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Clone a Directed Graph

Certification: Intermediate Level Accuracy: 0% Submissions: 0 Points: 12

Write a C# program to clone a directed graph. The input graph is represented by a list of nodes, where each node contains a value and a list of its neighbors. Return a deep copy (clone) of the graph.

Example 1
    
  
  • Input: adjList = [[2,4],[1,3],[2,4],[1,3]]
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  • Output: [[2,4],[1,3],[2,4],[1,3]]
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  • Explanation: 
    
      
      
    • Node 1 has neighbors: Node 2 and Node 4
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    • Node 2 has neighbors: Node 1 and Node 3
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    • Node 3 has neighbors: Node 2 and Node 4
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    • Node 4 has neighbors: Node 1 and Node 3
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    • The returned graph has the same structure.
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Example 2
    
  
  • Input: adjList = [[]]
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  • Output: [[]]
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  • Explanation: 
    
      
      
    • The graph has only one node with no neighbors.
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Constraints
    
  
  • The number of nodes in the graph is in the range [0, 100]
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  • 1 ≤ Node.val ≤ 100
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  • Node.val is unique for each node
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  • There are no repeated edges and no self-loops in the graph
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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|) for storing the visited nodes
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Hint
Solution

Solution Hints

    
  
  • Use depth-first search (DFS) or breadth-first search (BFS) to traverse the graph.
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  • Keep a mapping between original nodes and cloned nodes to avoid duplicate cloning.
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  • For each original node, create a corresponding clone node if it doesn't exist.
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  • For each neighbor of the original node, create a clone if it doesn't exist and add it to the current clone's neighbors.
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  • Return the clone of the provided node.
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Steps to solve by this approach:

 Step 1: Create a dictionary to map original nodes to their cloned counterparts.
 Step 2: Use DFS or BFS to traverse the original graph.
 Step 3: For each node we visit, check if we've already created a clone for it.
 Step 4: If not, create a new node with the same value as the original.
 Step 5: Store the mapping between the original and clone in the dictionary.
 Step 6: Recursively process all neighbors of the current node.
 Step 7: For each neighbor, get its clone (or create one if it doesn't exist) and add it to the current node's neighbors list.

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