Find the Jaccard Index and Jaccard Distance between the two given sets
Given two sets of integers s1 and s2, the task is to find the Jaccard Index and the Jaccard Distance between the two sets.
Examples:
Input: s1 = {1, 2, 3, 4, 5}, s2 = {4, 5, 6, 7, 8, 9, 10}
Output:
Jaccard index = 0.2
Jaccard distance = 0.8Input: s1 = {1, 2, 3, 4, 5}, s2 = {4, 5, 6, 7, 8}
Output:
Jaccard index = 0.25
Jaccard distance = 0.75
Approach: The Jaccard Index and the Jaccard Distance between the two sets can be calculated by using the formula:
![\[ Jaccard Index = \frac {| A \cap B |}{| A \cup B |} = \frac {|A \cap B |}{|A| +|B| -|A \cap B |} \] \[ Jaccard Distance = 1 - Jaccard Index \]](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-44046533fcd54e98cb53619b3390e083_l3.png "Rendered by QuickLaTeX.com")
Below is the implementation of the above approach:
C++
// C++ implementation of the approach#include <bits/stdc++.h>using namespace std; // Function to return the// intersection set of s1 and s2set<int> intersection(set<int> s1, set<int> s2){ set<int> intersect; // Find the intersection of the two sets set_intersection(s1.begin(), s1.end(), s2.begin(), s2.end(), inserter(intersect, intersect.begin())); return intersect;} // Function to return the Jaccard index of two setsdouble jaccard_index(set<int> s1, set<int> s2){ // Sizes of both the sets double size_s1 = s1.size(); double size_s2 = s2.size(); // Get the intersection set set<int> intersect = intersection(s1, s2); // Size of the intersection set double size_in = intersect.size(); // Calculate the Jaccard index // using the formula double jaccard_in = size_in / (size_s1 + size_s2 - size_in); // Return the Jaccard index return jaccard_in;} // Function to return the Jaccard distancedouble jaccard_distance(double jaccardIndex){ // Calculate the Jaccard distance // using the formula double jaccard_dist = 1 - jaccardIndex; // Return the Jaccard distance return jaccard_dist;} // Driver codeint main(){ // Elements of the 1st set set<int> s1; s1.insert(1); s1.insert(2); s1.insert(3); s1.insert(4); s1.insert(5); // Elements of the 2nd set set<int> s2; s2.insert(4); s2.insert(5); s2.insert(6); s2.insert(7); s2.insert(8); s2.insert(9); s2.insert(10); double jaccardIndex = jaccard_index(s1, s2); // Print the Jaccard index and Jaccard distance cout << "Jaccard index = " << jaccardIndex << endl; cout << "Jaccard distance = " << jaccard_distance(jaccardIndex); return 0;} |
Python3
# Python3 implementation of the approach # Function to return the # intersection set of s1 and s2 def intersection(s1, s2) : # Find the intersection of the two sets intersect = s1 & s2 ; return intersect; # Function to return the Jaccard index of two sets def jaccard_index(s1, s2) : # Sizes of both the sets size_s1 = len(s1); size_s2 = len(s2); # Get the intersection set intersect = intersection(s1, s2); # Size of the intersection set size_in = len(intersect); # Calculate the Jaccard index # using the formula jaccard_in = size_in / (size_s1 + size_s2 - size_in); # Return the Jaccard index return jaccard_in; # Function to return the Jaccard distance def jaccard_distance(jaccardIndex) : # Calculate the Jaccard distance # using the formula jaccard_dist = 1 - jaccardIndex; # Return the Jaccard distance return jaccard_dist; # Driver code if __name__ == "__main__" : # Elements of the 1st set s1 = set(); s1.add(1); s1.add(2); s1.add(3); s1.add(4); s1.add(5); # Elements of the 2nd set s2 = set(); s2.add(4); s2.add(5); s2.add(6); s2.add(7); s2.add(8); s2.add(9); s2.add(10); jaccardIndex = jaccard_index(s1, s2); # Print the Jaccard index and Jaccard distance print("Jaccard index = ",jaccardIndex); print("Jaccard distance = ",jaccard_distance(jaccardIndex)); # This code is contributed by AnkitRai01 |
Output:
Jaccard index = 0.2 Jaccard distance = 0.8
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