Add disjoint set (#1194)

* Add disjoint set

* disjoint set: add doctest, make code more Pythonic

* disjoint set: replace x.p with x.parent

* disjoint set: add test and refercence

data_structures/disjoint_set/disjoint_set.py

@@ -0,0 +1,79 @@
+"""
+    disjoint set
+    Reference: https://en.wikipedia.org/wiki/Disjoint-set_data_structure
+"""
+
+
+class Node:
+    def __init__(self, data):
+        self.data = data
+
+
+def make_set(x):
+    """
+    make x as a set.
+    """
+    # rank is the distance from x to its' parent
+    # root's rank is 0
+    x.rank = 0
+    x.parent = x
+
+
+def union_set(x, y):
+    """
+    union two sets.
+    set with bigger rank should be parent, so that the
+    disjoint set tree will be more flat.
+    """
+    x, y = find_set(x), find_set(y)
+    if x.rank > y.rank:
+        y.parent = x
+    else:
+        x.parent = y
+        if x.rank == y.rank:
+            y.rank += 1
+
+
+def find_set(x):
+    """
+    return the parent of x
+    """
+    if x != x.parent:
+        x.parent = find_set(x.parent)
+    return x.parent
+
+
+def find_python_set(node: Node) -> set:
+    """
+    Return a Python Standard Library set that contains i.
+    """
+    sets = ({0, 1, 2}, {3, 4, 5})
+    for s in sets:
+        if node.data in s:
+            return s
+    raise ValueError(f"{node.data} is not in {sets}")
+
+
+def test_disjoint_set():
+    """
+    >>> test_disjoint_set()
+    """
+    vertex = [Node(i) for i in range(6)]
+    for v in vertex:
+        make_set(v)
+
+    union_set(vertex[0], vertex[1])
+    union_set(vertex[1], vertex[2])
+    union_set(vertex[3], vertex[4])
+    union_set(vertex[3], vertex[5])
+
+    for node0 in vertex:
+        for node1 in vertex:
+            if find_python_set(node0).isdisjoint(find_python_set(node1)):
+                assert find_set(node0) != find_set(node1)
+            else:
+                assert find_set(node0) == find_set(node1)
+
+
+if __name__ == "__main__":
+    test_disjoint_set()