I'm back with another similar question. I am currently working on a Java program that will check if a graph is 2-colorable, i.e. if it contains no odd cycles (cycles of odd number length). The entire algorithm is supposed to run in O(V+E) time (V being all vertices and E being all edges in the graph). My current algorithm does a Depth First Search, recording all vertices in the path it takes, then looks for a back edge, and then records between which vertices the edge is between. Next it traces a path from one end of the back edge until it hits the other vertex on the other end of the edge, thus retracing the cycle that the back edge completes.
I was under the impression that this kind of traversing could be done in O(V+E) time for all cycles that exist in my graph, but I must be missing something, because my algorithm is running for a ridiculously long time for very large graphs (10k nodes, no idea how many edges).
Is my algorithm completely wrong? And if so, can anyone point me in the right direction for a better way to record these cycles or possibly tell if they have odd numbers of vertices? Thanks for any and all help you guys can give. Code is below if you need it.
Addition: Sorry I forgot, if the graph is not 2-colorable, I need to provide an odd cycle that proves that it is not.
package algorithms311;
import java.util.*;
import java.io.*;
public class CS311 {
public static LinkedList[] DFSIter(Vertex[] v) {
LinkedList[] VOandBE = new LinkedList[2];
VOandBE[0] = new LinkedList();
VOandBE[1] = new LinkedList();
Stack stack = new Stack();
stack.push(v[0]);
v[0].setColor("gray");
while(!stack.empty()) {
Vertex u = (Vertex) stack.peek();
LinkedList adjList = u.getAdjList();
VOandBE[0].add(u.getId());
boolean allVisited = true;
for(int i = 0; i < adjList.size(); i++) {
if(v[(Integer)adjList.get(i)].getColor().equals("white")) {
allVisited = false;
break;
}
else if(v[(Integer)adjList.get(i)].getColor().equals("gray") && u.getPrev() != (Integer)adjList.get(i)) {
int[] edge = new int[2]; //pair of vertices
edge[0] = u.getId(); //from u
edge[1] = (Integer)adjList.get(i); //to v
VOandBE[1].add(edge);
}
}
if(allVisited) {
u.setColor("black");
stack.pop();
}
else {
for(int i = 0; i < adjList.size(); i++) {
if(v[(Integer)adjList.get(i)].getColor().equals("white")) {
stack.push(v[(Integer)adjList.get(i)]);
v[(Integer)adjList.get(i)].setColor("gray");
v[(Integer)adjList.get(i)].setPrev(u.getId());
break;
}
}
}
}
return VOandBE;
}
public static void checkForTwoColor(String g) { //input is a graph formatted as assigned
String graph = g;
try {
// --Read First Line of Input File
// --Find Number of Vertices
FileReader file1 = new FileReader("W:\\Documents\\NetBeansProjects\\algorithms311\\src\\algorithms311\\" + graph);
BufferedReader bReaderNumEdges = new BufferedReader(file1);
String numVertS = bReaderNumEdges.readLine();
int numVert = Integer.parseInt(numVertS);
System.out.println(numVert + " vertices");
// --Make Vertices
Vertex vertex[] = new Vertex[numVert];
for(int k = 0; k <= numVert - 1; k++) {
vertex[k] = new Vertex(k);
}
// --Adj Lists
FileReader file2 = new FileReader("W:\\Documents\\NetBeansProjects\\algorithms311\\src\\algorithms311\\" + graph);
BufferedReader bReaderEdges = new BufferedReader(file2);
bReaderEdges.readLine(); //skip first line, that's how many vertices there are
String edge;
while((edge = bReaderEdges.readLine()) != null) {
StringTokenizer ST = new StringTokenizer(edge);
int vArr[] = new int[2];
for(int j = 0; ST.hasMoreTokens(); j++) {
vArr[j] = Integer.parseInt(ST.nextToken());
}
vertex[vArr[0]-1].addAdj(vArr[1]-1);
vertex[vArr[1]-1].addAdj(vArr[0]-1);
}
LinkedList[] l = new LinkedList[2];
l = DFSIter(vertex);//DFS(vertex);
System.out.println(l[0]);
for(int i = 0; i < l[1].size(); i++) {
int[] j = (int[])l[1].get(i);
System.out.print(" [" + j[0] + ", " + j[1] + "] ");
}
LinkedList oddCycle = new LinkedList();
boolean is2Colorable = true;
//System.out.println("iterate through list of back edges");
for(int i = 0; i < l[1].size(); i++) { //iterate through the list of back edges
