Damerau–Levenshtein distance (Edit Distance with Transposition) c implementation - c++

Question

I implemented the Damerau–Levenshtein distance in c++ but it does not give correct o/p for the input (pantera,aorta) the correct o/p is 4 but my code gives 5.....
int editdist(string s,string t,int n,int m)
{
int d1,d2,d3,cost;
int i,j;
for(i=0;i<=n;i++)
{
for(j=0;j<=m;j++)
{
if(s[i+1]==t[j+1])
cost=0;
else
cost=1;
d1=d[i][j+1]+1;
d2=d[i+1][j]+1;
d3=d[i][j]+cost;
d[i+1][j+1]=minimum(d1,d2,d3);
if(i>0 && j>0 && s[i+1]==t[j] && s[i]==t[j+1] ) //transposition
{
d[i+1][j+1]=min(d[i+1][j+1],d[i-1][j-1]+cost);
}
}
}
return d[n+1][m+1];
}
I don't see any errors. Can someone find a problem with the code?

Answer 1

The algorithm in the post does not compute Damerau-Levenshtein distance. In a wikipedia article this algorithm is defined as the Optimal String Alignment Distance.
A java implementation of DL distance algorithm can be found in another SO post.
To get the correct values of OSA distance please change the lines marked with - below with the lines marked with +
int editdist(string s,string t,int n,int m)
{
int d1,d2,d3,cost;
int i,j;
for(i=0;i<=n;i++)
{
for(j=0;j<=m;j++)
{
- if(s[i+1]==t[j+1])
+ if(s[i+1]==t[j+1])
cost=0;
else
cost=1;
d1=d[i][j+1]+1;
d2=d[i+1][j]+1;
d3=d[i][j]+cost;
d[i+1][j+1]=minimum(d1,d2,d3);
- if(i>0 && j>0 && s[i+1]==t[j] && s[i]==t[j+1] ) //transposition
+ if(i>0 && j>0 && s[i]==t[j-1] && s[i-1]==t[j] ) //transposition
{
d[i+1][j+1]=min(d[i+1][j+1],d[i-1][j-1]+cost);
}
}
}
return d[n+1][m+1];
}
It looks as if the code was copied from a program written in a programming language where array indices start at 1 by default. Therefore all references to the elements of the distance array d were incremented. However the references to the characters within the strings are references to 0-based arrays, therefore they should not be updated.
To compute the distance the distance array has to be properly initialized:
for( i = 0; i < n + 1; i++)
d[i][0] = i;
for( j = 1; j < m + 1; j++)
d[0][j] = j;
Since you have got the answer 5, you probably have your distance array already initialized correctly.
Since the above algorithm does not compute the DL distance, here is a sketch of a C implementation of the DL algorithm (derived from the SO post with a java impl. derived from an ActionScript impl. in the Wikipedia article).
#define d(i,j) dd[(i) * (m+2) + (j) ]
#define min(x,y) ((x) < (y) ? (x) : (y))
#define min3(a,b,c) ((a)< (b) ? min((a),(c)) : min((b),(c)))
#define min4(a,b,c,d) ((a)< (b) ? min3((a),(c),(d)) : min3((b),(c),(d)))
int dprint(int* dd, int n,int m){
int i,j;
for (i=0; i < n+2;i++){
for (j=0;j < m+2; j++){
printf("%02d ",d(i,j));
}
printf("\n");
}
printf("\n");
return 0;
}
int dldist2(char *s, char* t, int n, int m) {
int *dd;
int i, j, cost, i1,j1,DB;
int INFINITY = n + m;
int DA[256 * sizeof(int)];
memset(DA, 0, sizeof(DA));
if (!(dd = (int*) malloc((n+2)*(m+2)*sizeof(int)))) {
return -1;
}
d(0,0) = INFINITY;
for(i = 0; i < n+1; i++) {
d(i+1,1) = i ;
d(i+1,0) = INFINITY;
}
for(j = 0; j<m+1; j++) {
d(1,j+1) = j ;
d(0,j+1) = INFINITY;
}
dprint(dd,n,m);
for(i = 1; i< n+1; i++) {
DB = 0;
for(j = 1; j< m+1; j++) {
i1 = DA[t[j-1]];
j1 = DB;
cost = ((s[i-1]==t[j-1])?0:1);
if(cost==0) DB = j;
d(i+1,j+1) =
min4(d(i,j)+cost,
d(i+1,j) + 1,
d(i,j+1)+1,
d(i1,j1) + (i-i1-1) + 1 + (j-j1-1));
}
DA[s[i-1]] = i;
dprint(dd,n,m);
}
cost = d(n+1,m+1);
free(dd);
return cost;
}

Answer 2

Here is my C++ version of this algorithm:
int damerau_levenshtein_distance(std::string p_string1, std::string p_string2)
{
int l_string_length1 = p_string1.length();
int l_string_length2 = p_string2.length();
int d[l_string_length1+1][l_string_length2+1];
int i;
int j;
int l_cost;
for (i = 0;i <= l_string_length1;i++)
{
d[i][0] = i;
}
for(j = 0; j<= l_string_length2; j++)
{
d[0][j] = j;
}
for (i = 1;i <= l_string_length1;i++)
{
for(j = 1; j<= l_string_length2; j++)
{
if( p_string1[i-1] == p_string2[j-1] )
{
l_cost = 0;
}
else
{
l_cost = 1;
}
d[i][j] = std::min(
d[i-1][j] + 1, // delete
std::min(d[i][j-1] + 1, // insert
d[i-1][j-1] + l_cost) // substitution
);
if( (i > 1) &&
(j > 1) &&
(p_string1[i-1] == p_string2[j-2]) &&
(p_string1[i-2] == p_string2[j-1])
)
{
d[i][j] = std::min(
d[i][j],
d[i-2][j-2] + l_cost // transposition
);
}
}
}
return d[l_string_length1][l_string_length2];
}