The Hamming Distance

The Hamming Distance

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The Hamming distance between two binary integers is the number of bit positions that differs (read more about the Hamming distance on Wikipedia). For example:

    117 = 0 1 1 1 0 1 0 1
     17 = 0 0 0 1 0 0 0 1
      H = 0+1+1+0+0+1+0+0 = 3

You are given two positive integers N, M in decimal form. You should calculate the Hamming distance between these two numbers in binary form.

Input: Two arguments as integers (int).

Output: The Hamming distance as an integer (int).

Examples:

assert checkio(117, 17) == 3
assert checkio(1, 2) == 2
assert checkio(16, 15) == 5
assert checkio(255, 1) == 7

How it is used:

This is a basis for Hamming code and other linear error-correcting programs. The Hamming distance is used in systematics as a measure of genetic distance. On a grid (ie: a chessboard,) the Hamming distance is the minimum number of moves it would take a rook to move from one cell to the other.

Precondition:

  • 0 < n, m < 106

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