# C# - same solution but different take on explaination

• To me it is easier to see the solution if you leave the array as is and rotate the factors left (same result as rotating array right).

For simplicity take an array with 4 elements
[a,b,c,d]

f(0) = 0a + 1b + 2c +3d
f(1) = 3a + 0b + 1c +2d
f(2) = 2a + 3b + 0c +1d
f(3) = 1a + 2b + 3c +0d

Now look what happens when you take difference between f(k) - f(k-1)
f(1) - f(0) = 3a - b - c - d = 4a - (a + b + c + d) = length * a - sum
f(2) - f(1) = -a + 3b - c - d = 4b - (a + b + c + d) = length * b - sum
f(3) - f(2) = -a - b +3c - d = 4c - (a + b + c + d) = length * c - sum

You can see if you calculate (manually) f(0) you can get f(1) by adding length * a and subtracting the sum.

So initially you need to compute the sum and f(0) then just iterate through and get the value of f(i) for each i and record the max.

Hope that helps!

``````public int MaxRotateFunction(int[] A) {

int sum = 0;
for (int i = 0; i < A.Length; i++) sum += A[i];

int prev = 0;
for (int i = 0; i < A.Length; i++) prev += i * A[i];

int max = prev;
for (int i = 1; i < A.Length; i++)
{
int curr = prev - sum + A[i-1]*A.Length;
max = curr > max ? curr : max;
prev = curr;
}

return max;
}``````

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