Note that a graph is represented as an adjacency list.
I've heard of 2 approaches to find a cycle in a graph:
Keep an array of boolean values to keep track of whether you visited a node before. If you run out of new nodes to go to (without hitting a node you have already been), then just backtrack and try a different branch.
The one from Cormen's CLRS or Skiena: For depth-first search in undirected graphs, there are two types of edges, tree and back. The graph has a cycle if and only if there exists a back edge.
Can somebody explain what are the back edges of a graph and what's the diffirence between the above 2 methods.
Thanks.
Update: Here's the code to detect cycles in both cases. Graph is a simple class that represents all graph-nodes as unique numbers for simplicity, each node has its adjacent neighboring nodes (g.getAdjacentNodes(int)):
public class Graph {
private int[][] nodes; // all nodes; e.g. int[][] nodes = {{1,2,3}, {3,2,1,5,6}...};
public int[] getAdjacentNodes(int v) {
return nodes[v];
}
// number of vertices in a graph
public int vSize() {
return nodes.length;
}
}
Java code to detect cycles in an undirected graph:
public class DFSCycle {
private boolean marked[];
private int s;
private Graph g;
private boolean hasCycle;
// s - starting node
public DFSCycle(Graph g, int s) {
this.g = g;
this.s = s;
marked = new boolean[g.vSize()];
findCycle(g,s,s);
}
public boolean hasCycle() {
return hasCycle;
}
public void findCycle(Graph g, int v, int u) {
marked[v] = true;
for (int w : g.getAdjacentNodes(v)) {
if(!marked[w]) {
marked[w] = true;
findCycle(g,w,v);
} else if (v != u) {
hasCycle = true;
return;
}
}
}
}
Java code to detect cycles in a directed graph:
public class DFSDirectedCycle {
private boolean marked[];
private boolean onStack[];
private int s;
private Graph g;
private boolean hasCycle;
public DFSDirectedCycle(Graph g, int s) {
this.s = s
this.g = g;
marked = new boolean[g.vSize()];
onStack = new boolean[g.vSize()];
findCycle(g,s);
}
public boolean hasCycle() {
return hasCycle;
}
public void findCycle(Graph g, int v) {
marked[v] = true;
onStack[v] = true;
for (int w : g.adjacentNodes(v)) {
if(!marked[w]) {
findCycle(g,w);
} else if (onStack[w]) {
hasCycle = true;
return;
}
}
onStack[v] = false;
}
}
