Jaro and Jaro-Winkler similarity

Jaro Similarity

Jaro Similarity is the measure of similarity between two strings. The value of Jaro distance ranges from 0 to 1. where 1 means the strings are equal and 0 means no similarity between the two strings. 

Examples:

Input: s1 = “CRATE”, s2 = “TRACE”; 
Output: Jaro Similarity = 0.733333

Input: s1 = “DwAyNE”, s2 = “DuANE”; 
Output: Jaro Similarity = 0.822222

Algorithm:
The Jaro Similarity is calculated using the following formula 

where:

• m is the number of matching characters
• t is half the number of transpositions
• where |s1| and |s2| are the lengths of strings s1 and s2 respectively.

The characters are said to be matching if they are the same and the characters are not further than 
Transpositions are half the number of matching characters in both strings but in a different order.
Calculation:

• Let s1=”arnab”, s2=”raanb”, so the maximum distance to which each character is matched is 1.
• It is evident that both the strings have 5 matching characters, but the order is not the same, so the number of characters that are not in order is 4, so the number of transpositions is 2.
• Therefore, Jaro similarity can be calculated as follows: 
  Jaro Similarity = (1/3) * {(5/5) + (5/5) + (5-2)/5 } = 0.86667

Below is the implementation of the above approach.

C++

// C++ implementation of above approach
#include <bits/stdc++.h>
using namespace std;

// Function to calculate the
// Jaro Similarity of two strings
double jaro_distance(string s1, string s2)
{
    // If the strings are equal
    if (s1 == s2)
        return 1.0;

    // Length of two strings
    int len1 = s1.length(),
        len2 = s2.length();

    // Maximum distance upto which matching
    // is allowed
    int max_dist = floor(max(len1, len2) / 2) - 1;

    // Count of matches
    int match = 0;

    // Hash for matches
    int hash_s1[s1.length()] = { 0 },
        hash_s2[s2.length()] = { 0 };

    // Traverse through the first string
    for (int i = 0; i < len1; i++) {

        // Check if there is any matches
        for (int j = max(0, i - max_dist);
             j < min(len2, i + max_dist + 1); j++)

            // If there is a match
            if (s1[i] == s2[j] && hash_s2[j] == 0) {
                hash_s1[i] = 1;
                hash_s2[j] = 1;
                match++;
                break;
            }
    }

    // If there is no match
    if (match == 0)
        return 0.0;

    // Number of transpositions
    double t = 0;

    int point = 0;

    // Count number of occurrences
    // where two characters match but
    // there is a third matched character
    // in between the indices
    for (int i = 0; i < len1; i++)
        if (hash_s1[i]) {

            // Find the next matched character
            // in second string
            while (hash_s2[point] == 0)
                point++;

            if (s1[i] != s2[point++])
                t++;
        }

    t /= 2;

    // Return the Jaro Similarity
    return (((double)match) / ((double)len1)
            + ((double)match) / ((double)len2)
            + ((double)match - t) / ((double)match))
           / 3.0;
}

// Driver code
int main()
{
    string s1 = "CRATE", s2 = "TRACE";

    // Print jaro Similarity of two strings
    cout << jaro_distance(s1, s2) << endl;

    return 0;
}

Java

// Java implementation of above approach
class GFG
{

// Function to calculate the
// Jaro Similarity of two Strings
static double jaro_distance(String s1, String s2)
{
    // If the Strings are equal
    if (s1 == s2)
        return 1.0;

    // Length of two Strings
    int len1 = s1.length(),
        len2 = s2.length();

    // Maximum distance upto which matching
    // is allowed
    int max_dist = (int) (Math.floor(Math.max(len1, len2) / 2) - 1);

    // Count of matches
    int match = 0;

    // Hash for matches
    int hash_s1[] = new int[s1.length()];
    int hash_s2[] = new int[s2.length()];

    // Traverse through the first String
    for (int i = 0; i < len1; i++)
    {

        // Check if there is any matches
        for (int j = Math.max(0, i - max_dist);
            j < Math.min(len2, i + max_dist + 1); j++)

            // If there is a match
            if (s1.charAt(i) == s2.charAt(j) && hash_s2[j] == 0)
            {
                hash_s1[i] = 1;
                hash_s2[j] = 1;
                match++;
                break;
            }
    }

    // If there is no match
    if (match == 0)
        return 0.0;

    // Number of transpositions
    double t = 0;

    int point = 0;

