3627 - Maximum Median Sum of Subsequences of Size 3.

Medium

You are given an integer array nums with a length divisible by 3.

You want to make the array empty in steps. In each step, you can select any three elements from the array, compute their median , and remove the selected elements from the array.

The median of an odd-length sequence is defined as the middle element of the sequence when it is sorted in non-decreasing order.

Return the maximum possible sum of the medians computed from the selected elements.

Example 1:

Input: nums = 2,1,3,2,1,3

Output: 5

Explanation:

• In the first step, select elements at indices 2, 4, and 5, which have a median 3. After removing these elements, nums becomes [2, 1, 2].

• In the second step, select elements at indices 0, 1, and 2, which have a median 2. After removing these elements, nums becomes empty.

Hence, the sum of the medians is 3 + 2 = 5.

Example 2:

Input: nums = 1,1,10,10,10,10

Output: 20

Explanation:

• In the first step, select elements at indices 0, 2, and 3, which have a median 10. After removing these elements, nums becomes [1, 10, 10].

• In the second step, select elements at indices 0, 1, and 2, which have a median 10. After removing these elements, nums becomes empty.

Hence, the sum of the medians is 10 + 10 = 20.

Constraints:

• <code>1 <= nums.length <= 5 * 10⁵</code>

• nums.length % 3 == 0

• <code>1 <= numsi<= 10⁹</code>