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AlexTitenkoAlexTitenko
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Added string comparison functions
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‎User_Defined_Function/udf_StringComparisonsLevenshteinFull-matrix.sql

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alter FUNCTION LevenschteinDifference
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(
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@FirstString nVarchar(255), @SecondString nVarchar(255)
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)
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RETURNS int
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as begin
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Declare @PseudoMatrix table
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(location int identity primary key,
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firstorder int not null,
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Firstch nchar(1),
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secondorder int not null,
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Secondch nchar(1),
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Thevalue int not null default 0,
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PreviousRowValues varchar(200)
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)
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insert into @PseudoMatrix (firstorder, firstch, secondorder, secondch, TheValue )
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SELECT TheFirst.number,TheFirst.ch, TheSecond.number,TheSecond.ch,0
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FROM --divide up the first string into a table of characters/sequence
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(SELECT number, SUBSTRING(@FirstString,number,1) AS ch
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FROM numbers WHERE number <= LEN(@FirstString) union all Select 0,Char(0)) TheFirst
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cross JOIN --divide up the second string into a table of characters/sequence
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(SELECT number, SUBSTRING(@SecondString,number,1) AS ch
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FROM numbers WHERE number <= LEN(@SecondString) union all Select 0,Char(0)) TheSecond
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--ON Thefirst.ch= Thesecond.ch --do all valid matches
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order by TheFirst.number, TheSecond.number
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Declare @current Varchar(255)
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Declare @previous Varchar(255)
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Declare @TheValue int
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Declare @Deletion int, @Insertion int, @Substitution int, @minim int
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Select @current='', @previous=''
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Update @PseudoMatrix
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Set
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@Deletion=@TheValue+1,
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@Insertion=ascii(substring(@previous,secondorder+1,1))+1,
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@Substitution=ascii(substring(@previous,(secondorder),1)) +1,
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@minim=case when @Deletion<@Insertion then @Deletion else @insertion end,
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@TheValue = Thevalue = case --when Firstorder+SecondOrder=0 then 0
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when SecondOrder=0 then FirstOrder
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When FirstOrder=0 then Secondorder
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when FirstCh=SecondCh then ascii(substring(@previous,(secondorder),1))
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else case when @Minim<@Substitution then @Minim else @Substitution end
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end,
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@Previous=PreviousRowValues=case when secondorder =0 then @current else @Previous end,
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@current= case when secondorder =0 then char(@TheValue) else @Current+char(@TheValue) end
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return @TheValue
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End
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Go

