Added Kruskal's Algorithm (more organized than the one present) (#2218)

* Added Kruskal's Algorithm

* Added Type Hints

* fixup! Format Python code with psf/black push

* Added Type Hints V2

* Implemented suggestions + uniform naming convention

* removed redundant variable (self.nodes)

* updating DIRECTORY.md

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

DIRECTORY.md

@@ -267,6 +267,7 @@
   * [Karger](https://github.com/TheAlgorithms/Python/blob/master/graphs/karger.py)
   * [Minimum Spanning Tree Boruvka](https://github.com/TheAlgorithms/Python/blob/master/graphs/minimum_spanning_tree_boruvka.py)
   * [Minimum Spanning Tree Kruskal](https://github.com/TheAlgorithms/Python/blob/master/graphs/minimum_spanning_tree_kruskal.py)
+  * [Minimum Spanning Tree Kruskal2](https://github.com/TheAlgorithms/Python/blob/master/graphs/minimum_spanning_tree_kruskal2.py)
   * [Minimum Spanning Tree Prims](https://github.com/TheAlgorithms/Python/blob/master/graphs/minimum_spanning_tree_prims.py)
   * [Multi Heuristic Astar](https://github.com/TheAlgorithms/Python/blob/master/graphs/multi_heuristic_astar.py)
   * [Page Rank](https://github.com/TheAlgorithms/Python/blob/master/graphs/page_rank.py)

graphs/minimum_spanning_tree_kruskal2.py

@@ -0,0 +1,109 @@
+from __future__ import annotations
+
+
+class DisjointSetTreeNode:
+    # Disjoint Set Node to store the parent and rank
+    def __init__(self, key: int) -> None:
+        self.key = key
+        self.parent = self
+        self.rank = 0
+
+
+class DisjointSetTree:
+    # Disjoint Set DataStructure
+    def __init__(self):
+        # map from node name to the node object
+        self.map = {}
+
+    def make_set(self, x: int) -> None:
+        # create a new set with x as its member
+        self.map[x] = DisjointSetTreeNode(x)
+
+    def find_set(self, x: int) -> DisjointSetTreeNode:
+        # find the set x belongs to (with path-compression)
+        elem_ref = self.map[x]
+        if elem_ref != elem_ref.parent:
+            elem_ref.parent = self.find_set(elem_ref.parent.key)
+        return elem_ref.parent
+
+    def link(self, x: int, y: int) -> None:
+        # helper function for union operation
+        if x.rank > y.rank:
+            y.parent = x
+        else:
+            x.parent = y
+            if x.rank == y.rank:
+                y.rank += 1
+
+    def union(self, x: int, y: int) -> None:
+        # merge 2 disjoint sets
+        self.link(self.find_set(x), self.find_set(y))
+
+
+class GraphUndirectedWeighted:
+    def __init__(self):
+        # connections: map from the node to the neighbouring nodes (with weights)
+        self.connections = {}
+
+    def add_node(self, node: int) -> None:
+        # add a node ONLY if its not present in the graph
+        if node not in self.connections:
+            self.connections[node] = {}
+
+    def add_edge(self, node1: int, node2: int, weight: int) -> None:
+        # add an edge with the given weight
+        self.add_node(node1)
+        self.add_node(node2)
+        self.connections[node1][node2] = weight
+        self.connections[node2][node1] = weight
+
+    def kruskal(self) -> GraphUndirectedWeighted:
+        # Kruskal's Algorithm to generate a Minimum Spanning Tree (MST) of a graph
+        """
+        Details: https://en.wikipedia.org/wiki/Kruskal%27s_algorithm
+
+        Example:
+
+        >>> graph = GraphUndirectedWeighted()
+        >>> graph.add_edge(1, 2, 1)
+        >>> graph.add_edge(2, 3, 2)
+        >>> graph.add_edge(3, 4, 1)
+        >>> graph.add_edge(3, 5, 100) # Removed in MST
+        >>> graph.add_edge(4, 5, 5)
+        >>> assert 5 in graph.connections[3]
+        >>> mst = graph.kruskal()
+        >>> assert 5 not in mst.connections[3]
+        """
+
+        # getting the edges in ascending order of weights
+        edges = []
+        seen = set()
+        for start in self.connections:
+            for end in self.connections[start]:
+                if (start, end) not in seen:
+                    seen.add((end, start))
+                    edges.append((start, end, self.connections[start][end]))
+        edges.sort(key=lambda x: x[2])
+        # creating the disjoint set
+        disjoint_set = DisjointSetTree()
+        [disjoint_set.make_set(node) for node in self.connections]
+        # MST generation
+        num_edges = 0
+        index = 0
+        graph = GraphUndirectedWeighted()
+        while num_edges < len(self.connections) - 1:
+            u, v, w = edges[index]
+            index += 1
+            parentu = disjoint_set.find_set(u)
+            parentv = disjoint_set.find_set(v)
+            if parentu != parentv:
+                num_edges += 1
+                graph.add_edge(u, v, w)
+                disjoint_set.union(u, v)
+        return graph
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()