Levenshteinetäisyyttä

Levenshteinetäisyys, often referred to as edit distance, is a metric for measuring the difference between two sequences. It is defined as the minimum number of single-character edits required to change one word into the other. The allowed edits are insertion, deletion, and substitution.

For example, to transform the word "kitten" into "sitting", the following edits can be made:

1. substitute 'k' with 's' (kitten -> sitten)

2. substitute 'e' with 'i' (sitten -> sittin)

3. insert 'g' at the end (sittin -> sitting)

This requires 3 edits, so the Levenshteinetäisyys between "kitten" and "sitting" is 3.

The concept was introduced by Vladimir Levenshtein in 1965. It has numerous applications in areas such as spell checking, DNA sequence comparison, and natural language processing. The calculation of Levenshteinetäisyys can be efficiently performed using dynamic programming, typically employing a matrix to store intermediate results. The algorithm fills this matrix by considering the cost of each possible edit operation. The final value in the bottom-right corner of the matrix represents the Levenshteinetäisyys between the two sequences.