        long sum = 0;
        long fun = 0;

        for (int i = 0; i < A.size(); ++i) {
            sum += A[i];
            fun += i * A[i];
        }

        long ret = fun;
        for (int i = A.size() - 1; i > 0; --i) {
            int newFun = fun - A[i] * (A.size() - 1) + (sum - A[i]);
            fun = newFun;
            ret = max(ret, fun);
        }

        return ret;
    }
};