//System.out.println(i);
int[] q = (int[])(l[1].get(i)); // q = pair of vertices that make up a back edge
int u = q[0]; // edge (u,v)
int v = q[1];
LinkedList cycle = new LinkedList();
if(l[0].indexOf(u) < l[0].indexOf(v)) { //check if u is before v
for(int z = l[0].indexOf(u); z <= l[0].indexOf(v); z++) { //if it is, look for u first; from u to v
cycle.add(l[0].get(z));
}
}
else if(l[0].indexOf(v) < l[0].indexOf(u)) {
for(int z = l[0].indexOf(v); z <= l[0].indexOf(u); z++) { //if it is, look for u first; from u to v
cycle.add(l[0].get(z));
}
}
if((cycle.size() & 1) != 0) { //if it has an odd cycle, print out the cyclic nodes or write them to a file
is2Colorable = false;
oddCycle = cycle;
break;
}
}
if(!is2Colorable) {
System.out.println("Graph is not 2-colorable, odd cycle exists");
if(oddCycle.size() <= 50) {
System.out.println(oddCycle);
}
else {
try {
BufferedWriter outFile = new BufferedWriter(new FileWriter("W:\\Documents\\NetBeansProjects\\algorithms311\\src\\algorithms311\\" + graph + "OddCycle.txt"));
String cyc = oddCycle.toString();
outFile.write(cyc);
outFile.close();
}
catch (IOException e) {
System.out.println("Could not write file");
}
}
}
}
catch (IOException e) {
System.out.println("Could not open file");
}
System.out.println("Done!");
}
public static void main(String[] args) {
//checkForTwoColor("smallgraph1");
//checkForTwoColor("smallgraph2");
//checkForTwoColor("smallgraph3");
//checkForTwoColor("smallgraph4");
checkForTwoColor("smallgraph5");
//checkForTwoColor("largegraph1");
}
}
Vertex class
package algorithms311;
import java.util.*;
public class Vertex implements Comparable {
public int id;
public LinkedList adjVert = new LinkedList();
public String color = "white";
public int dTime;
public int fTime;
public int prev;
public boolean visited = false;
public Vertex(int idnum) {
id = idnum;
}
public int getId() {
return id;
}
public int compareTo(Object obj) {
Vertex vert = (Vertex) obj;
return id-vert.getId();
}
#Override public String toString(){
return "Vertex # " + id;
}
public void setColor(String newColor) {
color = newColor;
}
public String getColor() {
return color;
}
public void setDTime(int d) {
dTime = d;
}
public void setFTime(int f) {
fTime = f;
}
public int getDTime() {
return dTime;
}
public int getFTime() {
return fTime;
}
public void setPrev(int v) {
prev = v;
}
public int getPrev() {
return prev;
}
public LinkedList getAdjList() {
return adjVert;
}
public void addAdj(int a) { //adds a vertex id to this vertex's adj list
adjVert.add(a);
}
public void visited() {
visited = true;
}
public boolean wasVisited() {
return visited;
}
}
I was under the impression that this kind of traversing could be done in O(V+E) time for all cycles that exist in my graph
There may be much more cycles than O(V+E) in a graph. If you iterate all of them, you will run long.
Back to your original idea, you could just try to implement a straightforward algorithm to color graph in two colors (mark an arbitrary node as black, all neighbors in white, all their neighbors in black, etc; that would be a breadth-first search). That is indeed done in O(V+E) time. If you succeed, then graph is 2-colorable. If you fail, it's not.
Edit: If you need a cycle that proves graph is not 2-colorable, just record for each node the vertex you traversed into it from. When you happen to traverse from black vertex A to black vertex B (thus needing to color black B into white and proving your graph is not 2-colorable), you get the cycle by looking back to parents:
X -> Y -> Z -> U -> V -> P -> Q -> A
\-> D -> E -> B
Then, A-B-E-D-V-P-Q (the paths up to their common ancestor) is the cycle you needed.
Note that in this version you don't have to check all cycles, you just output a first cycle, where back-edge in the tree has both vertexes colored in the same color.
you are describing a bipartite graph. a bipartite graph is 2 colorable and it contains no odd length cycles. You can use BFS to prove that a graph is bipartite or not. Hope this helps.
