The Jaro distance is a measure of edit distance between two strings; its inverse, called the Jaro similarity, is a measure of two strings' similarity: the higher the value, the more similar the strings are. The score is normalized such that   0   equates to no similarities and   1   is an exact match.



Definition
The Jaro similarity   




d

j




{\displaystyle d_{j}}

   of two given strings   




s

1




{\displaystyle s_{1}}

   and   




s

2




{\displaystyle s_{2}}

   is

 




d

j


=

{




0



if 

m
=
0






1
3



(


m


|


s

1



|




+


m


|


s

2



|




+



m
−
t

m


)




otherwise









{\displaystyle d_{j}=\left\{{\begin{array}{l l}0&{\text{if }}m=0\\{\frac {1}{3}}\left({\frac {m}{|s_{1}|}}+{\frac {m}{|s_{2}|}}+{\frac {m-t}{m}}\right)&{\text{otherwise}}\end{array}}\right.}


Where:

 



m


{\displaystyle m}

   is the number of matching characters;
 



t


{\displaystyle t}

   is half the number of transpositions.


Two characters from   




s

1




{\displaystyle s_{1}}

   and   




s

2




{\displaystyle s_{2}}

   respectively, are considered matching only if they are the same and not farther apart than   




⌊



max
(

|


s

1



|

,

|


s

2



|

)

2


⌋

−
1


{\displaystyle \left\lfloor {\frac {\max(|s_{1}|,|s_{2}|)}{2}}\right\rfloor -1}

 characters.

Each character of   




s

1




{\displaystyle s_{1}}

   is compared with all its matching characters in   




s

2




{\displaystyle s_{2}}

. Each difference in position is half a transposition; that is, the number of transpositions is half the number of characters which are common to the two strings but occupy different positions in each one.



Example
Given the strings   




s

1




{\displaystyle s_{1}}

   DWAYNE   and   




s

2




{\displaystyle s_{2}}

   DUANE   we find:

 



m
=
4


{\displaystyle m=4}


 




|


s

1



|

=
6


{\displaystyle |s_{1}|=6}


 




|


s

2



|

=
5


{\displaystyle |s_{2}|=5}


 



t
=
0


{\displaystyle t=0}




We find a Jaro score of:

 




d

j


=


1
3



(


4
6


+


4
5


+



4
−
0

4


)

=
0.822


{\displaystyle d_{j}={\frac {1}{3}}\left({\frac {4}{6}}+{\frac {4}{5}}+{\frac {4-0}{4}}\right)=0.822}




Task
Implement the Jaro algorithm and show the similarity scores for each of the following pairs:

 ("MARTHA", "MARHTA")
 ("DIXON", "DICKSONX")
 ("JELLYFISH", "SMELLYFISH")


 See also
 Jaro–Winkler distance on Wikipedia.


use std::cmp;
 
pub fn jaro(s1: &str, s2: &str) -> f64 {
    let s1_len = s1.len();
    let s2_len = s2.len();
    if s1_len == 0 && s2_len == 0 { return 1.0; }
    let match_distance = cmp::max(s1_len, s2_len) / 2 - 1;
    let mut s1_matches = vec![false; s1_len];
    let mut s2_matches = vec![false; s2_len];
    let mut m: isize = 0;
    for i in 0..s1_len {
        let start = cmp::max(0, i as isize - match_distance as isize) as usize;
        let end = cmp::min(i + match_distance + 1, s2_len);
        for j in start..end {
            if !s2_matches[j] && s1.as_bytes()[i] == s2.as_bytes()[j] {
                s1_matches[i] = true;
                s2_matches[j] = true;
                m += 1;
                break;
            }
        }
    }
    if m == 0 { return 0.0; }
    let mut t = 0.0;
    let mut k = 0;
    for i in 0..s1_len {
        if s1_matches[i] {
            while !s2_matches[k] { k += 1; }
            if s1.as_bytes()[i] != s2.as_bytes()[k] { t += 0.5; }
            k += 1;
        }
    }
 
    let m = m as f64;
    (m / s1_len as f64 + m / s2_len as f64 + (m  - t) / m) / 3.0
}
 
fn main() {
    let pairs = [("MARTHA", "MARHTA"), ("DIXON", "DICKSONX"), ("JELLYFISH", "SMELLYFISH")];
    for p in pairs.iter() { println!("{}/{} = {}", p.0, p.1, jaro(p.0, p.1)); }
}