‎User_Defined_Function/udf_StringComparisonsLevenshteinString-based.sql

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alter function LEVENSHTEIN ( @SourceString nvarchar(100), @TargetString nvarchar(100) )
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--Returns the Levenshtein Distance between @SourceString string and @TargetString
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--Translated to TSQL by Joseph Gama
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--Updated slightly by Phil Factor
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returns int
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as
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BEGIN
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DECLARE @Matrix Nvarchar(4000), @LD int, @TargetStringLength int, @SourceStringLength int,
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@ii int, @jj int, @CurrentSourceChar nchar(1), @CurrentTargetChar nchar(1),@Cost int,
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@Above int,@AboveAndToLeft int,@ToTheLeft int, @MinimumValueOfCells int
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-- Step 1: Set n to be the length of s. Set m to be the length of t.
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-- If n = 0, return m and exit.
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-- If m = 0, return n and exit.
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-- Construct a matrix containing 0..m rows and 0..n columns.
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if @SourceString is null or @TargetString is null return null
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Select @SourceStringLength=LEN(@SourceString),
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@TargetStringLength=LEN(@TargetString),
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@Matrix=replicate(nchar(0),(@SourceStringLength+1)*(@TargetStringLength+1))
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If @SourceStringLength = 0 return @TargetStringLength
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If @TargetStringLength = 0 return @SourceStringLength
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if (@TargetStringLength+1)*(@SourceStringLength+1)> 4000 return -1
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--Step 2: Initialize the first row to 0..n.
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-- Initialize the first column to 0..m.
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SET @ii=0
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WHILE @ii<=@SourceStringLength
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BEGIN
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SET @Matrix=STUFF(@Matrix,@ii+1,1,nchar(@ii))--d(i, 0) = i
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SET @ii=@ii+1
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END
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SET @ii=0
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WHILE @ii<=@TargetStringLength
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BEGIN
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SET @Matrix=STUFF(@Matrix,@ii*(@SourceStringLength+1)+1,1,nchar(@ii))--d(0, j) = j
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SET @ii=@ii+1
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END
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--Step 3 Examine each character of s (i from 1 to n).
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SET @ii=1
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WHILE @ii<=@SourceStringLength
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BEGIN
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--Step 4 Examine each character of t (j from 1 to m).
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SET @jj=1
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WHILE @jj<=@TargetStringLength
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BEGIN
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--Step 5 and 6
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Select
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--Set cell d[i,j] of the matrix equal to the minimum of:
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--a. The cell immediately above plus 1: d[i-1,j] + 1.
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--b. The cell immediately to the left plus 1: d[i,j-1] + 1.
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--c. The cell diagonally above and to the left plus the cost: d[i-1,j-1] + cost
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@Above=unicode(substring(@Matrix,@jj*(@SourceStringLength+1)+@ii-1+1,1))+1,
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@ToTheLeft=unicode(substring(@Matrix,(@jj-1)*(@SourceStringLength+1)+@ii+1,1))+1,
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@AboveAndToLeft=unicode(substring(@Matrix,(@jj-1)*(@SourceStringLength+1)+@ii-1+1,1))
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+ case when (substring(@SourceString,@ii,1)) = (substring(@TargetString,@jj,1))
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then 0 else 1 end--the cost
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-- If s[i] equals t[j], the cost is 0.
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-- If s[i] doesn't equal t[j], the cost is 1.
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-- now calculate the minimum value of the three
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if (@Above < @ToTheLeft) AND (@Above < @AboveAndToLeft)
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select @MinimumValueOfCells=@Above
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else if (@ToTheLeft < @Above) AND (@ToTheLeft < @AboveAndToLeft)
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select @MinimumValueOfCells=@ToTheLeft
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else
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select @MinimumValueOfCells=@AboveAndToLeft
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Select @Matrix=STUFF(@Matrix,
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@jj*(@SourceStringLength+1)+@ii+1,1,
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nchar(@MinimumValueOfCells)),
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@jj=@jj+1
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END
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SET @ii=@ii+1
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END
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--Step 7 After iteration steps (3, 4, 5, 6) are complete, distance is found in cell d[n,m]
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return unicode(substring(
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@Matrix,@SourceStringLength*(@TargetStringLength+1)+@TargetStringLength+1,1
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))
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END
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go

