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Given two integers, a and b, determine the number of bit changes (i.e., bit flips) required to convert a into b. Essentially, you need to find the number of differing bits between the binary representations of a and b.

Clarifying Questions

1. What is the range of the integers a and b?
   • This would help in understanding if there are potentially any performance concerns.
2. Are the integers signed or unsigned?
   • This is relevant for handling possible negative values and their binary representations.
3. Can a and b be the same?
   • In this case, the number of bit changes would be zero.
4. Are there any constraints on the time or space complexity?

Strategy

1. XOR Operation:
   • Use the XOR operation between a and b. This will highlight the differing bits:
     • If a bit in the same position in both integers is different, the result will be 1; otherwise, it will be 0.
2. Counting Set Bits:
   • Count the number of set bits (bits with value 1) in the result of the XOR operation. Each set bit represents a difference that needs to be changed.

Steps:

1. Perform the XOR of a and b.
2. Use a loop (or an efficient method) to count the number of 1s in the result.

Code

def bit_change_count(a: int, b: int) -> int:
    # Perform XOR operation between a and b
    xor_result = a ^ b
    
    # Count the number of set bits
    count = 0
    while xor_result:
        count += xor_result & 1  # Increment if the least significant bit is 1
        xor_result >>= 1  # Right shift the bits to check next bit
    
    return count

Time Complexity

• Time Complexity: O(n), where n is the number of bits in the maximum of a or b. Here, each shift operation and bit count step is constant, but this has to be done for each bit.
• Space Complexity: O(1), as we are using a constant amount of space regardless of the input size.

This algorithm efficiently computes the number of differing bits by leveraging bitwise operations and simple counts. It operates in linear time relative to the number of bits, which is optimal for this type of problem.

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