Find XOR Sum of All Pairs Bitwise AND

arraymathbit manipulation

Problem Statement

The XOR sum of a list is the bitwise XOR of all its elements. If the list only contains one element, then its XOR sum will be equal to this element.

For example, the XOR sum of [1,2,3,4] is equal to 1 XOR 2 XOR 3 XOR 4 = 4 , and the XOR sum of [3] is equal to 3 .

You are given two 0-indexed arrays arr1 and arr2 that consist only of non-negative integers.

Consider the list containing the result of arr1[i] AND arr2[j] (bitwise AND ) for every (i, j) pair where 0 <= i < arr1.length and 0 <= j < arr2.length .

Return the XOR sum of the aforementioned list .

Examples

Example 1

Input: arr1 = [1,2,3], arr2 = [6,5]
Output: 0
The list = [1 AND 6, 1 AND 5, 2 AND 6, 2 AND 5, 3 AND 6, 3 AND 5] = [0,1,2,0,2,1].
The XOR sum = 0 XOR 1 XOR 2 XOR 0 XOR 2 XOR 1 = 0.

Example 2

Input: arr1 = [12], arr2 = [4]
Output: 4
The list = [12 AND 4] = [4]. The XOR sum = 4.

Constraints

1 <= arr1.length, arr2.length <= 10 ^5

0 <= arr1[i], arr2[j] <= 10 ^9

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Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicMath