[英]Finding all cycles in a directed graph using recursive backtracking
I am working on finding cycles in directed graph using recursive backtracking.我正在使用递归回溯在有向图中寻找循环。 There is a suggested pseudocode for this here , which is here:
有此建议的伪代码在这里,这是在这里:
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:使用起始节点调用上述函数:
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.虽然与
Tarjans algorithm
相比,这不是最有效的算法,但这对我来说已经足够简单了。 Currently, this code does not have a count of number cycles detected.目前,此代码没有检测到循环次数。
I implemented this in Java:我在 Java 中实现了这个:
//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:对于具有以下边的图:
(1 2),(2 3),(3 1),(2 5),(5 6),(6 2)
-- I get 6 cycles as output. (1 2),(2 3),(3 1),(2 5),(5 6),(6 2)
- 我得到 6 个周期作为输出。
(1 2),(2 3),(3 4),(4,1),(2 5),(5 6),(6 2)
-- I get 7 cycles as output. (1 2),(2 3),(3 4),(4,1),(2 5),(5 6),(6 2)
- 我得到 7 个周期作为输出。
I can see that my current code does cycle detection for each vertex that are already part of a previously detected cycle (eg: a cycle with three nodes gives me three cycles for each individual nodes while this must be one).我可以看到我当前的代码对每个顶点进行了循环检测,这些顶点已经是先前检测到的循环的一部分(例如:具有三个节点的循环为每个单独的节点提供了三个循环,而这必须是一个)。 I need some tips here as to what is going wrong and some fix.
我需要一些关于出现问题和修复的提示。
For (1 2),(2 3),(3 1)
, you're calling:对于
(1 2),(2 3),(3 1)
,您正在调用:
dfs(vertex1, vertex1, count)
, which gives you the cycle 1 -> 2 -> 3 -> 1
. dfs(vertex1, vertex1, count)
,它为您提供循环1 -> 2 -> 3 -> 1
。dfs(vertex2, vertex2, count)
, which gives you the cycle 2 -> 3 -> 1 -> 2
. dfs(vertex2, vertex2, count)
,它为您提供循环2 -> 3 -> 1 -> 2
。dfs(vertex3, vertex3, count)
, which gives you the cycle 3 -> 1 -> 2 -> 3
. dfs(vertex3, vertex3, count)
,它为您提供循环3 -> 1 -> 2 -> 3
。 So you're counting the same cycle multiple times.所以你多次计算同一个周期。
The simplest fix I can think of is simply setting the visited flag after the dfs
call.我能想到的最简单的解决方法是在
dfs
调用后简单地设置访问标志。
public int allCyclesDirectedmain(){
clearAll();
int[] count = new int[1];
for (Vertex v: vertexMap.values()){
dfs(v,v,count);
v.setVisited(true); // <---
}
return count[0];
}
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