Related
Can you please help me to put an error tarpping in my code. I have been doing it since yesterday but I think my braincell is already exhausted. Please send help po. And also can we print a graph in blueJ? how to print the graph? kinds of error trapping (i, i) = (0,0) same source destination, not allowed (i, j) = (i, j) existing edge, not allowed (i, j) = (j, i) existing edge, not allowed n (level of vertex) > n = not allowed
*
import java.util.Scanner;
import java.util.ArrayList;
import java.util.List;
import java.util.Stack;
public class AdjMatrixGraph{
List<List<Integer>> graph;
Scanner input = new Scanner(System.in);
ArrayList<Connection> Links = new ArrayList<Connection>();
boolean visited[];
int nodes;
int vertices;
int matrix[][];
class Node {//stores node information
String name;
boolean visited;
ArrayList<Node> neighbors = new ArrayList<Node>();
Node(String name) {
this.name = name;
visited = false;
}
}
class Connection {//stores edges information
double fare;
Node source, destination;
Connection(Node source, Node destination) {
this.source = source;
this.destination = destination;
}
}
public static void main(String[] args){
Scanner s = new Scanner(System.in);
System.out.println("Enter the number of vertices");
int V = s.nextInt();
AdjMatrixGraph amg = new AdjMatrixGraph(V);
System.out.println("Enter the number of edges");
int E = s.nextInt();
System.out.print("\n");
for(int i=0;i<E;i++){
System.out.println("Enter the endpoints");
int mark = s.nextInt();
int mac = s.nextInt();
if (mark == mac) { //checks if newly input edge is a loop
System.out.println("\nERROR TRAPPED!!\nNo Loops Allowed Here!\nAdd New Edge!");
i--;
continue;
}
amg.addEdge(mark,mac);
amg.addEdge1(mark,mac);
}
amg.printGraph();
System.out.print("\nSize of the graph: " + E);
System.out.print("\nOrder of the graph: " + V);
System.out.println(amg.ifGraphConnected());
}
AdjMatrixGraph(int vertices){
graph = new ArrayList<>();
visited = new boolean[vertices];
this.vertices=vertices;
matrix=new int[vertices][vertices];
for (int i = 0; i < vertices; i++){
graph.add(i, new ArrayList<>());
}
}
public void addEdge(int source,int destination){
matrix[source][destination]= 1;
matrix[destination][source]= 1;
}
public void addEdge1(int a, int b) {
graph.get(a).add(b);
graph.get(b).add(a);
}
public boolean ifGraphConnected() {
int startIndex = 0;
dfs(startIndex);
for(int i = 0; i < visited.length; i++) {
if(!visited[i]) {
System.out.println("\n");
System.out.println("The Graph is not connected!: ");
System.out.print("\nCreate another graph? \n1=Yes or 2=No\n");
String menu = input.nextLine();
if(menu.equals("1")){//goes back to the first menu and resets the list
input.close();
main(null);
}else if(menu.equals("2")){//terminates the program
System.exit(0);
}else{
System.out.println("\nERROR!");
}
return false;
}
}
System.out.println("\n");
System.out.println("The Graph is connected!");
System.out.print("\nCreate another graph? \n1=Yes or 2=No\n");
String menu = input.nextLine();
if(menu.equals("1")){//goes back to the first menu and resets the list
input.close();
main(null);
}else if(menu.equals("2")){//terminates the program
System.exit(0);
}else{
System.out.println("\nERROR!");
}
return true;
}//print true if it's connected
public void dfs(int start){ //the DFS traversal method for determining whether it is connected or not.
Stack<Integer> stack = new Stack<>(); //implement a stack that stores integers and traverse the graph
stack.push(start);
visited[start] = true; //places the vertex's start or address and sets it to true
while(!stack.isEmpty()) { //While the stack is not empty, the arguments in this block will be executed.
Integer vertices = stack.pop(); //the element is inserted into the stack
List<Integer> neighboursList = graph.get(vertices); //This will create a linked list of the graph's vertices
for(Integer neighbour: neighboursList) { //This will scan over all of the vertices that are related to the initial index.
if(!visited[neighbour]) {
stack.push(neighbour); //All the vertices that is related to vertex will be pushed.
visited[neighbour] = true; //Makes the vertex that is related to it true. It will then check to see if the stack is still full. If the loop is not empty, it will pop the visited vertex and proceed.
}
}
}
}
void printGraph(){ //printing Graph
System.out.print("\n");
System.out.println("The Adjacency Matrix is:");
for(int i=0;i<vertices;i++){ //using for loop method
for(int j = 0;j<vertices;j++){
System.out.print(matrix[i][j]+" ");
}
System.out.println();
}
}
}```
I using this exact code for this. I modified it a little. So far I added a start and end node index to the calculateShortestDistances() method. Also the path ArrayList for collecting the path node indexes. Also: new to Java...