‎User_Defined_Function/udf_StringComparisonsLongestCommonSubsequence.sql

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IF OBJECT_ID (N'LongestCommonSubsequence') IS NOT NULL
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DROP FUNCTION LongestCommonSubsequence
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GO
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Create FUNCTION LongestCommonSubsequence
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/**
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summary: >
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The longest common subsequence (LCS) problem is the problem of finding the
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longest subsequence common to all sequences in two sequences. It differs
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from problems of finding common substrings: unlike substrings, subsequences
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are not required to occupy consecutive positions within the original
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sequences. For example, the sequences "1234" and "1224533324" have an LCS
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of "1234":
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Author: Phil Factor
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Revision: 1.0
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date: 05 Dec 2014
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example:
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code: |
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Select dbo.LongestCommonSubsequence ('1234', '1224533324')
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Select dbo.LongestCommonSubsequence ('thisisatest', 'testing123testing')
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Select dbo.LongestCommonSubsequence ( 'XMJYAUZ', 'MZJAWXU')
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Select dbo.LongestCommonSubsequence ( 'beginning-middle-ending',
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'beginning-diddle-dum-ending')
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returns: >
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the longest common subsequence as a string
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**/
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(
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@firstString Varchar(max),
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@SecondString Varchar(max)
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)
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RETURNS varchar(max)
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as begin
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Declare @Array Varchar(MAX)
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Declare @ArrayMax int
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Declare @west char(1)
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Declare @Lines Varchar(max)
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Declare @ii int, @jj int, @iiMax int, @jjMax int, @index int
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Select @iiMax=len(@FirstString), --the length of the first string
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@jjMax=len(@SecondString), --the length of the second string
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@index=@jjMax+1 --where the first new item (matrix has an extra row & column)
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Select @ArrayMax=(@iiMax)*(@jjMax)--total length of the array iterated
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Select @Array=replicate(char(0), @jjMax+1) --add in the first nought-filled row
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Select
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@Index=@Index+case when (number-1) % @jjMax = 0 then 2 else 1 end, --current index
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@west=case when (number-1) % @jjMax = 0 then Char(0) else substring(@Array,@index-1,1) end,
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--as we add an extra column in, this is a dangerous operation otherwise
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@Array=@Array --we add a character to the string array, Char(0)--char
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+ case when (number-1) % @jjMax = 0 then Char(0) else '' end -- begin new row always zero
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+ case --check first to see if there was a match. If so, take north west number incremented
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when substring(@firstString,((Number-1)/@jjMax)+1,1)
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=substring(@SecondString, ((number-1)% @jjMax)+1 ,1)
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--remember to set the appropriate collation for this comparison!
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then Char(Ascii(substring(@Array,@index-@jjmax-2,1))+1)--increment the NW value
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when Ascii(substring(@Array,@index-@jjmax-1,1))>ascii(@west) --compare west to north
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then substring(@Array,@index-@jjmax-1,1) --and take the larger
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else @west-- number to west if larger
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end
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from numbers where number<=@ArrayMax
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--Now all we need to do is to backtrack through the matrix to find the best solution
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Declare @commonString Varchar(max), @X_Y int
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Select @CommonString ='' --this contains the string
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Select @ii=@iimax+1,@jj=@jjmax+1
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while (@ii>1 and @jj>1)
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begin
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Select @X_Y = ((@ii-1)*(@jjMax+1))+@jj --the current matrix location
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if (substring(@firststring,@ii-1,1) = substring(@Secondstring,@jj-1,1))
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BEGIN --if there is a match, add the character (we'll reverse it later)
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Select @CommonString=@CommonString+substring(@firststring,@ii-1,1)
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select @jj=@jj-1, @ii=@ii-1 --go north-west
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end
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else if ascii(Substring(@Array,@X_Y,1)) = ascii(Substring(@Array, @X_Y-@jjMax-1, 1))
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select @ii=@ii-1
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ELSE if ascii(Substring(@Array,@X_Y,1)) = ascii(Substring(@Array, @X_Y-1, 1))
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select @jj=@jj-1
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else break
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if @@error>0 break
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end
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return Reverse(@CommonString)
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end
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go
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Declare @timing datetime Select @Timing=GetDate()
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if dbo.LongestCommonSubsequence ('1234', '1224533324')<>'1234'
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raiserror('test 1 failed',16,1)
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if dbo.LongestCommonSubsequence ('thisisatest', 'testing123testing')<>'tsitest'
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raiserror('test 2 failed',16,1)
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if dbo.LongestCommonSubsequence ('XMJYAUZ', 'MZJAWXU')<>'MJAU'
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raiserror('test 3 failed',16,1)
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if dbo.LongestCommonSubsequence ('yab', 'xabyrbyab')<>'yab'
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raiserror('test 4 failed',16,1)
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if dbo.LongestCommonSubsequence ('beginning-middle-ending','beginning-diddle-dum-ending')
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<>'beginning-iddle-ending' raiserror('test 5 failed',16,1)
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select datediff(millisecond,@timing,GetDate()) as milliseconds

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