Minimize XOR

Problem Description

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.

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

Key Insights

• The problem requires finding a number with a specific number of set bits (1s) that minimizes the XOR with another number.
• The closer the bits of x are to the bits of num1, the smaller the result of x XOR num1 will be.
• We can utilize a greedy approach to construct x by prioritizing setting bits in positions that are already set in num1.

Space and Time Complexity

Time Complexity: O(log(num1) + log(num2)), which is mainly for counting bits and constructing x. Space Complexity: O(1), as we only use a fixed amount of additional space.

Solution

To solve the problem, we can follow these steps:

1. Count the number of set bits in num2.
2. Initialize a variable for x and a bit position counter.
3. Try to set bits in x starting from the most significant bit down to the least significant bit. For each bit position, if that bit is set in num1, we can set the corresponding bit in x.
4. If we have not yet reached the required number of set bits as in num2, continue setting the least significant bits until the count matches.
5. Return the constructed x.

Code Solutions