Minimum Number of Operations to Make Array XOR Equal to K

Minimum Number of Operations to Make Array XOR Equal to K

1. What is this problem about?

The Minimum Number of Operations to Make Array XOR Equal to K coding problem is a focused challenge on bitwise operations. You are given an array of integers and a target integer k. You can flip any bit in any element of the array (change 0 to 1 or 1 to 0). Your goal is to find the minimum number of bit flips required so that the XOR sum of all elements in the array becomes exactly k.

2. Why is this asked in interviews?

Meta and Amazon frequently use bit manipulation problems to test a candidate's understanding of binary logic and efficiency. This specific question evaluates whether you understand the fundamental property of XOR: that it is associative and commutative. Instead of trying to flip bits in specific elements, a savvy candidate will realize that the problem is about the XOR sum of the entire array compared to k.

3. Algorithmic pattern used

This problem follows the Array, Bit Manipulation interview pattern. The core insight is:

1. Calculate the current XOR sum of all elements in the array: current_xor = arr[0] ^ arr[1] ^ ... ^ arr[n-1].
2. Compare current_xor with the target k.
3. The number of operations is simply the number of bits that are different between current_xor and k. This is calculated as the number of set bits (1s) in the result of current_xor ^ k.

4. Example explanation

Array: [2, 1, 3], Target k: 1

1. Binary: 2 (10), 1 (01), 3 (11)
2. Current XOR: 10 ^ 01 ^ 11 = 11 ^ 11 = 00 (0 in decimal)
3. Target k: 1 (01 in binary)
4. XOR current with k: 00 ^ 01 = 01.
5. Bit count: There is one '1' in 01. Result: 1 flip needed. (You can flip the last bit of any number to make the total XOR 1).

5. Common mistakes candidates make

The most common mistake is trying to iterate through the array and decide which specific number to flip. This is unnecessary and complex. Another error is not knowing how to count set bits efficiently (using something like bin(x).count('1') in Python or __builtin_popcount in C++). Some candidates might also misinterpret "flip a bit" as "change a whole number," which would lead to a different problem entirely.

6. Interview preparation tip

Master the properties of XOR. It is its own inverse, and the XOR of a group of numbers is simply the aggregate of bit parities at each position. This property turns many complex-looking array problems into simple bit-counting tasks.