# Levenshtein Distance

Compute the levenshtein distance between Strings - see http://en.wikipedia.org/wiki/Levenshtein_distance

## Implementations

### Java

```public static int getLevenshteinDistance (String s, String t) {
if (s == null || t == null) {
throw new IllegalArgumentException("Strings must not be null");
}

/*
The difference between this impl. and the previous is that, rather
than creating and retaining a matrix of size s.length()+1 by t.length()+1,
we maintain two single-dimensional arrays of length s.length()+1.  The first, d,
is the 'current working' distance array that maintains the newest distance cost
counts as we iterate through the characters of String s.  Each time we increment
the index of String t we are comparing, d is copied to p, the second int[].  Doing so
allows us to retain the previous cost counts as required by the algorithm (taking
the minimum of the cost count to the left, up one, and diagonally up and to the left
of the current cost count being calculated).  (Note that the arrays aren't really
copied anymore, just switched...this is clearly much better than cloning an array
or doing a System.arraycopy() each time  through the outer loop.)

Effectively, the difference between the two implementations is this one does not
cause an out of memory condition when calculating the LD over two very large strings.
*/

int n = s.length(); // length of s
int m = t.length(); // length of t

if (n == 0) {
return m;
} else if (m == 0) {
return n;
}

int p[] = new int[n+1]; //'previous' cost array, horizontally
int d[] = new int[n+1]; // cost array, horizontally
int _d[]; //placeholder to assist in swapping p and d

// indexes into strings s and t
int i; // iterates through s
int j; // iterates through t

char t_j; // jth character of t

int cost; // cost

for (i = 0; i<=n; i++) {
p[i] = i;
}

for (j = 1; j<=m; j++) {
t_j = t.charAt(j-1);
d = j;

for (i=1; i<=n; i++) {
cost = s.charAt(i-1)==t_j ? 0 : 1;
// minimum of cell to the left+1, to the top+1, diagonally left and up +cost
d[i] = Math.min(Math.min(d[i-1]+1, p[i]+1),  p[i-1]+cost);
}

// copy current distance counts to 'previous row' distance counts
_d = p;
p = d;
d = _d;
}

// our last action in the above loop was to switch d and p, so p now
// actually has the most recent cost counts
return p[n];
}
```

### Ruby

```def levenshtein_distance(s, t)
m = s.size
n = t.size
d = Array.new(m+1) { Array.new(n+1) }
for i in 0..m
d[i] = i
end
for j in 0..n
d[j] = j
end
for j in 0...n
for i in 0...m
if s[i,1] == t[j,1]
d[i+1][j+1] = d[i][j]
else
d[i+1][j+1] = [d[i  ][j+1] + 1, # deletion
d[i+1][j  ] + 1, # insertion
d[i  ][j  ] + 1  # substitution
].min
end
end
end
d[m][n]
end

s = "sitting"
t = "kitten"
p levenshtein_distance(s, t)    #=> 3
```

### Erlang

```levenshtein_distance(S, T) ->
M = length(S),
N = length(T),
St = list_to_tuple(S),
Tt = list_to_tuple(T),
lists:foreach(fun(I) -> put({I, 0}, I) end, lists:seq(0, M)),
lists:foreach(fun(J) -> put({0, J}, J) end, lists:seq(0, N)),
lists:foreach(fun(J) ->
lists:foreach(fun(I) ->
levenshtein_distance(St, Tt, I, J)
end, lists:seq(1, M))
end, lists:seq(1,N)),
get({M, N}).

levenshtein_distance(S, T, I, J) ->
V = case element(I, S) =:= element(J, T) of
true  -> get({I-1, J-1});
false ->
lists:min( [get({I-1, J  }) + 1,     % deletion
get({I,   J-1}) + 1,     % insertion
get({I-1, J-1}) + 1] )   % substitution
end,
put({I, J}, V).
```