Create alternate_disjoint_set.py (#2302)

* Create alternate_disjoint_set.py

This code implements a disjoint set using Lists 
with added heuristics for efficiency
Union by Rank Heuristic and Path Compression

* Update alternate_disjoint_set.py

Added typehints, doctests and some suggested variable name change

* Update alternate_disjoint_set.py

* Formatted with Black

* More formatting

* Formatting on line 28

* Error in Doctest

* Doctest Update in alternate disjoint set

* Fixed build error

* Fixed doctest

data_structures/disjoint_set/alternate_disjoint_set.py

@@ -0,0 +1,68 @@
+"""
+Implements a disjoint set using Lists and some added heuristics for efficiency
+Union by Rank Heuristic and Path Compression
+"""
+
+
+class DisjointSet:
+    def __init__(self, set_counts: list) -> None:
+        """
+        Initialize with a list of the number of items in each set
+        and with rank = 1 for each set
+        """
+        self.set_counts = set_counts
+        self.max_set = max(set_counts)
+        num_sets = len(set_counts)
+        self.ranks = [1] * num_sets
+        self.parents = list(range(num_sets))
+
+    def merge(self, src: int, dst: int) -> bool:
+        """
+        Merge two sets together using Union by rank heuristic
+        Return True if successful
+        Merge two disjoint sets
+        >>> A = DisjointSet([1, 1, 1])
+        >>> A.merge(1, 2)
+        True
+        >>> A.merge(0, 2)
+        True
+        >>> A.merge(0, 1)
+        False
+        """
+        src_parent = self.get_parent(src)
+        dst_parent = self.get_parent(dst)
+
+        if src_parent == dst_parent:
+            return False
+
+        if self.ranks[dst_parent] >= self.ranks[src_parent]:
+            self.set_counts[dst_parent] += self.set_counts[src_parent]
+            self.set_counts[src_parent] = 0
+            self.parents[src_parent] = dst_parent
+            if self.ranks[dst_parent] == self.ranks[src_parent]:
+                self.ranks[dst_parent] += 1
+            joined_set_size = self.set_counts[dst_parent]
+        else:
+            self.set_counts[src_parent] += self.set_counts[dst_parent]
+            self.set_counts[dst_parent] = 0
+            self.parents[dst_parent] = src_parent
+            joined_set_size = self.set_counts[src_parent]
+
+        self.max_set = max(self.max_set, joined_set_size)
+        return True
+
+    def get_parent(self, disj_set: int) -> int:
+        """
+        Find the Parent of a given set
+        >>> A = DisjointSet([1, 1, 1])
+        >>> A.merge(1, 2)
+        True
+        >>> A.get_parent(0)
+        0
+        >>> A.get_parent(1)
+        2
+        """
+        if self.parents[disj_set] == disj_set:
+            return disj_set
+        self.parents[disj_set] = self.get_parent(self.parents[disj_set])
+        return self.parents[disj_set]