Is Minimum XOR Sum of Two Arrays easy or hard?

Minimum XOR Sum of Two Arrays is classified as a Hard problem. The challenge comes from recognizing that the pairing constraint forms a permutation problem and solving it efficiently using bitmask dynamic programming.

Minimum XOR Sum of Two Arrays Python/Java solution

Python and Java implementations typically use DP with a bitmask integer representing used elements of nums2. The algorithm iterates through all masks, counts set bits to determine the index in nums1, and updates the DP state with the XOR cost. The same logic works across Python, Java, C++, and JavaScript.

How to solve Minimum XOR Sum of Two Arrays in O(n)?

An O(n) solution is not possible because the problem requires evaluating pairings between two arrays, which is essentially a permutation optimization problem. The best known approach uses dynamic programming with bitmasking and runs in O(n * 2^n) time.

What is the best approach for Minimum XOR Sum of Two Arrays?

Dynamic programming with bitmasking is the most efficient approach. Each bitmask represents which elements from nums2 are already paired, and DP stores the minimum XOR cost for that state. This reduces the permutation search from O(n!) to O(n * 2^n), which is manageable for n up to about 14.

Is Minimum XOR Sum of Two Arrays asked at Google/Amazon/Meta?

This type of problem appears in interviews at companies like Google, Amazon, and Meta because it tests bitmask dynamic programming and permutation optimization. Variations of assignment problems and XOR minimization are common in advanced algorithm rounds.

What data structure is used in Minimum XOR Sum of Two Arrays?

The core technique uses a bitmask integer to represent which elements of nums2 are already used. A dynamic programming array or hash map stores the minimum XOR sum for each mask state. Efficient bit manipulation operations check and update the mask during transitions.

What is the time complexity of Minimum XOR Sum of Two Arrays?

The optimal solution runs in O(n * 2^n) time. There are 2^n possible masks representing used elements of nums2, and for each state you try up to n pairings. Space complexity is O(2^n) for the DP table or memoization cache.

Description Hints 2 Solution Video 38:14

1879. Minimum XOR Sum of Two Arrays

Hard52.0% acceptance1 company

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

Asked at 1 company

Medianet

Topics

Hints open one at a time

Hint 1

Since n <= 14, we can consider every subset of nums2.

Hint 2

We can represent every subset of nums2 using bitmasks.

38:14

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