Package g2101_2200.s2172_maximum_and_sum_of_array

Class Solution

java.lang.Object
g2101_2200.s2172_maximum_and_sum_of_array.Solution
public class Solution extends java.lang.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 Summary

    Constructors
    Constructor
    Description
    Solution()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    int
    maximumANDSum(int[] nums, int numSlots)
     

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • maximumANDSum

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