Bitwise XOR of All Pairings

class Solution {
public:
    int xorBothArrays(vector<int>& array1, vector<int>& array2) {
        int resultXor1 = 0;
        int resultXor2 = 0;
        int count1 = array1.size();
        int count2 = array2.size();

        if (count2 % 2 != 0) {
            for (int value : array1) {
                resultXor1 ^= value;
            }
        }

        if (count1 % 2 != 0) {
            for (int value : array2) {
                resultXor2 ^= value;
            }
        }

        return resultXor1 ^ resultXor2;
    }
};

Here's a concise summary of the solution in C++ to find the bitwise XOR of all pairings between two arrays:

This solution defines a class, Solution, with the method xorBothArrays that takes two vectors of integers as inputs, array1 and array2. It initializes two zero integers, resultXor1 and resultXor2, to hold the XOR computation results for the arrays. The function also calculates the size of each input array.

The method proceeds to check the count of elements in array2. If this count is odd, the function XORs all elements of array1 and stores the result in resultXor1.

Similarly, the function checks the count of elements in array1. If this count is odd, all elements of array2 are XORed together and the result is stored in resultXor2.

Finally, the method returns the XOR of resultXor1 and resultXor2. This result represents the XOR of all possible element pairings between the two arrays based on whether count of elements in arrays are odd, combining the outcomes effectively.

This approach focuses on minimizing computations by leveraging the properties of XOR and the parity of the counts of the arrays to determine whether full array iteration is necessary.

class Solution {

    public int xorCombined(int[] array1, int[] array2) {
        int result1 = 0;
        int result2 = 0;

        int length1 = array1.length;
        int length2 = array2.length;

        if (length2 % 2 != 0) {
            for (int item : array1) {
                result1 ^= item;
            }
        }

        if (length1 % 2 != 0) {
            for (int item : array2) {
                result2 ^= item;
            }
        }

        return result1 ^ result2;
    }
}

In this solution, the method xorCombined calculates the bitwise XOR of all possible pairings from two different arrays. Below is a breakdown of the method's functionality in Java:

1. Initialize two integers, result1 and result2, to zero. These variables store the XOR results for each array.

2. Determine the lengths of array1 and array2.

3. Check if the length of array2 is odd:

   • If true, iterate through each element in array1 and apply the XOR operation, storing the result in result1.

4. Similarly, check if the length of array1 is odd:

   • If true, iterate through each element in array2 and apply the XOR operation, storing the result in result2.

5. Finally, XOR the results stored in result1 and result2 to get the final result.

This approach leverages the property of XOR where the XOR of an element with itself results in zero, and the XOR of an element with zero leaves the element unchanged. This property is pivotal when combined with odd counts in the arrays, ensuring that elements contributing to the final result are all effectively utilized.

class Solution:
    def xorOperationOverSets(self, set1: List[int], set2: List[int]) -> int:
        xor_result1, xor_result2 = 0, 0
        set1_length, set2_length = len(set1), len(set2)

        if set2_length % 2:
            for element in set1:
                xor_result1 ^= element

        if set1_length % 2:
            for element in set2:
                xor_result2 ^= element

        return xor_result1 ^ xor_result2

The problem involves computing the Bitwise XOR for all pairings between two sets of integers. In Python, given two lists set1 and set2, calculate this combined XOR based on certain conditions.

• Initialize two integers xor_result1 and xor_result2 to zero, which will store the interim XOR results of elements from set1 and set2 respectively.
• Determine the lengths of set1 and set2.
• If the length of set2 is odd, XOR all elements of set1 together and store this in xor_result1.
• If the length of set1 is odd, proceed similarly by XORing all elements of set2 to store the result in xor_result2.
• Finally, XOR xor_result1 and xor_result2 to get and return the cumulative result. This approach effectively applies the properties of XOR operation and leverages the parity of the sets' lengths to compute the result efficiently.