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Topological Sort

Certification: Advanced Level Accuracy: 66.67% Submissions: 3 Points: 15

Write a Python function that performs topological sorting on a Directed Acyclic Graph (DAG). Topological sorting is a linear ordering of vertices such that for every directed edge (u, v), vertex u comes before v in the ordering.

Example 1
    
  
  • Input: {0: [1, 2], 1: [3], 2: [3], 3: [], 4: [0, 1]}
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  • Output: [4, 0, 2, 1, 3]
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  • Explanation:
    
      
      
    • Step 1: Build the graph from the adjacency list.
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    • Step 2: Perform DFS with visited tracking.
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    • Step 3: Return the topological order [4, 0, 2, 1, 3].
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Example 2
    
  
  • Input: {0: [1, 2], 1: [], 2: [3], 3: []}
    • 
  
  • Output: [0, 2, 3, 1]
    • 
  
  • Explanation:
    
      
      
    • Step 1: Build the graph from the adjacency list.
      • 
      
    • Step 2: Perform DFS with visited tracking.
      • 
      
    • Step 3: Return the topological order [0, 2, 3, 1].
      • 
    
    
  
    •
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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  • Graph is a DAG (no cycles)
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  • Time Complexity: O(V + E), where V is the number of vertices and E is the number of edges
    • 
  
  • Space Complexity: O(V)
    •
GraphAlgorithmsGoogleEY
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Hint
Solution

Solution Hints

    
  
  • Use Depth-First Search (DFS) to explore vertices
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  • Keep track of visited vertices and vertices currently in the recursion stack
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  • Use a stack to store vertices in the post-order of DFS
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  • Check for cycles using a "visited" and "in_stack" array
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  • Reverse the final stack to get the topological order
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Steps to solve by this approach:

 Step 1: Calculate the in-degree (number of incoming edges) for each node in the graph.

 Step 2: Initialize a queue with all nodes that have zero in-degree.

 Step 3: Process nodes from the queue, adding them to the topological order.

 Step 4: For each processed node, decrease the in-degree of all its neighbors.

 Step 5: If a neighbor's in-degree becomes zero, add it to the queue.

 Step 6: Continue until the queue is empty and verify that all nodes were processed.

 Step 7: Return the topological order or empty list if a cycle is detected.

Submitted Code :