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,visited):
if (visited[node]):
if (node == start):
"found a path"
return;
visited[node]=YES;
for child in adj[node]:
dfs(adj,child,visited)
visited[node]=NO;
Call the above function with the start node:
visited = {}
dfs(adj,start,visited)
While this is not the most efficient algorithm when compared to Tarjans algorithm
, this is simple enough me for me to understand. Currently, this code does not have a count of number cycles detected.
I implemented this in Java:
//this is the main method that calls the helper DFS which runs on each node
public int allCyclesDirectedmain(){
//this initializes all vertices
clearAll();
int[] count = new int[1];
for (Vertex v: vertexMap.values()){
//System.out.println(v.name);
//clearAll();
dfs(v,v,count);
}
return count[0];
}
//start and v are same when the method first fires.
public void dfs(Vertex start, Vertex v,int[] count){
if (v.isVisited){
if (start==v){
//found a path
count[0]++;
}
return ;
}
v.setVisited(true);
for (Edge e : v.adj){
Vertex next = e.target;
dfs(start,next,count);
}
v.setVisited(false);
}
For the graph with following edges:
(1 2),(2 3),(3 1),(2 5),(5 6),(6 2)
-- I get 6 cycles as output.
(1 2),(2 3),(3 4),(4,1),(2 5),(5 6),(6 2)
-- I get 7 cycles as output.
I can see that my current code does cycle detection for each vertex that are already part of a previously detected cycle (e.g.: a cycle with three nodes gives me three cycles for each individual nodes while this must be one). I need some tips here as to what is going wrong and some fix.
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];
}