solve: number of connected components in an undirected graph

Author: sounmind

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

@@ -0,0 +1,47 @@
+from typing import List
+
+
+class Solution:
+    """
+    @param n: the number of vertices
+    @param edges: the edges of undirected graph
+    @return: the number of connected components
+    """
+
+    def count_components(self, n: int, edges: List[List[int]]) -> int:
+        # Initialize each node to be its own parent
+        vertex_list = list(range(n))
+
+        # Helper function to find the root of a node
+        def find(node):
+            while vertex_list[node] != node:
+                node = vertex_list[node]
+            return node
+
+        # Iterate through each edge and perform union
+        for edge in edges:
+            root1 = find(edge[0])
+            root2 = find(edge[1])
+
+            # If roots are different, union the components
+            if root1 != root2:
+                for i in range(n):
+                    if vertex_list[i] == root1:
+                        vertex_list[i] = root2
+
+        # Find all unique roots to count the number of connected components
+        unique_roots = set(find(i) for i in range(n))
+        return len(unique_roots)
+
+
+# Test Cases
+solution = Solution()
+
+print(solution.count_components(4, [[0, 1], [2, 3], [3, 1]]))  # Output: 1
+print(solution.count_components(5, [[0, 1], [1, 2], [3, 4]]))  # Output: 2
+print(solution.count_components(5, [[0, 1], [1, 2], [2, 3], [3, 4]]))  # Output: 1
+print(solution.count_components(3, [[0, 1], [1, 2], [2, 0]]))  # Output: 1
+print(solution.count_components(4, []))  # Output: 4
+print(
+    solution.count_components(7, [[0, 1], [1, 2], [3, 4], [4, 5], [5, 6]])
+)  # Output: 2