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Check if a Graph Has a Cycle

Certification: Intermediate Level Accuracy: 0% Submissions: 0 Points: 10

Write a C# program to detect if an undirected graph has a cycle. Implement a method that takes the number of vertices and edges of a graph as input and determines whether the graph contains at least one cycle.

Example 1
    
  
  • Input:
    
      
      
    • Number of vertices: 5
      • 
      
    • Edges: [[0,1], [1,2], [2,3], [3,4]]
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    • 
  
  • Output: false
    • 
  
  • Explanation:
    
      
      
    • The given graph is a simple path from vertex 0 to 4 with no cycles.
      • 
    
    
  
    •
Example 2
    
  
  • Input:
    
      
      
    • Number of vertices: 5
      • 
      
    • Edges: [[0,1], [1,2], [2,0], [3,4]]
      • 
    
    
  
    • 
  
  • Output: true
    • 
  
  • Explanation:
    
      
      
    • The vertices 0, 1, and 2 form a cycle (0-1-2-0).
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    •
Constraints
    
  
  • 1 ≤ number of vertices ≤ 1000
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  • 0 ≤ number of edges ≤ 3000
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  • All vertices are numbered from 0 to n-1
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  • No self-loops or multiple edges between the same pair of vertices
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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)
    •
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Hint
Solution

Solution Hints

    
  
  • You can use either Depth-First Search (DFS) or Breadth-First Search (BFS)
    • 
  
  • Track visited vertices to avoid processing the same vertex multiple times
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  • For undirected graphs, you need to keep track of the parent vertex to avoid false cycle detection
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  • If a vertex is already visited and not the parent of the current vertex, a cycle exists
    • 
  
  • Implement the graph using an adjacency list for efficient traversal
    •

Steps to solve by this approach:

 Step 1: Create an adjacency list representation of the graph.

 Step 2: Initialize a boolean array to keep track of visited vertices.
 Step 3: For each unvisited vertex, perform a DFS traversal.

 Step 4: During DFS, mark the current vertex as visited.

 Step 5: For each adjacent vertex, if it's not visited, recursively call DFS.

 Step 6: If an adjacent vertex is already visited and not the parent of the current vertex, a cycle exists.

 Step 7: If no cycle is found after checking all vertices, return false.

Submitted Code :