added Boruvka's MST algorithm (TheAlgorithms#2026)

* added Boruvka's MST algorithm

* Add files via upload

* fixup! Format Python code with psf/black push

* Updated Boruvka with doctest

* updating DIRECTORY.md

* Update minimum_spanning_tree_boruvka.py

* No blank line in doctest

* <BLANKLINE>

* Avoid mutable default values

https://docs.python-guide.org/writing/gotchas/

* Update minimum_spanning_tree_boruvka.py

* Avoid mutable default values

* fixup! Format Python code with psf/black push

* Update minimum_spanning_tree_boruvka.py

* Update minimum_spanning_tree_boruvka.py

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Christian Clauss <[email protected]>

DIRECTORY.md

@@ -246,6 +246,7 @@
   * [Greedy Best First](https://github.com/TheAlgorithms/Python/blob/master/graphs/greedy_best_first.py)
   * [Kahns Algorithm Long](https://github.com/TheAlgorithms/Python/blob/master/graphs/kahns_algorithm_long.py)
   * [Kahns Algorithm Topo](https://github.com/TheAlgorithms/Python/blob/master/graphs/kahns_algorithm_topo.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 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)

graphs/minimum_spanning_tree_boruvka.py

@@ -0,0 +1,195 @@
+class Graph:
+    """
+    Data structure to store graphs (based on adjacency lists)
+    """
+
+    def __init__(self):
+
+        self.num_vertices = 0
+        self.num_edges = 0
+        self.adjacency = {}
+
+    def add_vertex(self, vertex):
+        """
+        Adds a vertex to the graph
+
+        """
+        if vertex not in self.adjacency:
+            self.adjacency[vertex] = {}
+            self.num_vertices += 1
+
+    def add_edge(self, head, tail, weight):
+        """
+        Adds an edge to the graph
+
+        """
+
+        self.add_vertex(head)
+        self.add_vertex(tail)
+
+        if head == tail:
+            return
+
+        self.adjacency[head][tail] = weight
+        self.adjacency[tail][head] = weight
+
+    def distinct_weight(self):
+        """
+        For Boruvks's algorithm the weights should be distinct
+        Converts the weights to be distinct
+
+        """
+        edges = self.get_edges()
+        for edge in edges:
+            head, tail, weight = edge
+            edges.remove((tail, head, weight))
+        for i in range(len(edges)):
+            edges[i] = list(edges[i])
+
+        edges.sort(key=lambda e: e[2])
+        for i in range(len(edges) - 1):
+            if edges[i][2] >= edges[i + 1][2]:
+                edges[i + 1][2] = edges[i][2] + 1
+        for edge in edges:
+            head, tail, weight = edge
+            self.adjacency[head][tail] = weight
+            self.adjacency[tail][head] = weight
+
+    def __str__(self):
+        """
+        Returns string representation of the graph
+        """
+        string = ""
+        for tail in self.adjacency:
+            for head in self.adjacency[tail]:
+                weight = self.adjacency[head][tail]
+                string += "%d -> %d == %d\n" % (head, tail, weight)
+        return string.rstrip("\n")
+
+    def get_edges(self):
+        """
+        Returna all edges in the graph
+        """
+        output = []
+        for tail in self.adjacency:
+            for head in self.adjacency[tail]:
+                output.append((tail, head, self.adjacency[head][tail]))
+        return output
+
+    def get_vertices(self):
+        """
+        Returns all vertices in the graph
+        """
+        return self.adjacency.keys()
+
+    @staticmethod
+    def build(vertices=None, edges=None):
+        """
+        Builds a graph from the given set of vertices and edges
+
+        """
+        g = Graph()
+        if vertices is None:
+            vertices = []
+        if edges is None:
+            edge = []
+        for vertex in vertices:
+            g.add_vertex(vertex)
+        for edge in edges:
+            g.add_edge(*edge)
+        return g
+
+    class UnionFind(object):
+        """
+        Disjoint set Union and Find for Boruvka's algorithm
+        """
+
+        def __init__(self):
+            self.parent = {}
+            self.rank = {}
+
+        def __len__(self):
+            return len(self.parent)
+
+        def make_set(self, item):
+            if item in self.parent:
+                return self.find(item)
+
+            self.parent[item] = item
+            self.rank[item] = 0
+            return item
+
+        def find(self, item):
+            if item not in self.parent:
+                return self.make_set(item)
+            if item != self.parent[item]:
+                self.parent[item] = self.find(self.parent[item])
+            return self.parent[item]
+
+        def union(self, item1, item2):
+            root1 = self.find(item1)
+            root2 = self.find(item2)
+
+            if root1 == root2:
+                return root1
+
+            if self.rank[root1] > self.rank[root2]:
+                self.parent[root2] = root1
+                return root1
+
+            if self.rank[root1] < self.rank[root2]:
+                self.parent[root1] = root2
+                return root2
+
+            if self.rank[root1] == self.rank[root2]:
+                self.rank[root1] += 1
+                self.parent[root2] = root1
+                return root1
+
+    def boruvka_mst(graph):
+        """
+        Implementation of Boruvka's algorithm
+        >>> g = Graph()
+        >>> g = Graph.build([0, 1, 2, 3], [[0, 1, 1], [0, 2, 1],[2, 3, 1]])
+        >>> g.distinct_weight()
+        >>> bg = Graph.boruvka_mst(g)
+        >>> print(bg)
+        1 -> 0 == 1
+        2 -> 0 == 2
+        0 -> 1 == 1
+        0 -> 2 == 2
+        3 -> 2 == 3
+        2 -> 3 == 3
+        """
+        num_components = graph.num_vertices
+
+        union_find = Graph.UnionFind()
+        mst_edges = []
+        while num_components > 1:
+            cheap_edge = {}
+            for vertex in graph.get_vertices():
+                cheap_edge[vertex] = -1
+
+            edges = graph.get_edges()
+            for edge in edges:
+                head, tail, weight = edge
+                edges.remove((tail, head, weight))
+            for edge in edges:
+                head, tail, weight = edge
+                set1 = union_find.find(head)
+                set2 = union_find.find(tail)
+                if set1 != set2:
+                    if cheap_edge[set1] == -1 or cheap_edge[set1][2] > weight:
+                        cheap_edge[set1] = [head, tail, weight]
+
+                    if cheap_edge[set2] == -1 or cheap_edge[set2][2] > weight:
+                        cheap_edge[set2] = [head, tail, weight]
+            for vertex in cheap_edge:
+                if cheap_edge[vertex] != -1:
+                    head, tail, weight = cheap_edge[vertex]
+                    if union_find.find(head) != union_find.find(tail):
+                        union_find.union(head, tail)
+                        mst_edges.append(cheap_edge[vertex])
+                        num_components = num_components - 1
+        mst = Graph.build(edges=mst_edges)
+        return mst