How do I collect the indexes of nodes in the path ArrayList?
I just can't come up with the solution on a level that I am not even positive this code could do what I want. I only have intuition on my side and little time.
What I tried:
Adding the nextNode value to the list then removing it if it was not
a shorter distance.
Adding the neighbourIndex to the list then removing it if it was not a shorter distance.
I made a Path.java with ArrayList but that was went nowhere (it was a class with a public variable named path) but it went nowhere.
Main.java:
public class Main {
public static void main(String[] args) {
Edge[] edges = {
new Edge(0, 2, 1), new Edge(0, 3, 4), new Edge(0, 4, 2),
new Edge(0, 1, 3), new Edge(1, 3, 2), new Edge(1, 4, 3),
new Edge(1, 5, 1), new Edge(2, 4, 1), new Edge(3, 5, 4),
new Edge(4, 5, 2), new Edge(4, 6, 7), new Edge(4, 7, 2),
new Edge(5, 6, 4), new Edge(6, 7, 5)
};
Graph g = new Graph(edges);
g.calculateShortestDistances(4,6);
g.printResult(); // let's try it !
System.out.println(g.path);
}
}
Graph.java:
This is the Graph.java file. Here I added a sAt and eAt variable, so I can tell it what path I am after. Also I created a public path ArrayList, where I intend to collect the path.
import java.util.ArrayList;
// now we must create graph object and implement dijkstra algorithm
public class Graph {
private Node[] nodes;
private int noOfNodes;
private Edge[] edges;
private int noOfEdges;
private int sAt;
private int eAt;
public ArrayList<Integer> path = new ArrayList<>();
public Graph(Edge[] edges) {
this.edges = edges;
// create all nodes ready to be updated with the edges
this.noOfNodes = calculateNoOfNodes(edges);
this.nodes = new Node[this.noOfNodes];
for (int n = 0; n < this.noOfNodes; n++) {
this.nodes[n] = new Node();
}
// add all the edges to the nodes, each edge added to two nodes (to and from)
this.noOfEdges = edges.length;
for (int edgeToAdd = 0; edgeToAdd < this.noOfEdges; edgeToAdd++) {
this.nodes[edges[edgeToAdd].getFromNodeIndex()].getEdges().add(edges[edgeToAdd]);
this.nodes[edges[edgeToAdd].getToNodeIndex()].getEdges().add(edges[edgeToAdd]);
}
}
private int calculateNoOfNodes(Edge[] edges) {
int noOfNodes = 0;
for (Edge e : edges) {
if (e.getToNodeIndex() > noOfNodes)
noOfNodes = e.getToNodeIndex();
if (e.getFromNodeIndex() > noOfNodes)
noOfNodes = e.getFromNodeIndex();
}
noOfNodes++;
return noOfNodes;
}
public void calculateShortestDistances(int startAt, int endAt) {
// node 0 as source
this.sAt = startAt;
this.eAt = endAt;
this.nodes[startAt].setDistanceFromSource(0);
int nextNode = startAt;
// visit every node
for (int i = 0; i < this.nodes.length; i++) {
// loop around the edges of current node
ArrayList<Edge> currentNodeEdges = this.nodes[nextNode].getEdges();
for (int joinedEdge = 0; joinedEdge < currentNodeEdges.size(); joinedEdge++) {
int neighbourIndex = currentNodeEdges.get(joinedEdge).getNeighbourIndex(nextNode);
// only if not visited
if (!this.nodes[neighbourIndex].isVisited()) {
int tentative = this.nodes[nextNode].getDistanceFromSource() + currentNodeEdges.get(joinedEdge).getLength();
if (tentative < nodes[neighbourIndex].getDistanceFromSource()) {
nodes[neighbourIndex].setDistanceFromSource(tentative);
}
}
}
// all neighbours checked so node visited
nodes[nextNode].setVisited(true);
// next node must be with shortest distance
nextNode = getNodeShortestDistanced();
}
}
// now we're going to implement this method in next part !
private int getNodeShortestDistanced() {
int storedNodeIndex = 0;
int storedDist = Integer.MAX_VALUE;
for (int i = 0; i < this.nodes.length; i++) {
int currentDist = this.nodes[i].getDistanceFromSource();
if (!this.nodes[i].isVisited() && currentDist < storedDist) {
storedDist = currentDist;
storedNodeIndex = i;
}
}
return storedNodeIndex;
}
// display result
public void printResult() {
String output = "Number of nodes = " + this.noOfNodes;
output += "\nNumber of edges = " + this.noOfEdges;
output += "\nDistance from "+sAt+" to "+eAt+":" + nodes[eAt].getDistanceFromSource();
System.out.println(output);
}
public Node[] getNodes() {
return nodes;
}
public int getNoOfNodes() {
return noOfNodes;
}
public Edge[] getEdges() {
return edges;
}
public int getNoOfEdges() {
return noOfEdges;
}
}
Addittionally here are the Edge.java and the Node.java classes.
