2172 - Maximum AND Sum of Array.

Hard

You are given an integer array nums of length n and an integer numSlots such that 2 * numSlots >= n. There are numSlots slots numbered from 1 to numSlots.

You have to place all n integers into the slots such that each slot contains at most two numbers. The AND sum of a given placement is the sum of the bitwise AND of every number with its respective slot number.

• For example, the AND sum of placing the numbers [1, 3] into slot 1 and [4, 6] into slot 2 is equal to (1 AND 1) + (3 AND 1) + (4 AND 2) + (6 AND 2) = 1 + 1 + 0 + 2 = 4.

Return the maximum possible AND sum of nums given numSlots slots.

Example 1:

Input: nums = 1,2,3,4,5,6, numSlots = 3

Output: 9

Explanation: One possible placement is 1, 4 into slot 1, 2, 6 into slot 2, and 3, 5 into slot 3.

This gives the maximum AND sum of (1 AND 1) + (4 AND 1) + (2 AND 2) + (6 AND 2) + (3 AND 3) + (5 AND 3) = 1 + 0 + 2 + 2 + 3 + 1 = 9.

Example 2:

Input: nums = 1,3,10,4,7,1, numSlots = 9

Output: 24

Explanation: One possible placement is 1, 1 into slot 1, 3 into slot 3, 4 into slot 4, 7 into slot 7, and 10 into slot 9.

This gives the maximum AND sum of (1 AND 1) + (1 AND 1) + (3 AND 3) + (4 AND 4) + (7 AND 7) + (10 AND 9) = 1 + 1 + 3 + 4 + 7 + 8 = 24.

Note that slots 2, 5, 6, and 8 are empty which is permitted.

Constraints:

• n == nums.length

• 1 <= numSlots <= 9

• 1 <= n <= 2 * numSlots

• 1 <= nums[i] <= 15