Merge pull request himanshu-03#84 from surya-mu/main

add: Prim's Algorithm to Find MST.

Author: himanshu-03

Graphs/Prims_Algorithm_Minimum_Spanning_Tree.py

@@ -0,0 +1,59 @@
+//Prim's Algo to calculate the minimum spanning tree with user-input, using the Fibonacci Heap Method.
+
+import sys
+import heapq
+
+class UniqueGraph:
+    def __init(self, vertices_count):
+        self.V = vertices_count
+        self.edges = [[] for _ in range(vertices_count)]
+
+    def find_min_edge(self, key_values, mst_set):
+        min_value = sys.maxsize
+        min_index = 0
+
+        for vertex in range(self.V):
+            if key_values[vertex] < min_value and not mst_set[vertex]:
+                min_value = key_values[vertex]
+                min_index = vertex
+
+        return min_index
+
+    def find_minimum_spanning_tree(self):
+        parents = [None] * self.V
+        key_values = [sys.maxsize] * self.V
+        key_values[0] = 0
+        mst_set = [False] * self.V
+
+        parents[0] = -1
+        min_heap = [(0, 0)]
+
+        while min_heap:
+            current_value, current_vertex = heapq.heappop(min_heap)
+            mst_set[current_vertex] = True
+
+            for edge in self.edges[current_vertex]:
+                adjacent_vertex, weight = edge
+                if not mst_set[adjacent_vertex] and key_values[adjacent_vertex] > weight:
+                    key_values[adjacent_vertex] = weight
+                    parents[adjacent_vertex] = current_vertex
+                    heapq.heappush(min_heap, (key_values[adjacent_vertex], adjacent_vertex))
+
+        self.print_minimum_spanning_tree(parents, key_values)
+
+    def print_minimum_spanning_tree(self, parents, key_values):
+        print("Edge \tWeight")
+        for vertex in range(1, self.V):
+            print(f"{parents[vertex]} - {vertex}\t{key_values[vertex]}")
+
+# Input the graph from the user
+V = int(input("Enter the number of vertices: "))
+g = UniqueGraph(V)
+print("Enter the edges and their weights (e.g., '1 2 3' means an edge from vertex 1 to vertex 2 with weight 3):")
+
+for _ in range(V - 1):
+    u, v, w = map(int, input().split())
+    g.edges[u].append((v, w))
+    g.edges[v].append((u, w))
+
+g.find_minimum_spanning_tree()