numberOfConnectedComponentsInAnUndirectedGraph

Author: yolophg

number-of-connected-components-in-an-undirected-graph/yolophg.py

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+# Time Complexity: O(N + E) - go through all nodes & edges.
+# Space Complexity: O(N) - store parent info for each node.
+
+class Solution:
+    def count_components(self, n: int, edges: List[List[int]]) -> int:
+
+        # set up the Union-Find structure
+        parent = [i for i in range(n)]  # initially, each node is its own parent
+        rank = [1] * n  # used for optimization in Union operation
+
+        # find function (with path compression)
+        def find(node):
+            if parent[node] != node:
+                parent[node] = find(parent[node])  # path compression
+            return parent[node]
+
+        # union function (using rank to keep tree flat)
+        def union(node1, node2):
+            root1, root2 = find(node1), find(node2)
+            if root1 != root2:
+                if rank[root1] > rank[root2]:
+                    parent[root2] = root1
+                elif rank[root1] < rank[root2]:
+                    parent[root1] = root2
+                else:
+                    parent[root2] = root1
+                    rank[root1] += 1
+                return True  # union was successful (i.e., we merged two components)
+            return False  # already in the same component
+
+        # connect nodes using Union-Find
+        for a, b in edges:
+            union(a, b)
+
+        # count unique roots (number of connected components)
+        return len(set(find(i) for i in range(n)))