Minimum Number of Operations to Make Array XOR Equal to K

class Solution {
public:
    int minimumOperations(vector<int>& numbers, int target) {
        int xorSum = 0;
        for (int value : numbers) {
            xorSum ^= value;
        }
            
        return __builtin_popcount(xorSum ^ target);
    }
};

The provided C++ code defines a function, minimumOperations, intended to determine the minimum number of operations required to make the XOR of an array equal to a specified target value (denoted as target in the code). The function accomplishes this by executing the following steps:

1. Initialize xorSum to zero. This variable will store the cumulative XOR of all elements in the input array numbers.
2. Iterate over each element in the array numbers and perform a XOR operation with xorSum.
3. Compute the XOR of xorSum and target to find the difference that needs to be corrected.
4. Use the __builtin_popcount function to count the number of 1's in the binary representation of the result from the previous step. This count represents the minimum number of operations needed, where each operation involves flipping a bit.

This function effectively uses bitwise operations to analyze the discrepancy between the current XOR of the array and the desired XOR (target). The use of __builtin_popcount serves as a direct method to quantify the minimum changes required by counting the differing bits.

class Solution {
    public int minimumSteps(int[] array, int target) {
        int resultXor = 0;
        for (int num : array) {
            resultXor ^= num;
        }
            
        return Integer.bitCount(resultXor ^ target);
    }
}

To solve the problem of determining the minimum number of operations required to make the XOR of an array equal to a given target value, consider the following breakdown using Java:

• Initialize a variable resultXor to zero to hold the cumulative XOR of all elements in the array.
• Iterate through each element in the array, updating resultXor by XORing it with the current element. This computes the XOR for the entire array.
• Determine the number of differing bits between resultXor and the target integer. This is achieved by XORing resultXor with the target to highlight bits that differ between the two values and then counting these bits using Integer.bitCount.
• The count from the previous step directly indicates the minimum number of operations required. Each differing bit represents a required operation to flip that particular bit to match the target.

This method provides a straightforward and efficient way to compute the necessary transformations, leveraging the properties of the XOR operation and bit manipulation functions available in Java.

class Solution:
    def minimumOperations(self, numbers: List[int], target: int) -> int:
        result_xor = 0
        for number in numbers:
            result_xor ^= number
            
        return bin(result_xor ^ target).count('1')

The function minimumOperations accepts two parameters: a list of integers called numbers and a single integer named target. The goal is to determine the minimum number of operations required to make the XOR of all elements in the numbers list equal to target.

• Initialize result_xor to zero.
• XOR all elements in numbers using a loop, updating result_xor.
• XOR the result of the aggregation (result_xor) with target.
• Convert the final XOR result to its binary form and count the number of '1's, which represent the necessary operations to transform the combined XOR of the list to the target value.

The number of '1's counted in the binary form of the final XOR result is returned, indicating the minimum number of operations needed. This solution effectively uses bitwise operations to achieve the desired outcome.