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Number of Connected Components in a Graph

Certification: Advanced Level Accuracy: 100% Submissions: 3 Points: 15

Write a Python function that counts the number of connected components in an undirected graph represented as an adjacency list. A connected component is a subgraph in which any two vertices are connected to each other by paths.

Example 1
    
  
  • Input: {0: [1, 2], 1: [0], 2: [0], 3: [4], 4: [3], 5: []}
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  • Output: 3
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  • Explanation:
    
      
      
    • Step 1: Initialize a visited array to keep track of visited vertices.
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    • Step 2: Perform DFS/BFS on each unvisited vertex to explore its connected component.
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    • Step 3: Count the number of times we need to start a new DFS/BFS (3 components).
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    • Step 4: Return 3 as the number of connected components.
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Example 2
    
  
  • Input: {0: [1, 2, 3], 1: [0, 2], 2: [0, 1], 3: [0]}
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  • Output: 1
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  • Explanation:
    
      
      
    • Step 1: Initialize a visited array.
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    • Step 2: Start DFS from vertex 0 and mark all reachable vertices as visited.
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    • Step 3: All vertices are visited after one DFS traversal, indicating one connected component.
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    • Step 4: Return 1 as the number of connected components.
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Constraints
    
  
  • 1 ≤ number of vertices ≤ 10^5
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  • 0 ≤ number of edges ≤ 10^6
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  • Graph is represented as an adjacency list
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  • Time Complexity: O(V + E), where V is the number of vertices and E is the number of edges
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  • Space Complexity: O(V)
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GraphRecursionAlgorithmsTCS (Tata Consultancy Services)HCL Technologies
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Hint
Solution

Solution Hints

    
  
  • Use Depth-First Search (DFS) or Breadth-First Search (BFS) to explore all vertices in a component
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  • Keep track of visited vertices to avoid revisiting
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  • Increment component count each time you start a new DFS/BFS from an unvisited vertex
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  • Use a recursive approach for DFS or a queue for BFS
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  • Handle disconnected vertices (vertices with no edges) as separate components
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Steps to solve by this approach:

 Step 1: Initialize a visited array to track which nodes have been processed.

 Step 2: Initialize a counter for the number of connected components.

 Step 3: For each unvisited node, increment the counter and perform DFS.

 Step 4: During DFS, mark the current node as visited and recursively visit all its unvisited neighbors.

 Step 5: Return the final count of connected components.

Submitted Code :