396. Rotate Function

这题我用了一个没有用到数学的方法，用list滚动乘数的index去跟A相乘。其实滚动int [] A里的数字去跟index相乘也一样，同样要用一个list来滚动。

    public int maxRotateFunction(int[] A) {
        if (A == null || A.length == 0) return 0;
        int n = A.length;
        int max = Integer.MIN_VALUE;
        List<Integer> list = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            list.add(i);
        }
        for (int i = 0; i < n; i++) {
            int product = 0;
            for (int j = 0; j < n; j++) {
                product += list.get(j) * A[j];
            }
            max = Math.max(max, product);
            list.add(list.remove(0));
        }
        return max;
    }

看了答案，高票的用了一些数学方法，找了个简单的理解了下：

   public int maxRotateFunction(int[] A) {
        if(A.length == 0){
            return 0;
        }
        
        int sum =0, iteration = 0, len = A.length;
        
        for(int i=0; i<len; i++){
            sum += A[i];
            iteration += (A[i] * i);
        }
        
        int max = iteration;
        for(int j=1; j<len; j++){
            // for next iteration lets remove one entry value of each entry and the prev 0 * k
            iteration = iteration - sum + A[j-1]*len;
            max = Math.max(max, iteration);
        }
        
        return max;
    }