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The Hamming distance between two integers is the number of positions at which the corresponding bits are different. Given two integers x and y, calculate the Hamming distance.

Example:

Input: x = 1, y = 4
Output: 2
Explanation:
1 (in binary)  = 0001
4 (in binary)  = 0100
The positions where the bits are different are 1 and 3. Therefore, the Hamming distance is 2.

Clarifying Questions

1. Range of the integers: What are the constraints for the integers x and y?
   • The integers x and y will be non-negative and fit within the typical integer range.
2. Input type: Will the inputs always be integers?
   • Yes, we are guaranteed that x and y are integers.
3. Output type: Should the output be an integer representing the Hamming distance?
   • Yes, the output will be an integer.

With this information, we can proceed to the strategy for the solution.

Strategy

1. XOR Operation: Perform an XOR operation on the two integers x and y. The XOR operation will yield a number where the bits set to 1 represent the positions where the bits of x and y differ.
2. Count 1s: Convert the result of the XOR operation to its binary representation and count the number of 1s. This count represents the Hamming distance.

Code

def hammingDistance(x: int, y: int) -> int:
    # Perform XOR to get differing bits
    xor_result = x ^ y
    # Convert to binary string and count '1's
    distance = bin(xor_result).count('1')
    return distance

Time Complexity

• Time Complexity: O(1)
  • Explanation: The XOR operation and counting the number of 1s in the result (which involves a fixed number of bits for integers) both take constant time. Python handles integers with a fixed bit-length, making the operations effectively O(1).

This completes the solution.

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