230 lines
8.5 KiB
Julia
Executable File
230 lines
8.5 KiB
Julia
Executable File
"""
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Jaro()
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Creates the Jaro distance
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The Jaro distance is defined as
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``1 - (m / |s1| + m / |s2| + (m - t) / m) / 3``
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where ``m`` is the number of matching characters and
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``t`` is half the number of transpositions.
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"""
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struct Jaro <: SemiMetric end
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## http://alias-i.com/lingpipe/docs/api/com/aliasi/spell/JaroWinklerDistance.html
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## accepts any iterator, including AbstractString
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function (dist::Jaro)(s1, s2)
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((s1 === missing) | (s2 === missing)) && return missing
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s1, s2 = reorder(s1, s2)
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len1, len2 = length(s1), length(s2)
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# If both are empty, the formula in Wikipedia gives 0
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# Add this line so that not the case
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len2 == 0 && return 0.0
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maxdist = max(0, div(len2, 2) - 1)
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flag = fill(false, len2)
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ch1_match = Vector{eltype(s1)}()
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for (i1, ch1) in enumerate(s1)
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for (i2, ch2) in enumerate(s2)
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# greedy alignement
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if (i2 <= i1 + maxdist) && (i2 >= i1 - maxdist) && (ch1 == ch2) && !flag[i2]
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flag[i2] = true
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push!(ch1_match, ch1)
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break
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end
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end
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end
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# m counts number matching characters
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m = length(ch1_match)
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m == 0 && return 1.0
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# t counts number transpositions
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t = 0
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i1 = 0
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for (i2, ch2) in enumerate(s2)
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if flag[i2]
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i1 += 1
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t += ch2 != ch1_match[i1]
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end
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end
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return 1.0 - (m / len1 + m / len2 + (m - t/2) / m) / 3.0
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end
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"""
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Levenshtein()
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Creates the Levenshtein distance
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The Levenshtein distance is the minimum number of operations (consisting of insertions, deletions,
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substitutions of a single character) required to change one string into the other.
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"""
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struct Levenshtein <: Metric end
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## Source: http://blog.softwx.net/2014/12/optimizing-levenshtein-algorithm-in-c.html
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# Return max_value + 1 if distance higher than max_value
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# This makes it possible to differentiate distance equalt to max_value vs strictly higher
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# This is important for find_all
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function (dist::Levenshtein)(s1, s2, max_value = nothing)
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((s1 === missing) | (s2 === missing)) && return missing
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s1, s2 = reorder(s1, s2)
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len1, len2 = length(s1), length(s2)
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max_value !== nothing && len2 - len1 > max_value && return max_value + 1
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# prefix common to both strings can be ignored
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k = common_prefix(s1, s2)
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k == len1 && return len2 - k
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# distance initialized to first row of matrix
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# distance between "" and s2[1:i]
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v = collect(1:(len2-k))
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current = 0
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for (i1, ch1) in enumerate(s1)
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i1 <= k && continue
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left = current = i1 - k - 1
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max_value !== nothing && (value_lb = left - 1)
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for (i2, ch2) in enumerate(s2)
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i2 <= k && continue
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above, current, left = current, left, v[i2 - k]
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if ch1 != ch2
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current = min(current, above, left) + 1
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end
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max_value !== nothing && (value_lb = min(value_lb, left))
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v[i2 - k] = current
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end
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max_value !== nothing && value_lb > max_value && return max_value + 1
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end
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max_value !== nothing && current > max_value && return max_value + 1
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return current
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end
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"""
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DamerauLevenshtein()
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Creates the restricted DamerauLevenshtein distance
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The DamerauLevenshtein distance is the minimum number of operations (consisting of insertions,
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deletions or substitutions of a single character, or transposition of two adjacent characters)
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required to change one string into the other.
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The restricted distance differs slightly from the classic Damerau-Levenshtein algorithm by imposing
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the restriction that no substring is edited more than once. So for example, "CA" to "ABC" has an edit
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distanceof 2 by a complete application of Damerau-Levenshtein, but a distance of 3 by this method that
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uses the optimal string alignment algorithm. In particular, the restricted distance does not satisfy
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the triangle inequality.
