Minimum XOR Sum of Two Arrays

arraydynamic programmingbit manipulation

Problem Statement

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 .

Examples

Example 1

Input: nums1 = [1,2], nums2 = [2,3]
Output: 2
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
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] <= 10 ^7

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Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicDynamic Programming