Finding all cycles in a directed graph using recursive backtracking

Question

I am working on finding cycles in directed graph using recursive backtracking. There is a suggested pseudocode for this here, which is here:

dfs(adj,node,vis         


        

Answer 1

For (1 2),(2 3),(3 1), you're calling:

• dfs(vertex1, vertex1, count), which gives you the cycle 1 -> 2 -> 3 -> 1.
• dfs(vertex2, vertex2, count), which gives you the cycle 2 -> 3 -> 1 -> 2.
• dfs(vertex3, vertex3, count), which gives you the cycle 3 -> 1 -> 2 -> 3.

So you're counting the same cycle multiple times.

The simplest fix I can think of is simply setting the visited flag after the dfs call.

public int allCyclesDirectedmain(){
    clearAll();
    int[] count = new int[1];
    for (Vertex v: vertexMap.values()){
        dfs(v,v,count);
        v.setVisited(true); // <---
    }
    return count[0];
}