    // Count number of occurrences
    // where two characters match but
    // there is a third matched character
    // in between the indices
    for (int i = 0; i < len1; i++)
        if (hash_s1[i] == 1)
        {

            // Find the next matched character
            // in second String
            while (hash_s2[point] == 0)
                point++;

            if (s1.charAt(i) != s2.charAt(point++) )
                t++;
        }

    t /= 2;

    // Return the Jaro Similarity
    return (((double)match) / ((double)len1)
            + ((double)match) / ((double)len2)
            + ((double)match - t) / ((double)match))
        / 3.0;
}

// Driver code
public static void main(String[] args)
{
    String s1 = "CRATE", s2 = "TRACE";

    // Print jaro Similarity of two Strings
    System.out.print(jaro_distance(s1, s2) +"\n");
}
}

// This code is contributed by PrinciRaj1992

Python3

# Python3 implementation of above approach
from math import floor, ceil

# Function to calculate the
# Jaro Similarity of two s
def jaro_distance(s1, s2):

    # If the s are equal
    if (s1 == s2):
        return 1.0

    # Length of two s
    len1 = len(s1)
    len2 = len(s2)

    # Maximum distance upto which matching
    # is allowed
    max_dist = floor(max(len1, len2) / 2) - 1

    # Count of matches
    match = 0

    # Hash for matches
    hash_s1 = [0] * len(s1)
    hash_s2 = [0] * len(s2)

    # Traverse through the first
    for i in range(len1):

        # Check if there is any matches
        for j in range(max(0, i - max_dist),
                       min(len2, i + max_dist + 1)):

            # If there is a match
            if (s1[i] == s2[j] and hash_s2[j] == 0):
                hash_s1[i] = 1
                hash_s2[j] = 1
                match += 1
                break

    # If there is no match
    if (match == 0):
        return 0.0

    # Number of transpositions
    t = 0
    point = 0

    # Count number of occurrences
    # where two characters match but
    # there is a third matched character
    # in between the indices
    for i in range(len1):
        if (hash_s1[i]):

            # Find the next matched character
            # in second
            while (hash_s2[point] == 0):
                point += 1

            if (s1[i] != s2[point]):
                t += 1
            point += 1
    t = t//2

    # Return the Jaro Similarity
    return (match/ len1 + match / len2 +
            (match - t) / match)/ 3.0

# Driver code
s1 = "CRATE"
s2 = "TRACE"

# Prjaro Similarity of two s
print(round(jaro_distance(s1, s2),6))

# This code is contributed by mohit kumar 29

C#

// C# implementation of above approach
using System;

class GFG
{

    // Function to calculate the
    // Jaro Similarity of two Strings
    static double jaro_distance(string s1, string s2)
    {
        // If the Strings are equal
        if (s1 == s2)
            return 1.0;

        // Length of two Strings
        int len1 = s1.Length ;
        int len2 = s2.Length;

        // Maximum distance upto which matching
        // is allowed
        int max_dist = (int)(Math.Floor((double)(
                        (Math.Max(len1, len2) / 2) - 1)));

        // Count of matches
        int match = 0;

        // Hash for matches
        int []hash_s1 = new int[s1.Length];
        int []hash_s2 = new int[s2.Length];

        // Traverse through the first String
        for (int i = 0; i < len1; i++)
        {

            // Check if there is any matches
            for (int j = Math.Max(0, i - max_dist);
                j < Math.Min(len2, i + max_dist + 1); j++)

                // If there is a match
                if (s1[i] == s2[j] && hash_s2[j] == 0)
                {
                    hash_s1[i] = 1;
                    hash_s2[j] = 1;
                    match++;
                    break;
                }
        }

        // If there is no match
        if (match == 0)
            return 0.0;

        // Number of transpositions
        double t = 0;

        int point = 0;

        // Count number of occurrences
        // where two characters match but
        // there is a third matched character
        // in between the indices
        for (int i = 0; i < len1; i++)
            if (hash_s1[i] == 1)
            {

                // Find the next matched character
                // in second String
                while (hash_s2[point] == 0)
                    point++;

                if (s1[i] != s2[point++] )
                    t++;
            }

        t /= 2;

        // Return the Jaro Similarity
        return (((double)match) / ((double)len1)
                + ((double)match) / ((double)len2)
                + ((double)match - t) / ((double)match))
            / 3.0;
    }

    // Driver code
    public static void Main()
    {
        string s1 = "CRATE", s2 = "TRACE";

        // Print jaro Similarity of two Strings
        Console.WriteLine(jaro_distance(s1, s2));
    }
}

