Package g2101_2200.s2172_maximum_and_sum_of_array

Class Solution

  • public class Solution
extends Object
    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

    • Constructor Detail

      • Solution

        public Solution()

    • Method Detail

      • maximumANDSum

        public int maximumANDSum​(int[] nums,
                         int numSlots)