Levenshtein
(Edit)
DISTANCE
Algorithm
ABDULLAH ALSHAMMRI
overview
- What is it !?
-
Applications and Usages.
- How it works?
- Example and demo.
-
Complexity.
- Implementation.
- References.
EDIT DISTANCE
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Measures the similarity between two strings.
- Test is similar to Text
- By replacing ONE character s with x , it becomes the same
-
Levenshtein
is the name of a Russian scientist Vladimir Levenshtein who invented the
algorithm in 1965.
- It is a Dynamic Programming Algorithm.
Applications and usages
- Spell Checkers
- TRST => Do you mean Test?
- DNA Analysis
- Used among other algorithms
- It used in LCS, Longest Common Subsequence.
- I was going to discuss LCS, however, I found LCS depends on Edit Distance.
- LCS useful with File Comparison.
- Refer to the reference in the last slide for more information about LCS.
- Linux diff app depends on LCS witches depends on Edit Distance.
How IT WORKS?
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S1 is the first string and m is its length.
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S2 is the second string and n is its length
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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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create new 2d array called distance
- fill first row (0,1,2...to n) and fill first column (0,1,2,.. to m)
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and for each distance[i][j] do :
- The distance ( minimal operation needed ) is distance[n][m]
Example
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j=0
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j=1
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j=2
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j=3
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j=4
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j=5
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#
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E
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X
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I
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T
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i=0
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#
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0
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1
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2
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3
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4
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i=1
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E
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1
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i=2
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X
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2
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i=3
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I
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3
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i=4
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S
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4
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i=5
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T
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5
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i=6
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S
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6
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Example
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j=0
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j=1
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j=2
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j=3
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j=4
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j=5
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#
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E
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X
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I
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T
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i=0
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#
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0
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1
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2
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3
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4
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i=1
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E
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1
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0 |
1 |
2 |
3 |
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i=2
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X
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2
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i=3
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I
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3
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i=4
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S
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4
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i=5
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T
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5
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i=6
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S
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6
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Example
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j=0
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j=1
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j=2
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j=3
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j=4
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j=5
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#
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E
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X
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I
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T
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i=0
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#
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0
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1
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2
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3
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4
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i=1
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E
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1
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0 |
1 |
2 |
3 |
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i=2
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X
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2
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1 |
0 |
1 |
2 |
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i=3
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I
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3
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i=4
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S
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4
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i=5
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T
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5
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i=6
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S
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6
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Example
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j=0
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j=1
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j=2
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j=3
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j=4
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j=5
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#
|
E
|
X
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I
|
T
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i=0
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#
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0
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1
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2
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3
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4
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i=1
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E
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1
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0 |
1 |
2 |
3 |
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i=2
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X
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2
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1 |
0 |
1 |
2 |
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i=3
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I
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3
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2 |
1 |
0 |
1 |
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i=4
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S
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4
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3 |
2 |
1 |
1 |
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i=5
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T
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5
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4 |
3 |
2 |
1 |
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i=6
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S
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6
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5 |
4 |
3 |
2 |
Example
So The minimum operations needed to convert EXISTS to EXIT is 2
2 here is two deletion operations
EXISTS => EXIT
COMPLEXITY
- It's a Dynamic Programming paradigm , each iteration depends on the last operation to solve the current one.
- Time Complexity is Big O(MN) , or O(MN+M+N)
- Space Complexity is a 2D array O(MN)
- N and M is the length of tow strings S1 and S2
- Brute Force version is very complex
- HELLO and XXXXX needs more than 2523 STEPS to finish
- However , the Dynamic Programming version need +35 STEPS.
IMPLEMENTATION
REFERENCES
-
Levenshtein, Vladimir I. (February 1966). "Binary codes capable of
correcting deletions, insertions, and reversals". Soviet Physics Doklady.
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Hirschberg, D. S. (1975). "A linear space algorithm
for computing maximal common subsequences". Communications of the ACM .
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Levenshtein distance , http://en.wikipedia.org/wiki/Levenshtein_distance
THANKS
Levenshtein (Edit) Distance Algorithm
By abshammeri
