Package g3601_3700.s3630_partition_array_for_maximum_xor_and_and

Class Solution

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public final class Solution

    3630 - Partition Array for Maximum XOR and AND.

    Hard

    You are given an integer array nums.

    Partition the array into three (possibly empty) subsequences A, B, and C such that every element of nums belongs to exactly one subsequence.

    Your goal is to maximize the value of: XOR(A) + AND(B) + XOR(C)

    where:

    • XOR(arr) denotes the bitwise XOR of all elements in arr. If arr is empty, its value is defined as 0.

    • AND(arr) denotes the bitwise AND of all elements in arr. If arr is empty, its value is defined as 0.

    Return the maximum value achievable.

    Note: If multiple partitions result in the same maximum sum, you can consider any one of them.

    Example 1:

    Input: nums = 2,3

    Output: 5

    Explanation:

    One optimal partition is:

    • A = [3], XOR(A) = 3

    • B = [2], AND(B) = 2

    • C = [], XOR(C) = 0

    The maximum value of: XOR(A) + AND(B) + XOR(C) = 3 + 2 + 0 = 5. Thus, the answer is 5.

    Example 2:

    Input: nums = 1,3,2

    Output: 6

    Explanation:

    One optimal partition is:

    • A = [1], XOR(A) = 1

    • B = [2], AND(B) = 2

    • C = [3], XOR(C) = 3

    The maximum value of: XOR(A) + AND(B) + XOR(C) = 1 + 2 + 3 = 6. Thus, the answer is 6.

    Example 3:

    Input: nums = 2,3,6,7

    Output: 15

    Explanation:

    One optimal partition is:

    • A = [7], XOR(A) = 7

    • B = [2,3], AND(B) = 2

    • C = [6], XOR(C) = 6

    The maximum value of: XOR(A) + AND(B) + XOR(C) = 7 + 2 + 6 = 15. Thus, the answer is 15.

    Constraints:

    • 1 <= nums.length <= 19

    • <code>1 <= numsi<= 10<sup>9</sup></code>

    • Nested Class Summary

      Nested Classes 
      Modifier and Type Class Description

    • Field Summary

      Fields 
      Modifier and Type Field Description

    • Constructor Summary

      Constructors 
      Constructor Description
      Solution()

    • Enum Constant Summary

      Enum Constants 
      Enum Constant Description

    • Method Summary

      Modifier and Type Method Description
      final Long maximizeXorAndXor(IntArray nums)

      • Methods inherited from class java.lang.Object

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