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Java-based LeetCode algorithm problem solutions, regularly updated
package g0301_0400.s0396_rotate_function;
// #Medium #Array #Dynamic_Programming #Math #2022_07_15_Time_4_ms_(81.33%)_Space_86_MB_(54.94%)
/**
* 396 - Rotate Function\.
*
* Medium
*
* 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`
**/
public 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;
}
}