Minimum XOR Sum of Two Arrays — LeetCode 1879 Python Solution

The problem

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]) + ...

Example

Input

nums1 = [1,2], nums2 = [2,3]

Output

2

Explanation

Rearrange nums2 so that it becomes [3,2].

Python solution

class Solution:
    def minimumXORSum(self, nums1: List[int], nums2: List[int]) -> int:
        n = len(nums2)
        f = [[inf] * (1 << n) for _ in range(n + 1)]
        f[0][0] = 0
        for i, x in enumerate(nums1, 1):
            for j in range(1 << n):
                for k in range(n):
                    if j >> k & 1:
                        f[i][j] = min(f[i][j], f[i - 1][j ^ (1 << k)] + (x ^ nums2[k]))
        return f[-1][-1]

Complexity

Pattern: Bit Manipulation

Use XOR, masks and the low-bit trick to replace whole data structures with an integer. LeetCode 1879. Minimum XOR Sum of Two Arrays is filed here because LeetCode tags it Bit Manipulation and Bitmask, which is the vocabulary this hub collects.

The bit manipulation guide has the Python template for the pattern and the 194 LeetCode problems that use it.

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