// This code is contributed by AnkitRai01

Javascript

<script>

// Javascript implementation of above approach

// Function to calculate the
// Jaro Similarity of two strings
function jaro_distance(s1, s2)
{
    // If the strings are equal
    if (s1 == s2)
        return 1.0;

    // Length of two strings
    var len1 = s1.length,
        len2 = s2.length;

    // Maximum distance upto which matching
    // is allowed
    var max_dist = Math.floor(Math.max(len1, len2) / 2) - 1;

    // Count of matches
    var match = 0;

    // Hash for matches
    var hash_s1 = Array(s1.length).fill(0);
    var hash_s2 = Array(s1.length).fill(0);

    // Traverse through the first string
    for (var i = 0; i < len1; i++) {

        // Check if there is any matches
        for (var j = Math.max(0, i - max_dist);
             j < Math.min(len2, i + max_dist + 1); j++)

            // If there is a match
            if (s1[i] == s2[j] && hash_s2[j] == 0) {
                hash_s1[i] = 1;
                hash_s2[j] = 1;
                match++;
                break;
            }
    }

    // If there is no match
    if (match == 0)
        return 0.0;

    // Number of transpositions
    var t = 0;

    var point = 0;

    // Count number of occurrences
    // where two characters match but
    // there is a third matched character
    // in between the indices
    for (var i = 0; i < len1; i++)
        if (hash_s1[i]) {

            // Find the next matched character
            // in second string
            while (hash_s2[point] == 0)
                point++;

            if (s1[i] != s2[point++])
                t++;
        }

    t /= 2;

    // Return the Jaro Similarity
    return ((match) / (len1)
            + (match) / (len2)
            + (match - t) / (match))
           / 3.0;
}

// Driver code
var s1 = "CRATE", s2 = "TRACE";
// Print jaro Similarity of two strings
document.write( jaro_distance(s1, s2).toFixed(5));


</script>

Output:

0.733333

Time Complexity: O(N * M), where N is the length of string s1 and M is the length of string s2.

Auxiliary Space: O(N + M)

Jaro-Winkler Similarity

The Jaro-Winkler similarity is a string metric measuring edit distance between two strings. Jaro – Winkler Similarity is much similar to Jaro Similarity. They both differ when the prefix of two string match. Jaro – Winkler Similarity uses a prefix scale ‘p’ which gives a more accurate answer when the strings have a common prefix up to a defined maximum length l. 
Examples:

Input: s1 = “DwAyNE”, s2 = “DuANE”; 
Output: Jaro-Winkler Similarity =0.84

Input: s1=”TRATE”, s2=”TRACE”; 
Output: Jaro-Winkler similarity = 0.906667

Calculation:

• Jaro Winkler similarity is defined as follows 
  Sw = Sj + P * L * (1 – Sj)
  where, 
  • Sj, is jaro similarity
  • Sw, is jaro- winkler similarity
  • P is the scaling factor (0.1 by default)
  • L is the length of the matching prefix up to a maximum of 4 characters.
• Let s1=”arnab”, s2=”aranb”. The Jaro similarity of the two strings is 0.933333 (From the above calculation.)
• The length of the matching prefix is 2 and we take the scaling factor as 0.1.
• Substituting in the formula; 
  Jaro-Winkler Similarity= 0.9333333 + 0.1 * 2 * (1-0.9333333) = 0.946667

Below is the implementation of the above approach. 

C++

// C++ implementation of above approach
#include <bits/stdc++.h>
using namespace std;

// Function to calculate the
// Jaro Similarity of two strings
double jaro_distance(string s1, string s2)
{
    // If the strings are equal
    if (s1 == s2)
        return 1.0;

    // Length of two strings
    int len1 = s1.length(),
        len2 = s2.length();

    if (len1 == 0 || len2 == 0)
        return 0.0;

    // Maximum distance upto which matching
    // is allowed
    int max_dist = floor(max(len1, len2) / 2) - 1;

    // Count of matches
    int match = 0;

    // Hash for matches
    int hash_s1[s1.length()] = { 0 },
        hash_s2[s2.length()] = { 0 };

    // Traverse through the first string
    for (int i = 0; i < len1; i++) {

        // Check if there is any matches
        for (int j = max(0, i - max_dist);
             j < min(len2, i + max_dist + 1); j++)
            // If there is a match
            if (s1[i] == s2[j] && hash_s2[j] == 0) {
                hash_s1[i] = 1;
                hash_s2[j] = 1;
                match++;
                break;
            }
    }

