Create kruskals_algo.py

kruskals_algo.py

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+# Class to represent a disjoint set (Union-Find)
+class DisjointSet:
+    def __init__(self, n):
+        self.parent = list(range(n))
+        self.rank = [0] * n
+
+    def find(self, u):
+        if self.parent[u] != u:
+            self.parent[u] = self.find(self.parent[u])
+        return self.parent[u]
+
+    def union(self, u, v):
+        root_u = self.find(u)
+        root_v = self.find(v)
+
+        if root_u != root_v:
+            if self.rank[root_u] > self.rank[root_v]:
+                self.parent[root_v] = root_u
+            elif self.rank[root_u] < self.rank[root_v]:
+                self.parent[root_u] = root_v
+            else:
+                self.parent[root_v] = root_u
+                self.rank[root_u] += 1
+
+# Kruskal's Algorithm to find MST
+def kruskal(graph):
+    edges = []
+    n = len(graph)  # number of vertices
+    # Convert the adjacency list to a list of edges (u, v, weight)
+    for u in range(n):
+        for v, weight in graph[u]:
+            edges.append((weight, u, v))
+    # Sort all edges by weight
+    edges.sort()
+    disjoint_set = DisjointSet(n)
+    mst = []
+    mst_weight = 0
+    # Process each edge in increasing order of weight
+    for weight, u, v in edges:
+        # Check if the selected edge forms a cycle
+        if disjoint_set.find(u) != disjoint_set.find(v):
+            disjoint_set.union(u, v)
+            mst.append((u, v, weight))
+            mst_weight += weight
+    return mst, mst_weight
+
+# Function to take user input for adjacency list graph
+def input_graph():
+    graph = []
+    n = int(input("Enter the number of vertices: "))
+    print("Enter the adjacency list (vertex, weight) for each vertex (enter -1 to stop):")
+    for i in range(n):
+        edges = []
+        while True:
+            vertex, weight = map(int, input(f"Enter edge for vertex {i} (vertex weight): ").split())
+            if vertex == -1:
+                break
+            edges.append((vertex, weight))
+        graph.append(edges)
+
+    return graph
+
+# Example usage
+graph = input_graph()
+
+mst, total_weight = kruskal(graph)
+print("\nMinimum Spanning Tree:")
+for u, v, weight in mst:
+    print(f"Edge {u} - {v}: {weight}")
+print(f"Total weight of MST: {total_weight}")