Node.java:
import java.util.ArrayList;
public class Node {
private int distanceFromSource = Integer.MAX_VALUE;
private boolean visited;
private ArrayList<Edge> edges = new ArrayList<Edge>(); // now we must create edges
public int getDistanceFromSource() {
return distanceFromSource;
}
public void setDistanceFromSource(int distanceFromSource) {
this.distanceFromSource = distanceFromSource;
}
public boolean isVisited() {
return visited;
}
public void setVisited(boolean visited) {
this.visited = visited;
}
public ArrayList<Edge> getEdges() {
return edges;
}
public void setEdges(ArrayList<Edge> edges) {
this.edges = edges;
}
}
Edge.java
public class Edge {
private int fromNodeIndex;
private int toNodeIndex;
private int length;
public Edge(int fromNodeIndex, int toNodeIndex, int length) {
this.fromNodeIndex = fromNodeIndex;
this.toNodeIndex = toNodeIndex;
this.length = length;
}
public int getFromNodeIndex() {
return fromNodeIndex;
}
public int getToNodeIndex() {
return toNodeIndex;
}
public int getLength() {
return length;
}
// determines the neighbouring node of a supplied node, based on the two nodes connected by this edge
public int getNeighbourIndex(int nodeIndex) {
if (this.fromNodeIndex == nodeIndex) {
return this.toNodeIndex;
} else {
return this.fromNodeIndex;
}
}
}
I know it looks like a homework. Trust me it isn't. On the other hand I have not much time to finish it, that is why I do it at Sunday. Also I am aware how Dijkstra algorithm works, I understand the concept, I can do it on paper. But collecting the path is beyond me.
Thanks for Christian H. Kuhn's and second's comments I managed to come up with the code.
I modified it as follows (I only put in the relevant parts)
Node.java
Here I added a setPredecessor(Integer predecessor) and a getPredecessor() methods to set and get the value of the private variable predecessor (so I follow the original code's style too).
[...]
private int predecessor;
[...]
public int getPredecessor(){
return predecessor;
}
public void setPredecessor(int predecessor){
this.predecessor = predecessor;
}
[...]
Graph.java
Here I created the calculatePath() and getPath() methods. calculatePath() does what the commenters told me to do. The getPath() returns the ArrayLists for others to use.
[...]
private int sAt;
private int eAt;
private ArrayList<Integer> path = new ArrayList<Integer>();
[...]
public void calculateShortestDistances(int startAt, int endAt) {
[...]
if (tentative < nodes[neighbourIndex].getDistanceFromSource()) {
nodes[neighbourIndex].setDistanceFromSource(tentative);
nodes[neighbourIndex].setPredecessor(nextNode);
}
[...]
public void calculatePath(){
int nodeNow = eAt;
while(nodeNow != sAt){
path.add(nodes[nodeNow].getPredecessor());
nodeNow = nodes[nodeNow].getPredecessor();
}
}
public ArrayList<Integer> getPath(){
return path;
}
[...]
Main.java so here I can do this now:
[...]
Graph g = new Graph(edges);
g.calculateShortestDistances(5,8);
g.calculatePath();
String results = "";
ArrayList<Integer> path = g.getPath();
System.out.println(path);
[...]
I know it shows the path backwards, but that is not a problem, as I can always reverse it. The point is: I not only have the the distance from node to node, but the path through nodes too. Thank you for the help.
