RotateFunction396.java

/**
 * 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 class RotateFunction396 {
    public int maxRotateFunction(int[] A) {
        int sum = 0;
        for (int i=0; i<A.length; i++) {
            sum += A[i];
        }

        int rot = 0;
        for (int i=0; i<A.length; i++) {
            rot += i * A[i];
        }
        
        int res = rot;
        for (int i=0; i<A.length; i++) {
            rot += sum;
            rot -= A.length * A[A.length - 1 - i];
            if (rot > res) {
                res = rot;
            }
        }

        return res;
    }

}