Minimum Number of Operations to Make Array XOR Equal to K

Problem Description

You are given a 0-indexed integer array nums and a positive integer k. You can apply the following operation on the array any number of times: Choose any element of the array and flip a bit in its binary representation. Flipping a bit means changing a 0 to 1 or vice versa. Return the minimum number of operations required to make the bitwise XOR of all elements of the final array equal to k.

Key Insights

• The XOR operation has specific properties, such as a XOR a = 0 and a XOR 0 = a.
• The goal is to determine the XOR of the array and how many bits need to be flipped to achieve the target k.
• The difference between the current XOR of the array and k can be computed to find the necessary bit flips.
• Each differing bit between the current XOR and k corresponds to a potential operation.

Space and Time Complexity

Time Complexity: O(n) where n is the length of the nums array.
Space Complexity: O(1) as we use a constant amount of space regardless of input size.

Solution

To solve the problem, we first compute the XOR of all elements in the nums array. We then calculate the XOR of this result with k. The number of bits that differ between these two values indicates how many bit flips are needed. We can use the property of XOR to identify differing bits efficiently.

1. Compute the XOR of all elements in the nums array.
2. Calculate the XOR of the result with k to find the target difference.
3. Count the number of bits set to 1 in the resulting XOR value; this number will be the minimum operations needed.

Code Solutions