My implementation for directed graph works fine. It's a "lazy" version because it uses simple priority queues instead of indexed ones. I changed the code to get a solution for undirected graphs but it doesn't work. dijkstra(int s) is a method of a class Graph. The implementation of Graph is based on a list of adjacencies. The entire code is based on the explanations of Sedgewick's book.
public void dijkstra(int s) {
marked = new boolean[V];
distTo = new int[V];
edgeTo = new Edge[V];
Comparator<Edge> comparator = new Comparator<Edge>() {
public int compare(Edge e1, Edge e2) {
int dist1 = distTo[e1.either()] + e1.weight();
int dist2 = distTo[e2.either()] + e2.weight();
if (dist1 < dist2) {
return -1;
} else if (dist1 > dist2) {
return 1;
} else {
return 0;
}
}
};
pq = new PriorityQueue<Edge>(comparator);
for (int v = 0; v < V; ++v) {
distTo[v] = Integer.MAX_VALUE;
}
distTo[s] = 0;
relax(s);
while (!pq.isEmpty()) {
Edge e = pq.poll();
int v = e.either();
int w = e.other(v);
if (!marked[w]) {
relax(w);
}
}
}
private void relax(int v) {
marked[v] = true;
for (Edge e : adj[v]) {
int w = e.other(v);
if (distTo[w] > distTo[v] + e.weight()) {
distTo[w] = distTo[v] + e.weight();
edgeTo[w] = e;
pq.add(e);
}
}
}
I solved it. Stupid mistake. Instead of adding the edges
v->w and w->v
I added the edges
v->w and w->w
i.e. I added the same edge twice, without creating the reverse edge.
I have a DFS visit recursive method that sometimes throws a StackOverflowError. Since the size of the graph is large (around 20000 vertices), recursive calls are many, and so I tried to run with -Xss10M and everything works.
I'd just like to understand why adding at the beginning of the method a System.out.println, even without -Xss10M, the method doesn't throw any StackOverflowError. How is it possible?
This is the DFS visit method:
private int dfsVisit(Vertex<T> v, int time){
// System.out.println("Hello");
Vertex<T> n;
time++;
v.d = time;
v.color = Vertex.Color.GRAY;
for (Map.Entry<Vertex<T>, Float> a : v.neighbours.entrySet()){
n = a.getKey();
if(n.color == Vertex.Color.WHITE){
n.previous = v;
time = dfsVisit(n, time);
}
}
v.color = Vertex.Color.BLACK;
time++;
v.f = time;
return time;
}
This is the complete code
import java.io.*;
import java.util.*;
class Graph<T> {
private final Map<T, Vertex<T>> graph;
public static class Edge<T>{
public final T v1, v2;
public final float dist;
public Edge(T v1, T v2, float dist) {
this.v1 = v1;
this.v2 = v2;
this.dist = dist;
}
}
public static class Vertex<T> implements Comparable<Vertex>{ // SPOSTARE VAR IST NEL COSTRUTTORE
public enum Color {WHITE, GRAY, BLACK, UNKNOWN};
public final T name;
public float dist;
public Vertex<T> previous;
public final Map<Vertex<T>, Float> neighbours;
public Color color;
public int d, f;
public Vertex(T name) {
this.name = name;
dist = Float.MAX_VALUE;
previous = null;
neighbours = new HashMap<Vertex<T>, Float>(); // adjacency list
color = Color.UNKNOWN;
d = 0;
f = 0;
}
private void printPath() {
if (this == this.previous) {
System.out.print(this.name);
} else if (this.previous == null) {
System.out.print(this.name + " unreached");
} else {
this.previous.printPath();
System.out.print(" -> " + this.name + "(" + this.dist + ")");
}
}
public int compareTo(Vertex other){
if(this.dist == other.dist)
return 0;
else if(this.dist > other.dist)
return 1;
else
return -1;
}
}
// Builds a graph from an array of edges
public Graph(ArrayList<Graph.Edge> edges) {
graph = new HashMap<>(edges.size());
// add vertices
for (Edge<T> e : edges) {
if (!graph.containsKey(e.v1)) graph.put(e.v1, new Vertex<>(e.v1));
if (!graph.containsKey(e.v2)) graph.put(e.v2, new Vertex<>(e.v2));
}
// create adjacency list
for (Edge<T> e : edges) {
graph.get(e.v1).neighbours.put(graph.get(e.v2), e.dist);
graph.get(e.v2).neighbours.put(graph.get(e.v1), e.dist);
}
}
public void dijkstra(T startName) {
if (!graph.containsKey(startName)) {
System.err.println("Graph doesn't contain start vertex " + startName);
return;
}
final Vertex<T> source = graph.get(startName);
NavigableSet<Vertex<T>> q = new TreeSet<>(); // priority queue
// set-up vertices
for (Vertex<T> v : graph.values()) {
v.previous = v == source ? source : null;
v.dist = v == source ? 0 : Float.MAX_VALUE;
q.add(v);
}
dijkstra(q);
}
private void dijkstra(final NavigableSet<Vertex<T>> q) {
Vertex<T> u, v;
while (!q.isEmpty()) {
u = q.pollFirst();
if (u.dist == Float.MAX_VALUE) break; //???????????
