This code implements a cycle detection algorithm in a directed...

April 3, 2025 at 09:49 PM

public HashMap<Vertex,Edge> CycleDetectionWrapper(Vertex v){
        HashMap<Vertex,Edge> record = new HashMap<>();
        HashMap<Vertex,Edge> ancestors = new HashMap<>();
        record.put(v,null);
        ancestors.put(v,null);
        CycleDetection(record,v,ancestors);
        return record;
    }
    
    public boolean CycleDetection(HashMap<Vertex,Edge> record, Vertex u, HashMap<Vertex,Edge> ancestors){
        for (Edge e: u.outgoing){
            Vertex v = opposite(u, e);
            if(ancestors.containsKey(v)) return true;
            if(record.containsKey(v)==false){
                record.put(v,e);
                ancestors.put(v,null);
                if (CycleDetection(record,v,ancestors)==true) return true;
                ancestors.remove(v);
            }
        }
        return false;
    }

This code implements a cycle detection algorithm in a directed graph using Depth-First Search (DFS) traversal to check for cycles. Here's what each part of the code does:

CycleDetectionWrapper Method:
- Acts as a wrapper method to initialize structures and start the cycle detection process.
- Takes a starting vertex v as input.
- Creates two HashMap objects:
  - record: Tracks visited vertices and their associated edges. It stores the vertices that have already been visited during the DFS traversal and the edges used to reach them.
  - ancestors: Tracks the current path of traversal (the chain of recursive calls), helping determine if a back-edge exists (indicating a cycle).
- Adds the starting vertex v to both record and ancestors, with the associated edge set to null for the starting vertex since it does not have an incoming edge.
- Calls the recursive helper method CycleDetection to perform the cycle detection.
- Returns the record HashMap, which now contains all vertices visited during the DFS process.
CycleDetection Method:
- A recursive method to perform DFS traversal and detect cycles.
- Takes three inputs:
  - record: Keeps track of visited vertices and edges.
  - u: The current vertex being explored.
  - ancestors: Tracks vertices in the current DFS call stack (used to detect cycles).
- For each outgoing edge e of the current vertex u:
  - Identifies the opposite vertex v connected by the edge e using the method opposite(u, e).
  - Checks if v is already present in the ancestors map:
    - If yes, this indicates a cycle (a back-edge), so the method returns true.
  - If v is not present in the record map (meaning it hasn't been visited yet):
    - Adds v to both record and ancestors, marking it as visited and part of the current DFS path.
    - Recursively calls CycleDetection with v.
    - If the recursive call returns true (indicating a cycle was detected), this method immediately returns true as well.
    - If no cycle is detected in further recursion, removes v from the ancestors map as the current DFS call for v is complete.
- If all edges are explored without finding a cycle, the method returns false, indicating no cycle exists from the current vertex.

Key Points:

Cycle Detection: The cycle is detected when a vertex in the current DFS path (ancestors) is revisited (back-edge).
DFS Traversal Tracking: The record tracks visited vertices and edges, while ancestors tracks only the vertices in the current DFS path.
Directed Graph: This code is designed for directed graphs, where each edge has a specified direction.
Result: The result of calling CycleDetectionWrapper is a HashMap of visited vertices and the edges used to visit them, but the key functionality of the code lies in detecting cycles.

In summary, this code detects cycles in a directed graph starting from a given vertex v using DFS traversal and a combination of visited and ancestor tracking.

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