Minimum spanning tree - undirected graph

Author: ivanmmarkovic

Diff for: README.md

@@ -108,6 +108,8 @@ but it also contains other data structures, algorithms and problems.
     - [Priority Queue implementation](https://github.com/ivanmmarkovic/Problem-Solving-with-Algorithms-and-Data-Structures-using-Python/tree/master/graphs/dijkstra/priority-queue-impl-adjacency-map)
     - [Matrix implementation](https://github.com/ivanmmarkovic/Problem-Solving-with-Algorithms-and-Data-Structures-using-Python/tree/master/graphs/dijkstra/matrix-impl)
 - [Minimum Spanning Tree](https://github.com/ivanmmarkovic/Problem-Solving-with-Algorithms-and-Data-Structures-using-Python/tree/master/graphs/minimum-spanning-tree)
+    - [Minimum Spanning Tree in undirected graph]()
+        - perform breadth first search or depth first search and record previous edges
     - [Prim's algorithm - Minimum Spanning Tree in undirected weighted graph](https://github.com/ivanmmarkovic/Problem-Solving-with-Algorithms-and-Data-Structures-using-Python/tree/master/graphs/minimum-spanning-tree/prims-algorithm)
 - [Is graph bipartite](https://github.com/ivanmmarkovic/Problem-Solving-with-Algorithms-and-Data-Structures-using-Python/tree/master/graphs/is-graph-bipartite)
 

Diff for: graphs/minimum-spanning-tree/breadth-first-search/__pycache__/graph.cpython-39.pyc

@@ -0,0 +1,44 @@
+from queue import Queue
+
+
+class Graph:
+    def __init__(self):
+        self.vertices: list = []
+        self.adjacency_list: dict = {}
+        self.prev: dict = {}
+        self.distance: dict = {}
+        self.colors: dict = {}
+
+    def add_vertex(self, label: str):
+        self.vertices.append(label)
+        self.adjacency_list[label]: list = []
+        self.prev[label] = None
+        self.distance[label] = 0
+        self.colors[label] = "white"
+
+    def add_edge(self, label1: str, label2: str):
+        self.adjacency_list[label1].append(label2)
+        self.adjacency_list[label2].append(label1)
+
+    def minimum_spanning_tree(self, label: str) -> list:  # this is breadth first search
+        min_edges: list = []
+        q: Queue = Queue()
+        q.enqueue(label)
+        self.colors[label] = "gray"
+        while not q.is_empty():
+            tmp: str = q.dequeue()
+            for neighbour in self.adjacency_list[tmp]:
+                if self.colors[neighbour] == "white":
+                    min_edges.append([tmp, neighbour])
+                    self.prev[neighbour] = tmp
+                    self.distance[neighbour] = self.distance[tmp] + 1
+                    self.colors[neighbour] = "gray"
+                    q.enqueue(neighbour)
+            self.colors[tmp] = "black"
+        return min_edges
+
+    def return_path(self, label: str) -> str:
+        if self.prev[label] is None:
+            return label
+        else:
+            return self.return_path(self.prev[label]) + " -> " + label

Diff for: graphs/minimum-spanning-tree/breadth-first-search/__pycache__/queue.cpython-39.pyc

@@ -0,0 +1,23 @@
+from graph import Graph
+
+graph = Graph()
+
+my_vertices = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I']
+# add vertices
+for i in range(len(my_vertices)):
+    graph.add_vertex(my_vertices[i])
+
+graph.add_edge('A', 'B')
+graph.add_edge('A', 'C')
+graph.add_edge('A', 'D')
+graph.add_edge('C', 'D')
+graph.add_edge('C', 'G')
+graph.add_edge('D', 'G')
+graph.add_edge('D', 'H')
+graph.add_edge('B', 'E')
+graph.add_edge('B', 'F')
+graph.add_edge('E', 'I')
+
+edges: list = graph.minimum_spanning_tree("A")
+print(edges)
+print(graph.return_path("H"))

Diff for: graphs/minimum-spanning-tree/breadth-first-search/graph.py

@@ -0,0 +1,15 @@
+class Queue:
+    def __init__(self):
+        self.queue = []
+
+    def enqueue(self, item):
+        self.queue.insert(0, item)
+
+    def dequeue(self):
+        return self.queue.pop()
+
+    def size(self):
+        return len(self.queue)
+
+    def is_empty(self):
+        return self.queue == []