    // If there is no match
    if (match == 0)
        return 0.0;

    // Number of transpositions
    double t = 0;

    int point = 0;

    // Count number of occurrences
    // where two characters match but
    // there is a third matched character
    // in between the indices
    for (int i = 0; i < len1; i++)
        if (hash_s1[i]) {

            // Find the next matched character
            // in second string
            while (hash_s2[point] == 0)
                point++;

            if (s1[i] != s2[point++])
                t++;
        }

    t /= 2;

    // Return the Jaro Similarity
    return (((double)match) / ((double)len1)
            + ((double)match) / ((double)len2)
            + ((double)match - t) / ((double)match))
           / 3.0;
}

// Jaro Winkler Similarity
double jaro_Winkler(string s1, string s2)
{
    double jaro_dist = jaro_distance(s1, s2);

    // If the jaro Similarity is above a threshold
    if (jaro_dist > 0.7) {

        // Find the length of common prefix
        int prefix = 0;

        for (int i = 0;
             i < min(s1.length(), s2.length()); i++) {
            // If the characters match
            if (s1[i] == s2[i])
                prefix++;

            // Else break
            else
                break;
        }

        // Maximum of 4 characters are allowed in prefix
        prefix = min(4, prefix);

        // Calculate jaro winkler Similarity
        jaro_dist += 0.1 * prefix * (1 - jaro_dist);
    }

    return jaro_dist;
}

// Driver code
int main()
{
    string s1 = "TRATE", s2 = "TRACE";

    // Print Jaro-Winkler Similarity of two strings
    cout << "Jaro-Winkler Similarity ="
         << jaro_Winkler(s1, s2) << endl;

    return 0;
}

Java

// Java implementation of above approach
class GFG
{

    // Function to calculate the
    // Jaro Similarity of two strings
    static double jaro_distance(String s1, String s2)
    {
        // If the strings are equal
        if (s1 == s2)
            return 1.0;

        // Length of two strings
        int len1 = s1.length(),
            len2 = s2.length();

        if (len1 == 0 || len2 == 0)
            return 0.0;

        // Maximum distance upto which matching
        // is allowed
        int max_dist = (int)Math.floor(Math.max(len1, len2) / 2) - 1;

        // Count of matches
        int match = 0;

        // Hash for matches
        int hash_s1[] = new int [s1.length()];
        int hash_s2[] = new int[s2.length()];

        // Traverse through the first string
        for (int i = 0; i < len1; i++)
        {

            // Check if there is any matches
            for (int j = Math.max(0, i - max_dist);
                j < Math.min(len2, i + max_dist + 1); j++)

                // If there is a match
                if (s1.charAt(i) == s2.charAt(j) &&
                                hash_s2[j] == 0)
                {
                    hash_s1[i] = 1;
                    hash_s2[j] = 1;
                    match++;
                    break;
                }
        }

        // If there is no match
        if (match == 0)
            return 0.0;

        // Number of transpositions
        double t = 0;

        int point = 0;

        // Count number of occurrences
        // where two characters match but
        // there is a third matched character
        // in between the indices
        for (int i = 0; i < len1; i++)
            if (hash_s1[i] == 1)
            {

                // Find the next matched character
                // in second string
                while (hash_s2[point] == 0)
                    point++;

                if (s1.charAt(i) != s2.charAt(point++))
                    t++;
            }

        t /= 2;

        // Return the Jaro Similarity
        return (((double)match) / ((double)len1)
                + ((double)match) / ((double)len2)
                + ((double)match - t) / ((double)match))
            / 3.0;
    }

    // Jaro Winkler Similarity
    static double jaro_Winkler(String s1, String s2)
    {
        double jaro_dist = jaro_distance(s1, s2);

        // If the jaro Similarity is above a threshold
        if (jaro_dist > 0.7)
        {

            // Find the length of common prefix
            int prefix = 0;

            for (int i = 0;
                i < Math.min(s1.length(), s2.length()); i++)
            {

                // If the characters match
                if (s1.charAt(i) == s2.charAt(i))
                    prefix++;

                // Else break
                else
                    break;
            }

            // Maximum of 4 characters are allowed in prefix
            prefix = Math.min(4, prefix);

            // Calculate jaro winkler Similarity
            jaro_dist += 0.1 * prefix * (1 - jaro_dist);
        }
        return jaro_dist;
    }