for (Map.Entry<Vertex<T>, Float> a : u.neighbours.entrySet()) {
v = a.getKey();
final float alternateDist = u.dist + a.getValue();
if (alternateDist < v.dist) {
q.remove(v);
v.dist = alternateDist;
v.previous = u;
q.add(v);
}
}
}
}
public void printPath(T endName) {
if (!graph.containsKey(endName)) {
System.err.println("Graph doesn't contain end vertex " + "\"" + endName + "\"" );
return;
}
graph.get(endName).printPath();
System.out.println();
}
public void printAllPaths() {
for (Vertex<T> v : graph.values()) {
v.printPath();
System.out.println();
}
}
public Vertex<T> getVertex(T key){
if(graph.containsKey(key))
return graph.get(key);
return null;
}
public void printAdjacencyList(){
System.out.println("Adjacency list:");
for(Vertex<T> v : graph.values()){
System.out.print(v.name + ":\t");
for (Map.Entry<Vertex<T>, Float> a : v.neighbours.entrySet()){
System.out.print(a.getKey().name + "(" + a.getValue() + ") | ");
}
System.out.println();
}
}
/*
P.S. I know that if only used to calculate the connected components of the graph, dfs visit
could be written differently but I preferred to write it in a more general way, so that it
can be reused if necessary.
*/
private int dfsVisit(Vertex<T> v, int time){
// System.out.println("ciao");
Vertex<T> n;
time++;
v.d = time;
v.color = Vertex.Color.GRAY;
for (Map.Entry<Vertex<T>, Float> a : v.neighbours.entrySet()){
n = a.getKey();
if(n.color == Vertex.Color.WHITE){
n.previous = v;
time = dfsVisit(n, time);
}
}
v.color = Vertex.Color.BLACK;
time++;
v.f = time;
return time;
}
/*
Print the size of the connected components of the graph
*/
public void connectedComponents(){
for(Vertex<T> v : graph.values()){
v.color = Vertex.Color.WHITE;
v.previous = null;
}
for(Vertex<T> v : graph.values()){
if(v.color == Vertex.Color.WHITE)
System.out.println(dfsVisit(v, 0)/2);
}
}
}
here's the test class
import java.io.*;
import java.util.*;
public class Dijkstra {
private static ArrayList<Graph.Edge> a = new ArrayList<Graph.Edge>();
private static final String START = "torino";
private static final String END = "catania";
public static void main(String[] args) {
String fileName = "italian_dist_graph.txt";
try{
Scanner inputStream = new Scanner(new File(fileName));
String record;
while(inputStream.hasNextLine()){
record = inputStream.nextLine();
String[] array = record.split(",");
String from = array[0];
String to = array[1];
float dist = Float.parseFloat(array[2]);
a.add(new Graph.Edge(from, to, dist));
}
inputStream.close();
} catch(FileNotFoundException e){
System.out.println("Impossibile trovare il file "+fileName);
}
Graph<String> g = new Graph<String>(a);
g.dijkstra(START);
g.printPath(END);
//System.out.printf("%f\n", g.getVertex(END).dist/1000.0f);
g.connectedComponents();
}
}
N.B. try to comment g.dijkstra(START) and g.printPath(END); everything seems to work.
Here's the link to the data set
https://drive.google.com/open?id=0B7XZY8cd0L_fZVl1aERlRmhQN0k
Some general recommendations:
Your code mixes up attributes of vertices, that are related to a single run of dfs and such that are direct attributes of the vertices. Bad bad bad style. This is quite likely to break any more complex algorithm, can produce unexpected behavior and would require clearing the states after each run, to ensure stability of the code. Instead keep states that are related to a single run of a algorithm only visible to that function. E.g. store the states inside a Map, use the decorator-pattern to create a datastructure that provides additional attributes and that has method-local scope, etc.. As an example: running your code twice on the same graph (same Object) with the same input without clearing all states will lead to a wrong result (1).
In addition: creating an iterative version of DFS isn't exactly hard, so you should give it a try, especially since your graph appears to be pretty large.
