Favorite Algorithms (guys)-Levenshtein distance

String Matching:levenshtein Distance

• Purpose:to use as little effort to convert one string into the other
• Intuition behind the method:replacement, addition or deletion of a charcter in a string
• Steps

Step	Description
1	Set N to is the length of S. Set m to is the length of T. If n = 0, return m and exit. If m = 0, return n and exit. Construct a matrix containing 0..m rows and 0..N columns.
2	Initialize the first row to 0..N. Initialize the first column to 0..M.
3	Examine each character of s (i from 1 to n).
4	Examine each character of T (J from 1 to M).
5	If s[i] equals t[j], the cost is 0. If s[i] doesn ' t equal t[j], the cost is 1.
6	Set Cell d[i,j] of the matrix equal to the minimum of: A. The cell immediately above plus 1:d[i-1,j] + 1. B. The cell immediately to the left plus 1:d[i,j-1] + 1. C. The cell diagonally above and to the left plus the cost:d[i-1,j-1] + cost.
7	After the iteration steps (3, 4, 5, 6) was complete, the distance was found in cell d[n,m].

• Example

This section shows how the Levenshtein distance was computed when the source string was "GUMBO" and the target string is "GA Mbol ".

Steps 1 and 2

		G	U	M	B	O
	0	1	2	3	4	5
G	1
A	2
M	3
B	4
O	5
L	6

Steps 3 to 6 when i = 1 /tr>

		G	U	M	B	O
	0	1	2	3	4	5
G	1	0
A	2	1
M	3	2
B	4	3
O	5	4
L	6	5

Steps 3 to 6 when i = 2

		G	U	M	B	O
	0	1	2	3	4	5
G	1	0	1
A	2	1	1
M	3	2	2
B	4	3	3
O	5	4	4
L	6	5	5

Steps 3 to 6 when i = 3

		G	U	M	B	O
	0	1	2	3	4	5
G	1	0	1	2
A	2	1	1	2
M	3	2	2	1
B	4	3	3	2
O	5	4	4	3
L	6	5	5	4

Steps 3 to 6 when i = 4

		G	U	M	B	O
	0	1	2	3	4	5
G	1	0	1	2	3
A	2	1	1	2	3	&NB SP;
M	3	2	2	1	2
B	4	3	3	2	1
O	5	4	4	3	2
L	6	5	5	4	3

Steps 3 to 6 when i = 5

		G	U	M	B	O
	0	1	2	3	4	5
G	1	0	1	2	3	4
A	2	1	1	2	3	4
M	3	2	2	1	2	3
B	4	3	3	2	1	2
O	5	4	4	3	2	1
L	6	5	5	4	3	2

Step 7

The distance is in the lower right hand corner of the matrix, i.e. 2. This intuitive realization "GUMBO" can is transformed into "Gambol" by substituting "A" for "U" corresponds D adding "L" (one substitution and 1 insertion = 2 changes).

Favorite Algorithms (guys)-Levenshtein distance