    // Driver code
    public static void main (String[] args)
    {
        String s1 = "TRATE", s2 = "TRACE";

        // Print Jaro-Winkler Similarity of two strings
        System.out.println("Jaro-Winkler Similarity =" +
                            jaro_Winkler(s1, s2));
    }
}

// This code is contributed by AnkitRai01

Python3

# Python3 implementation of above approach
from math import floor

# Function to calculate the
# Jaro Similarity of two strings
def jaro_distance(s1, s2) :

    # If the strings are equal
    if (s1 == s2) :
        return 1.0;

    # Length of two strings
    len1 = len(s1);
    len2 = len(s2);

    if (len1 == 0 or len2 == 0) :
        return 0.0;

    # Maximum distance upto which matching
    # is allowed
    max_dist = (max(len(s1), len(s2)) // 2 ) - 1;

    # Count of matches
    match = 0;

    # Hash for matches
    hash_s1 = [0] * len(s1) ;
    hash_s2 = [0] * len(s2) ;

    # Traverse through the first string
    for i in range(len1) :

        # Check if there is any matches
        for j in range( max(0, i - max_dist),
                    min(len2, i + max_dist + 1)) :

            # If there is a match
            if (s1[i] == s2[j] and hash_s2[j] == 0) :
                hash_s1[i] = 1;
                hash_s2[j] = 1;
                match += 1;
                break;

    # If there is no match
    if (match == 0) :
        return 0.0;

    # Number of transpositions
    t = 0;

    point = 0;

    # Count number of occurrences
    # where two characters match but
    # there is a third matched character
    # in between the indices
    for i in range(len1) :
        if (hash_s1[i]) :

            # Find the next matched character
            # in second string
            while (hash_s2[point] == 0) :
                point += 1;

            if (s1[i] != s2[point]) :
                point += 1;
                t += 1;
            else :
                point += 1;

        t /= 2;

    # Return the Jaro Similarity
    return ((match / len1 + match / len2 +
            (match - t) / match ) / 3.0);

# Jaro Winkler Similarity
def jaro_Winkler(s1, s2) :

    jaro_dist = jaro_distance(s1, s2);

    # If the jaro Similarity is above a threshold
    if (jaro_dist > 0.7) :

        # Find the length of common prefix
        prefix = 0;

        for i in range(min(len(s1), len(s2))) :

            # If the characters match
            if (s1[i] == s2[i]) :
                prefix += 1;

            # Else break
            else :
                break;

        # Maximum of 4 characters are allowed in prefix
        prefix = min(4, prefix);

        # Calculate jaro winkler Similarity
        jaro_dist += 0.1 * prefix * (1 - jaro_dist);

    return jaro_dist;

# Driver code
if __name__ == "__main__" :

    s1 = "TRATE"; s2 = "TRACE";

    # Print Jaro-Winkler Similarity of two strings
    print("Jaro-Winkler Similarity =", jaro_Winkler(s1, s2)) ;

# This code is contributed by AnkitRai01

C#

// C# implementation of above approach
using System;

class GFG
{

    // Function to calculate the
    // Jaro Similarity of two strings
    static double jaro_distance(string s1, string s2)
    {
        // If the strings are equal
        if (s1 == s2)
            return 1.0;

        // Length of two strings
        int len1 = s1.Length,
            len2 = s2.Length;

        if (len1 == 0 || len2 == 0)
            return 0.0;

        // Maximum distance upto which matching
        // is allowed
        int max_dist = (int)Math.Floor((double)
                        Math.Max(len1, len2) / 2) - 1;

        // Count of matches
        int match = 0;

        // Hash for matches
        int []hash_s1 = new int [s1.Length];
        int []hash_s2 = new int[s2.Length];

        // Traverse through the first string
        for (int i = 0; i < len1; i++)
        {

            // Check if there is any matches
            for (int j = Math.Max(0, i - max_dist);
                j < Math.Min(len2, i + max_dist + 1); j++)

                // If there is a match
                if (s1[i] == s2[j] &&
                    hash_s2[j] == 0)
                {
                    hash_s1[i] = 1;
                    hash_s2[j] = 1;
                    match++;
                    break;
                }
        }

        // If there is no match
        if (match == 0)
            return 0.0;

        // Number of transpositions
        double t = 0;

        int point = 0;

        // Count number of occurrences
        // where two characters match but
        // there is a third matched character
        // in between the indices
        for (int i = 0; i < len1; i++)
            if (hash_s1[i] == 1)
            {

