Is Minimize XOR easy or hard?

Minimize XOR is generally rated Medium difficulty. The implementation is short, but the key insight is understanding how XOR magnitude depends on bit positions and why matching higher bits first leads to the optimal result.

Minimize XOR Python/Java solution

Python and Java implementations follow the same idea: count the set bits in num2, iterate through the bits of num1 from most significant to least significant, and build the result integer greedily. If more bits are required, set them starting from the least significant positions.

How to solve Minimize XOR in O(n)?

The problem is typically solved in O(log M) or constant time rather than O(n). Count the set bits in num2, then greedily copy matching set bits from num1 starting from the most significant position. If more bits are needed, fill them from the least significant positions until the count matches.

What is the best approach for Minimize XOR?

The greedy bit setting strategy is the most efficient approach. It first matches the highest set bits of num1 to reduce XOR impact, then fills remaining bits from the least significant positions. This guarantees the smallest possible XOR while maintaining the required number of set bits. The runtime is effectively O(1) since integers have a fixed bit width.

Is Minimize XOR asked at Google/Amazon/Meta?

Bit manipulation and greedy reasoning problems like Minimize XOR commonly appear in interviews at companies such as Google, Amazon, and Meta. Variants often test understanding of bit significance, popcount operations, and constructing numbers with constraints.

What data structure is used in Minimize XOR?

No complex data structures are required. The solution mainly uses bit manipulation operations such as bit shifting, masking, and counting set bits. The algorithm works directly on integer bit representations.

What is the time complexity of Minimize XOR?

The optimal solution runs in O(1) time with O(1) space because it processes a fixed number of bits (typically 32 or 64 depending on the integer type). Even when expressed as O(log M), where M is the maximum integer value, the complexity remains very small in practice.

Description Hints 2 Solution Video 52:17

2429. Minimize XOR

Medium62.4% acceptance6 companies

Given two positive integers num1 and num2, find the positive integer x such that:

x has the same number of set bits as num2, and
The value x XOR num1 is minimal.

Note that XOR is the bitwise XOR operation.

Return the integer x. The test cases are generated such that x is uniquely determined.

The number of set bits of an integer is the number of 1's in its binary representation.

Example 1:

Input: num1 = 3, num2 = 5
Output: 3
Explanation:
The binary representations of num1 and num2 are 0011 and 0101, respectively.
The integer 3 has the same number of set bits as num2, and the value 3 XOR 3 = 0 is minimal.

Example 2:

Input: num1 = 1, num2 = 12
Output: 3
Explanation:
The binary representations of num1 and num2 are 0001 and 1100, respectively.
The integer 3 has the same number of set bits as num2, and the value 3 XOR 1 = 2 is minimal.

Constraints: