Problem
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.length1 <= n <= 10^5-100 <= nums[i] <= 100
Solution
class Solution {
public int maxRotateFunction(int[] nums) {
int allSum = 0;
int len = nums.length;
int f = 0;
for (int i = 0; i < len; i++) {
f += i * nums[i];
allSum += nums[i];
}
int max = f;
for (int i = len - 1; i >= 1; i--) {
f = f + allSum - len * nums[i];
max = Math.max(f, max);
}
return max;
}
}
Explain:
nope.
Complexity:
- Time complexity : O(n).
- Space complexity : O(n).