1879. Minimum XOR Sum of Two Arrays

Problem Link

Description

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You are given two integer arrays nums1 and nums2 of length n.

The XOR sum of the two integer arrays is (nums1[0] XOR nums2[0]) + (nums1[1] XOR nums2[1]) + ... + (nums1[n - 1] XOR nums2[n - 1]) (0-indexed).

• For example, the XOR sum of [1,2,3] and [3,2,1] is equal to (1 XOR 3) + (2 XOR 2) + (3 XOR 1) = 2 + 0 + 2 = 4.

Rearrange the elements of nums2 such that the resulting XOR sum is minimized.

Return the XOR sum after the rearrangement.

 

Example 1:

Input: nums1 = [1,2], nums2 = [2,3]
Output: 2
Explanation: Rearrange nums2 so that it becomes [3,2].
The XOR sum is (1 XOR 3) + (2 XOR 2) = 2 + 0 = 2.

Example 2:

Input: nums1 = [1,0,3], nums2 = [5,3,4]
Output: 8
Explanation: Rearrange nums2 so that it becomes [5,4,3]. 
The XOR sum is (1 XOR 5) + (0 XOR 4) + (3 XOR 3) = 4 + 4 + 0 = 8.

 

Constraints:

• n == nums1.length
• n == nums2.length
• 1 <= n <= 14
• 0 <= nums1[i], nums2[i] <= 107

Solution

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Python3

class Solution:
    def minimumXORSum(self, nums1: List[int], nums2: List[int]) -> int:
        n = len(nums1)
        
        @cache
        def dp(i, mask):
            if i == n: return 0
            
            res = float('inf')
            
            for j in range(n):
                if mask & (1 << j) > 0:
                    res = min(res, dp(i + 1, mask ^ (1 << j)) + (nums1[i] ^ nums2[j]))
                
            return res
        
        return dp(0, (1 << n) - 1)