Jaro Distance


Difficulty: 3 | Problem written by mesakarghm
Problem reported in interviews at


Jaro Distance is a measure of similarity between two strings.The Jaro Similarity is calculated using the formula: 

\(\begin{aligned} Sim_J (s_1, s_2) = \begin{cases} 0 &\text{if } m = 0, \\ \frac{1}{3}\left( \frac{m}{|s_1|} + \frac{m}{|s_2|} + \frac{m - t}{m} \right) &\text{otherwise}. \end{cases} \end{aligned}\)

m is the number of matching characters
t is half the number of transpositions
|s1| and |s2| is the length of string s1 and s2 respectively. 

The value of Jaro Distance should always be between 0 and 1. A distance value of 0 means the strings are not similar at all and a distance value of 1 means that the strings are really similar. 

Write a function jaro_distance(s1,s2) which calculates the Jaro distance between the given two strings. 


Sample Input:
<class 'str'>
s1: arow
<class 'str'>
s2: arrow

Expected Output:
<class 'float'>

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numpy has been already imported as np (import numpy as np)