kruskal_alog is coded

Author: Anantbhardwaj2003

graphs/kruskal_algo.py

@@ -0,0 +1,56 @@
+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:
+            # Union by rank
+            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
+
+def kruskal_algorithm(vertices, edges):
+    # Step 1: Sort edges based on weight
+    edges.sort(key=lambda x: x[2])
+    
+    # Step 2: Initialize Disjoint Set
+    ds = DisjointSet(vertices)
+    
+    mst = []
+    mst_weight = 0
+    
+    # Step 3: Iterate through sorted edges
+    for u, v, weight in edges:
+        # Check if adding this edge creates a cycle
+        if ds.find(u) != ds.find(v):
+            ds.union(u, v)
+            mst.append((u, v, weight))
+            mst_weight += weight
+    
+    return mst, mst_weight
+
+# Example usage:
+vertices = 4
+edges = [
+    (0, 1, 10),
+    (0, 2, 6),
+    (0, 3, 5),
+    (1, 3, 15),
+    (2, 3, 4)
+]
+
+mst, total_weight = kruskal_algorithm(vertices, edges)
+print("Edges in the MST:", mst)
+print("Total weight of the MST:", total_weight)