Hammingtávolság

Hammingtávolság, often referred to as Hamming distance, is a metric for comparing two strings of equal length. It is defined as the number of positions at which the corresponding symbols are different. In simpler terms, it's the minimum number of substitutions required to change one string into the other.

For example, the Hamming distance between "karolin" and "kathrin" is 3. This is because the letters differ at the 2nd, 4th, and 5th positions. Similarly, the Hamming distance between "1011101" and "1001001" is 2, as the bits differ at the 3rd and 5th positions.

The concept of Hamming distance is named after Richard Hamming, an American mathematician and cryptographer who introduced it in 1950. It finds applications in various fields, including coding theory, information theory, and bioinformatics. In coding theory, it's used to measure the error rate in transmitted data. A smaller Hamming distance between codewords indicates a more robust error detection and correction capability. In bioinformatics, it can be used to compare DNA sequences or protein sequences.

It's important to note that Hamming distance is only defined for strings of equal length. If the strings have different lengths, other distance metrics like Levenshtein distance are used. The Hamming distance is always a non-negative integer.