## Algorithm

Problem Name: 396. Rotate Function

You are given an integer array nums of length n.

Assume arrk to be an array obtained by rotating nums by k positions clock-wise. We define the rotation function F on nums as follow:

• F(k) = 0 * arrk[0] + 1 * arrk[1] + ... + (n - 1) * arrk[n - 1].

Return the maximum value of F(0), F(1), ..., F(n-1).

The test cases are generated so that the answer fits in a 32-bit integer.

Example 1:

Input: nums = [4,3,2,6]
Output: 26
Explanation:
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.

Example 2:

Input: nums = [100]
Output: 0

Constraints:

• n == nums.length
• 1 <= n <= 105
• -100 <= nums[i] <= 100

## Code Examples

### #1 Code Example with Java Programming

Code - Java Programming

class Solution {
public int maxRotateFunction(int[] A) {

if (A.length == 0) return 0;
int maxVal = Integer.MIN_VALUE;

int c = 1;

while (c  < = A.length) {
int temp = 0;
for (int i=0;i < A.length;i++) {
temp += i*A[i];
}

maxVal = Math.max(maxVal, temp);

rotateArr(A);
c++;
}

return maxVal;
}

public void rotateArr(int[] arr) {
int last = arr[arr.length-1];
for (int i = arr.length-1;i>0;i--) {
arr[i] = arr[i-1];
}

arr[0] = last;
}
}
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Input

cmd
nums = [4,3,2,6]

Output

cmd
26

### #2 Code Example with Javascript Programming

Code - Javascript Programming

const maxRotateFunction = function(A) {
if(A.length === 0) return 0;
let sum = 0, iteration = 0, len = A.length;
for(let i = 0; i < len; i++){
sum += A[i];
iteration += (A[i] * i);
}
let max = iteration;
for(let 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;
};
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Input

cmd
nums = [4,3,2,6]

Output

cmd
26

### #3 Code Example with Python Programming

Code - Python Programming

class Solution:
def maxRotateFunction(self, A):
"""
:type A: List[int]
:rtype: int
"""
mx, sm = 0, sum(A)
for i in range(len(A)):
mx += i * A[i]
curr = mx
for i in range(1, len(A)):
curr = curr - sm + A[i - 1] * len(A)
mx = max(mx, curr)
return mx
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Input

cmd
nums = [100]