                // Find the next matched character
                // in second string
                while (hash_s2[point] == 0)
                    point++;

                if (s1[i] != s2[point++])
                    t++;
            }
        t /= 2;

        // Return the Jaro Similarity
        return (((double)match) / ((double)len1)
                + ((double)match) / ((double)len2)
                + ((double)match - t) / ((double)match))
            / 3.0;
    }

    // Jaro Winkler Similarity
    static double jaro_Winkler(string s1, string s2)
    {
        double jaro_dist = jaro_distance(s1, s2);

        // If the jaro Similarity is above a threshold
        if (jaro_dist > 0.7)
        {

            // Find the length of common prefix
            int prefix = 0;

            for (int i = 0; i < Math.Min(s1.Length,
                                        s2.Length); i++)
            {

                // If the characters match
                if (s1[i] == s2[i])
                    prefix++;

                // Else break
                else
                    break;
            }

            // Maximum of 4 characters are allowed in prefix
            prefix = Math.Min(4, prefix);

            // Calculate jaro winkler Similarity
            jaro_dist += 0.1 * prefix * (1 - jaro_dist);
        }
        return jaro_dist;
    }

    // Driver code
    public static void Main ()
    {
        string s1 = "TRATE", s2 = "TRACE";

        // Print Jaro-Winkler Similarity of two strings
        Console.WriteLine("Jaro-Winkler Similarity =" +
                            jaro_Winkler(s1, s2));
    }
}

// This code is contributed by AnkitRai01

Javascript

<script>
    // Javascript implementation of above approach

    // Function to calculate the
    // Jaro Similarity of two strings
    function jaro_distance(s1, s2)
    {
        // If the strings are equal
        if (s1 == s2)
            return 1.0;

        // Length of two strings
        let len1 = s1.length, len2 = s2.length;

        if (len1 == 0 || len2 == 0)
            return 0.0;

        // Maximum distance upto which matching
        // is allowed
        let max_dist = Math.floor(Math.max(len1, len2) / 2) - 1;

        // Count of matches
        let match = 0;

        // Hash for matches
        let hash_s1 = new Array(s1.length);
        hash_s1.fill(0);
        let hash_s2 = new Array(s2.length);
        hash_s2.fill(0);

        // Traverse through the first string
        for (let i = 0; i < len1; i++)
        {

            // Check if there is any matches
            for (let j = Math.max(0, i - max_dist);
                j < Math.min(len2, i + max_dist + 1); j++)

                // If there is a match
                if (s1[i] == s2[j] &&
                    hash_s2[j] == 0)
                {
                    hash_s1[i] = 1;
                    hash_s2[j] = 1;
                    match++;
                    break;
                }
        }

        // If there is no match
        if (match == 0)
            return 0.0;

        // Number of transpositions
        let t = 0;

        let point = 0;

        // Count number of occurrences
        // where two characters match but
        // there is a third matched character
        // in between the indices
        for (let i = 0; i < len1; i++)
            if (hash_s1[i] == 1)
            {

                // Find the next matched character
                // in second string
                while (hash_s2[point] == 0)
                    point++;

                if (s1[i] != s2[point++])
                    t++;
            }
        t /= 2;

        // Return the Jaro Similarity
        return ((match) / (len1)
                + (match) / (len2)
                + (match - t) / (match))
            / 3.0;
    }

    // Jaro Winkler Similarity
    function jaro_Winkler(s1, s2)
    {
        let jaro_dist = jaro_distance(s1, s2);

        // If the jaro Similarity is above a threshold
        if (jaro_dist > 0.7)
        {

            // Find the length of common prefix
            let prefix = 0;

            for (let i = 0; i < Math.min(s1.length,s2.length); i++)
            {

                // If the characters match
                if (s1[i] == s2[i])
                    prefix++;

                // Else break
                else
                    break;
            }

            // Maximum of 4 characters are allowed in prefix
            prefix = Math.min(4, prefix);

            // Calculate jaro winkler Similarity
            jaro_dist += 0.1 * prefix * (1 - jaro_dist);
        }
        return jaro_dist.toFixed(6);
    }

    let s1 = "TRATE", s2 = "TRACE";

    // Print Jaro-Winkler Similarity of two strings
    document.write("Jaro-Winkler Similarity =" +
                      jaro_Winkler(s1, s2));

</script>

Output:

Jaro-Winkler Similarity =0.906667

Time Complexity: O(N * M), where N is the length of string s1 and M is the length of string s2.
Auxiliary Space: O(N + M)