Github user yufcuy commented on the issue:
https://github.com/apache/commonslang/pull/189
Hello, @britter @kinow
The details of Levenshtein distance can be find at https://en.wikipedia.org/wiki/Levenshtein_distance,
as it describe, the algorithm is compute a matrix to hold the Levenshtein distances between
all prefixes of the first string and all prefixes of the second. For all i and j, d[i][j]
will hold the Levenshtein distance between the first i characters of s and the first j characters
of t.
The previous impl use two matrix rows for the construction. When we calculate the value
of d[i][j] we find only the value of d[i1][j1], d[i1][j] and d[i][j1] are used according
to the algorithm. And we use a matrix row p[] for the construction, when calculate p[j] at
the ith iteration, it actually calculate the value of d[i][j], and only d[i1][j1] is covered
by p[j1], so we use variable 'upper_left' to hold d[i1][j1], and use variable 'upper' to
hold next 'upper_left'.

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