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"""
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struct DamerauLevenshtein <: SemiMetric end
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## http://blog.softwx.net/2015/01/optimizing-damerau-levenshtein_15.html
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# Return max_value + 1 if distance higher than max_value
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function (dist::DamerauLevenshtein)(s1, s2, max_value = nothing)
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((s1 === missing) | (s2 === missing)) && return missing
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s1, s2 = reorder(s1, s2)
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len1, len2 = length(s1), length(s2)
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max_value !== nothing && len2 - len1 > max_value && return max_value + 1
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# prefix common to both strings can be ignored
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k = common_prefix(s1, s2)
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k == len1 && return len2 - k
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v = collect(1:(len2-k))
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w = similar(v)
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if max_value !== nothing
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i2_start = k + 1
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i2_end = max_value
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end
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prevch1, prevch2 = first(s1), first(s2)
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current = 0
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for (i1, ch1) in enumerate(s1)
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i1 <= k && continue
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left = current = i1 - k - 1
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nextTransCost = 0
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if max_value !== nothing
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i2_start += (i1 > 1 + max_value - (len2 - len1)) ? 1 : 0
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i2_end += (i2_end < len2) ? 1 : 0
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end
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for (i2, ch2) in enumerate(s2)
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i2 <= k && continue
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# no need to look beyond window of lower right diagonal - maxDistance cells (lower right diag is i1 - (len2 - len1)) and the upper left diagonal + max_value cells (upper left is i1)
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if (max_value !== nothing) && ((i2 < i2_start) | (i2 > i2_end))
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prevch2 = ch2
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else
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above, current, left = current, left, v[i2 - k]
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w[i2 - k], nextTransCost, thisTransCost = current, w[i2 - k], nextTransCost
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# left now equals current cost (which will be diagonal at next iteration)
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if ch1 != ch2
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current = min(left, current, above) + 1
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# note that it never happens at i2 = k + 1 because then the two previous characters were equal
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if (i1 > 1 + k) & (i2 > 1 + k) && (ch1 == prevch2) && (prevch1 == ch2)
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thisTransCost += 1
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current = min(current, thisTransCost)
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end
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end
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v[i2 - k] = current
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prevch2 = ch2
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end
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end
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max_value !== nothing && v[i1 - k + len2 - len1] > max_value && return max_value + 1
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prevch1 = ch1
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end
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max_value !== nothing && current > max_value && return max_value + 1
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return current
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end
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"""
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RatcliffObershelp()
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Creates the RatcliffObershelp distance
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The distance between two strings is defined as one minus the number of matching characters
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divided by the total number of characters in the two strings. Matching characters are those
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in the longest common subsequence plus, recursively, matching characters in the unmatched
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region on either side of the longest common subsequence.
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"""
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struct RatcliffObershelp <: SemiMetric end
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function (dist::RatcliffObershelp)(s1, s2)
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((s1 === missing) | (s2 === missing)) && return missing
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s1, s2 = reorder(s1, s2)
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n_matched = sum(last.(matching_blocks(s1, s2)))
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len1, len2 = length(s1), length(s2)
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len1 + len2 == 0 ? 0. : 1.0 - 2 * n_matched / (len1 + len2)
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end
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function matching_blocks(s1, s2)
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matching_blocks!(Set{Tuple{Int, Int, Int}}(), s1, s2, 1, 1)
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end
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function matching_blocks!(x::Set{Tuple{Int, Int, Int}}, s1, s2, start1::Integer, start2::Integer)
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n1, n2, len = longest_common_pattern(s1, s2)
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# exit if there is no common substring
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len == 0 && return x
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# add the info of the common to the existing set
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push!(x, (n1 + start1 - 1, n2 + start2 - 1, len))
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# add the longest common substring that happens before
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matching_blocks!(x, _take(s1, n1 - 1), _take(s2, n2 - 1), start1, start2)
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# add the longest common substring that happens after
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matching_blocks!(x, _drop(s1, n1 + len - 1), _drop(s2, n2 + len - 1),
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start1 + n1 + len - 1, start2 + n2 + len - 1)
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return x
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end
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function longest_common_pattern(s1, s2)
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if length(s1) > length(s2)
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start2, start1, len = longest_common_pattern(s2, s1)
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else
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start1, start2, len = 0, 0, 0
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p = zeros(Int, length(s2))
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for (i1, ch1) in enumerate(s1)
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oldp = 0
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for (i2, ch2) in enumerate(s2)
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newp = 0
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if ch1 == ch2
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newp = oldp > 0 ? oldp : i2
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currentlength = i2 - newp + 1
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if currentlength > len
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start1, start2, len = i1 - currentlength + 1, newp, currentlength
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end
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end
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p[i2], oldp = newp, p[i2]
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end
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end
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end
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return start1, start2, len
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end |