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--
-- This is an implementation of the Wagner Fischer algorithm, which
-- calculates the Levenshtein distance.
--
-- See https://en.wikipedia.org/wiki/Wagner%E2%80%93Fischer_algorithm
--
function LevenshteinDistance (first, second)
local n = first : len ()
local m = second : len ()
if n < m
then
first, second = second, first
n, m = m, n
end
distances = {}
for i = 0, n do
distances [i] = {}
for j = 0, m do
if i == 0 or j == 0
then
distances [i] [j] = i + j
else
local cost = 1
if string . sub (first, i, i) ==
string . sub (second, j, j)
then
cost = 0
end
distances [i] [j] = math . min (
distances [i - 1] [j] + 1,
distances [i] [j - 1] + 1,
distances [i - 1] [j - 1] + cost
)
end
end
--
-- We only need the previous row, so we can return the
-- memory of rows before that. This reduces the memory
-- usage from O (n * m) to O (min (n, m))
--
if i > 0
then
distances [i - 1] = nil
end
end
return distances [n] [m]
end
for line in io . lines () do
--
-- Extract words and put them into an array.
--
local words = {}
index = 0
for str in string . gmatch (line, "[^ ]+") do
index = index + 1
words [index] = str
end
--
-- Calculate the edit distance, and print the result.
--
io . write (LevenshteinDistance (words [1], words [2]), "\n")
end
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