P.S. if there are diffrent weightage for addition , replacement and deletion . Than is there any algorithm which could help me .
Or, what sort of modifications are required in Wagner–Fischer algorithm so as to minimize the edit distance if weights for addition/deletion and replacement are diffrent ?
Most optimal I know by far is Levenshtein, you can also have a look into this publication. Hope it helps :)
Don't know if you are aware, but since each line in edit distance PD depends only in the previous one, you can keep only the two last lines. This way you can achieve O(n) space complexity, instead of the O(n^2) in the naïve implementation.
Example in Python (assuming cost 2 for replacement, 3 for addition and 5 for deletion):
def levenshtein(s1, s2):
A = [0]*(len(s2)+1)
B = range(len(s2)+1)
for i, c1 in enumerate(s1, 1):
A[0] = i
for j, c2 in enumerate(s2, 1):
if c1 == c2:
A[j] = B[j-1]
else:
A[j] = min(B[j-1]+2, A[j-1]+3, B[j]+5)
A,B = B,A
return B[len(s2)]
print levenshtein('kitten', 'sitting')
I modified my implementation of Wagner Fischer with weightings for insertion, deletion and substitution (cins, cdel, csub).
#!/bin/bash
set -f
# based on https://github.com/osteslag/Changeset/blob/master/Sources/Changeset.swift
# https://en.wikipedia.org/wiki/Wagner%E2%80%93Fischer_algorithm
declare A="the quick brown fox jumps over a lazy dog"
declare B="the quick brown fox jumped lazy dog and a brown and black dog"
declare RET
join(){
local A="$1"
RET="$A"
RET="${RET//[?] [?]/ }"
RET="${RET//[+] [+]/ }"
RET="${RET//[-] [-]/ }"
return 0
}
edits(){
local -a A=("" ${1//[^a-zA-Z0-9]/ }) # remove all punctuation FIXME: could surround with space
local -a B=("" ${2//[^a-zA-Z0-9]/ })
local -i rows=${#A[*]}
local -i cols=${#B[*]}
local -a pROW=("")
local -a cROW
local -ia pdst=(0)
local -ia cdst=(0)
local -i min r c
local -i ins cins=1
local -i del cdel=1
local -i sub csub=10
# fill first row of insertions
for((c=1; c<cols; c++)); do # for each target +1
pROW[c]="${pROW[c-1]} +\e[42m${B[c]}\e[m+"
((pdst[c]=c*cins))
done
((rows==0)) && return 1
for((r=1; r<rows; r++)); do
# first column are deletions to get ""
cROW[0]="${pROW[0]} -\e[41m${A[r]}\e[m-"
((cdst[0]=pdst[0]+cdel))
((cols>0)) && {
# X 0 T1 T2 T3
# 0 0 i i i
# S1 d
# S2 d
# c-1 c
# r-1 SUB DEL
# r INS
for((c=1; c<cols\; c++)); do
if [[ "${A[r]}" = "${B[c]}" ]]; then # source and target match - no operation
cROW[c]="${pROW[c-1]} ${A[r]}"
((cdst[c]= pdst[c-1]))
else
((ins=cdst[c-1], sub=pdst[c-1], del=pdst[c] )) #
((min= (del<=ins) ? ((del<=sub)?del:sub) : ins))
if ((del==min)); then ((cdst[c]=min+cdel)); cROW[c]="${pROW[c ]} -\e[41m${A[r]}\e[m-"
elif ((ins==min)); then ((cdst[c]=min+cins)); cROW[c]="${cROW[c-1]} +\e[42m${B[c]}\e[m+"
else ((cdst[c]=min+csub)); cROW[c]="${pROW[c-1]} ?\e[41m${A[r]}\e[m-\e[42m${B[c]}\e[m?"
fi
#((cdst[c]=min+1))
fi
done
}
pROW=("${cROW[@]}")
pdst=( ${cdst[*]} )
done
# printf "%s " "${pROW[@]}" ; printf "\n"
# printf "%s\n\n" "${pROW[@]: -1}"
join "${pROW[*]: -1}"
printf "%b\n\n" "$RET"
return 0
}
edits "s e t t i n g" "k i t t e n"
edits "$A" "$B"
exit 0
Outputs:
$ ./pc-wf.bash
-s e- +k i+ t t -i n- +e+ ?g-n?
the quick brown fox -jumps over- +jumped lazy dog and+ a +brown and+ ?lazy-black? dog
