Create kruskals.py

Python/algorithms/graph_algorithms/kruskals.py

@@ -0,0 +1,68 @@
+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])  # Path compression
+        return self.parent[u]
+
+    def union(self, u, v):
+        rootU = self.find(u)
+        rootV = self.find(v)
+        if rootU != rootV:
+            if self.rank[rootU] < self.rank[rootV]:
+                self.parent[rootU] = rootV
+            elif self.rank[rootU] > self.rank[rootV]:
+                self.parent[rootV] = rootU
+            else:
+                self.parent[rootV] = rootU
+                self.rank[rootU] += 1
+            return True
+        return False
+
+class Graph:
+    def __init__(self, vertices):
+        self.V = vertices
+        self.edges = []  # Each edge: (weight, u, v)
+
+    def add_edge(self, u, v, w):
+        self.edges.append((w, u, v))
+
+    def kruskal(self):
+        self.edges.sort()
+        ds = DisjointSet(self.V)
+        mst = []
+        total_weight = 0
+
+        for w, u, v in self.edges:
+            if ds.union(u, v):  # If no cycle formed
+                mst.append((u, v, w))
+                total_weight += w
+
+        print("Edges in the MST:")
+        for u, v, w in mst:
+            print(f"{u} -- {v} == {w}")
+        print("Total weight of MST:", total_weight)
+
+# Example usage:
+if __name__ == "__main__":
+    g = Graph(6)
+    g.add_edge(0, 1, 4)
+    g.add_edge(0, 2, 4)
+    g.add_edge(1, 2, 2)
+    g.add_edge(1, 0, 4)
+    g.add_edge(2, 0, 4)
+    g.add_edge(2, 1, 2)
+    g.add_edge(2, 3, 3)
+    g.add_edge(2, 5, 2)
+    g.add_edge(2, 4, 4)
+    g.add_edge(3, 2, 3)
+    g.add_edge(3, 4, 3)
+    g.add_edge(4, 2, 4)
+    g.add_edge(4, 3, 3)
+    g.add_edge(5, 2, 2)
+    g.add_edge(5, 4, 3)
+
+    g.kruskal()