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.


package main
 
import "fmt"
 
func jaro(str1, str2 string) float64 {
    if len(str1) == 0 && len(str2) == 0 {
        return 1
    }
    if len(str1) == 0 || len(str2) == 0 {
        return 0
    }
    match_distance := len(str1)
    if len(str2) > match_distance {
        match_distance = len(str2)
    }
    match_distance = match_distance/2 - 1
    str1_matches := make([]bool, len(str1))
    str2_matches := make([]bool, len(str2))
    matches := 0.
    transpositions := 0.
    for i := range str1 {
        start := i - match_distance
        if start < 0 {
            start = 0
        }
        end := i + match_distance + 1
        if end > len(str2) {
            end = len(str2)
        }
        for k := start; k < end; k++ {
            if str2_matches[k] {
                continue
            }
            if str1[i] != str2[k] {
                continue
            }
            str1_matches[i] = true
            str2_matches[k] = true
            matches++
            break
        }
    }
    if matches == 0 {
        return 0
    }
    k := 0
    for i := range str1 {
        if !str1_matches[i] {
            continue
        }
        for !str2_matches[k] {
            k++
        }
        if str1[i] != str2[k] {
            transpositions++
        }
        k++
    }
    transpositions /= 2
    return (matches/float64(len(str1)) +
        matches/float64(len(str2)) +
        (matches-transpositions)/matches) / 3
}
 
func main() {
    fmt.Printf("%f\n", jaro("MARTHA", "MARHTA"))
    fmt.Printf("%f\n", jaro("DIXON", "DICKSONX"))
    fmt.Printf("%f\n", jaro("JELLYFISH", "SMELLYFISH"))
}