The Wagner–Fischer algorithm is a dynamic programming algorithm that measures the Levenshtein distance between two strings of characters.

For example, the Levenshtein distance between “kitten” and “sitting” is 3, since the following three edits change one into the other, and there is no way to do it with fewer than three edits:

**k**itten → **s**itten (substitution of ‘s’ for ‘k’)

sitt**e**n → sitt**i**n (substitution of ‘i’ for ‘e’)

sittin → sittin**g** (insertion of ‘g’ at the end).

Computing the Levenshtein distance is based on the observation that if we reserve a matrix to hold the Levenshtein distances between all prefixes of the first string and all prefixes of the second, then we can compute the values in the matrix by flood filling the matrix, and thus find the distance between the two full strings as the last value computed.

k i t t e n
0 1 2 3 4 5 6
s 1 1 2 3 4 5 6
i 2 2 1 2 3 4 5
t 3 3 2 1 2 3 4
t 4 4 3 2 1 2 3
i 5 5 4 3 2 2 3
n 6 6 5 4 3 3 2
g 7 7 6 5 4 4 3

CODE:

/* http://en.wikipedia.org/wiki/Wagner%E2%80%93Fischer_algorithm */
#include <stdio.h>
#include <math.h>
int d[100][100];
#define MIN(x,y) ((x) < (y) ? (x) : (y))
main()
{
int i,j,m,n,temp,tracker;
char s[] = "kitten";
char t[] = "sitting";
m = strlen(s);
n = strlen(t);
for(i=0;i<=m;i++)
d[0][i] = i;
for(j=0;j<=n;j++)
d[j][0] = j;
for (j=1;j<=m;j++)
{
for(i=1;i<=n;i++)
{
if(s[i-1] == t[j-1])
{
tracker = 0;
}
else{
tracker = 1;
}
temp = MIN((d[i-1][j]+1),(d[i][j-1]+1));
d[i][j] = MIN(temp,(d[i-1][j-1]+tracker));
}
}
printf("the Levinstein distance is %d\n",d[n][m]);
}

OUTPUT:

$ ./a.exe

the Levinstein distance is 3

References: Wikipedia entry for Levenshtein distance.

Thanks for reading !

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