adding jaccard similarity (TheAlgorithms#1270)

* adding jaccard similarity

* renaming files. zeebus! what an headache

Author: cozek

maths/jaccard_similarity.py

@@ -0,0 +1,80 @@
+"""
+The Jaccard similarity coefficient is a commonly used indicator of the
+similarity between two sets. Let U be a set and A and B be subsets of U,
+then the Jaccard index/similarity is defined to be the ratio of the number
+of elements of their intersection and the number of elements of their union.
+
+Inspired from Wikipedia and
+the book Mining of Massive Datasets [MMDS 2nd Edition, Chapter 3]
+
+https://en.wikipedia.org/wiki/Jaccard_index
+https://mmds.org
+
+Jaccard similarity is widely used with MinHashing.
+"""
+
+
+def jaccard_similariy(setA, setB, alternativeUnion=False):
+    """
+    Finds the jaccard similarity between two sets.
+    Essentially, its intersection over union.
+
+    The alternative way to calculate this is to take union as sum of the
+    number of items in the two sets. This will lead to jaccard similarity
+    of a set with itself be 1/2 instead of 1. [MMDS 2nd Edition, Page 77]
+
+    Parameters:
+        :setA (set,list,tuple): A non-empty set/list
+        :setB (set,list,tuple): A non-empty set/list
+        :alternativeUnion (boolean): If True, use sum of number of
+        items as union
+
+    Output:
+        (float) The jaccard similarity between the two sets.
+
+    Examples:
+    >>> setA = {'a', 'b', 'c', 'd', 'e'}
+    >>> setB = {'c', 'd', 'e', 'f', 'h', 'i'}
+    >>> jaccard_similariy(setA,setB)
+    0.375
+
+    >>> jaccard_similariy(setA,setA)
+    1.0
+
+    >>> jaccard_similariy(setA,setA,True)
+    0.5
+
+    >>> setA = ['a', 'b', 'c', 'd', 'e']
+    >>> setB = ('c', 'd', 'e', 'f', 'h', 'i')
+    >>> jaccard_similariy(setA,setB)
+    0.375
+    """
+
+    if isinstance(setA, set) and isinstance(setB, set):
+
+        intersection = len(setA.intersection(setB))
+
+        if alternativeUnion:
+            union = len(setA) + len(setB)
+        else:
+            union = len(setA.union(setB))
+
+        return intersection / union
+
+    if isinstance(setA, (list, tuple)) and isinstance(setB, (list, tuple)):
+
+        intersection = [element for element in setA if element in setB]
+
+        if alternativeUnion:
+            union = len(setA) + len(setB)
+        else:
+            union = setA + [element for element in setB if element not in setA]
+
+        return len(intersection) / len(union)
+
+
+if __name__ == "__main__":
+
+    setA = {"a", "b", "c", "d", "e"}
+    setB = {"c", "d", "e", "f", "h", "i"}
+    print(jaccard_similariy(setA, setB))