As for why your code works (or doesn't) the way it does:
This is hard to tell, since it depends upon quite a lot of factors. You didn't provide full code, so I can't rerun any tests, or verify that everything behaves the way it should. The most likely answers:
Vertex uses the default hash-code provided by Object. This leads to random ordering of the entries in the map of neighbours, thus the order in which specific paths are traversed is random in each run and most likely different. Thus you're traversing the graph using random paths, that quite likely (especially due to the size of your graph) differ for each run. The reason isn't the System.out.println, but the mere fact, that your code generates a different structure (from a ordering-POV, not mathematical), each time it runs plus the coincident, that for some pretty weird reason each build of the graph, that doesn't reach the necessary recursion-depth for a StackOverflow, and the code compiled with System.out.println appeared together.
The Java compiler, or JIT modifies the behavior of the code in a weird way. Modern compilers have the tendency to produce quite weird code in their attempts to optimize everything they can get hold off.
I'm writing a Java program that searches for and outputs cycles in a graph. I am using an adjacency list for storing my graph, with the lists stored as LinkedLists. My program takes an input formatted with the first line as the number of nodes in the graph and each subsequent line 2 nodes that form an edge e.g.:
3
1 2
2 3
3 1
My problem is that when the inputs get very large (the large graph I am using has 10k nodes and I don't know how many edges, the file is 23mb of just edges) I am getting a java.lang.StackOverflowError, but I don't get any errors with small inputs. I'm wondering if it would be better to use another data structure to form my adjacency lists or if there is some method I could use to avoid this error, as I'd rather not just have to change a setting on my local installation of Java (because I have to be sure this will run on other computers that I can't control the settings on as much). Below is my code, the Vertex class and then my main class. Thanks for any help you can give!
Vertex.java:
package algorithms311;
import java.util.*;
public class Vertex implements Comparable {
public int id;
public LinkedList adjVert = new LinkedList();
public String color = "white";
public int dTime;
public int fTime;
public int prev;
public Vertex(int idnum) {
id = idnum;
}
public int getId() {
return id;
}
public int compareTo(Object obj) {
Vertex vert = (Vertex) obj;
return id-vert.getId();
}
#Override public String toString(){
return "Vertex # " + id;
}
public void setColor(String newColor) {
color = newColor;
}
public String getColor() {
return color;
}
public void setDTime(int d) {
dTime = d;
}
public void setFTime(int f) {
fTime = f;
}
public int getDTime() {
return dTime;
}
public int getFTime() {
return fTime;
}
public void setPrev(int v) {
prev = v;
}
public int getPrev() {
return prev;
}
public LinkedList getAdjList() {
return adjVert;
}
public void addAdj(int a) { //adds a vertex id to this vertex's adj list
adjVert.add(a);
}
}
CS311.java:
package algorithms311;
import java.util.*;
import java.io.*;
public class CS311 {
public static final String GRAPH= "largegraph1";
public static int time = 0;
public static LinkedList[] DFS(Vertex[] v) {
LinkedList[] l = new LinkedList[2];
l[0] = new LinkedList();
l[1] = new LinkedList(); //initialize the array with blank lists, otherwise we get a nullpointerexception
for(int i = 0; i < v.length; i++) {
v[i].setColor("white");
v[i].setPrev(-1);
}
time = 0;
for(int i = 0; i < v.length; i++) {
if(v[i].getColor().equals("white")) {
l = DFSVisit(v, i, l);
}
}
return l;
}
public static LinkedList[] DFSVisit(Vertex[] v, int i, LinkedList[] l) { //params are a vertex of nodes and the node id you want to DFS from
LinkedList[] VOandBE = new LinkedList[2]; //two lists: visit orders and back edges
VOandBE[0] = l[0]; // l[0] is visit Order, a linked list of ints
VOandBE[1] = l[1]; // l[1] is back Edges, a linked list of arrays[2] of ints
VOandBE[0].add(v[i].getId());
v[i].setColor("gray"); //color[vertex i] <- GRAY
time++; //time <- time+1
v[i].setDTime(time); //d[vertex i] <- time
LinkedList adjList = v[i].getAdjList(); // adjList for the current vertex
for(int j = 0; j < adjList.size(); j++) { //for each v in adj[vertex i]
if(v[(Integer)adjList.get(j)].getColor().equals("gray") && v[i].getPrev() != v[(Integer)adjList.get(j)].getId()) { // if color[v] = gray and Predecessor[u] != v do
int[] edge = new int[2]; //pair of vertices
edge[0] = i; //from u
edge[1] = (Integer)adjList.get(j); //to v
VOandBE[1].add(edge);
}
if(v[(Integer)adjList.get(j)].getColor().equals("white")) { //do if color[v] = WHITE
v[(Integer)adjList.get(j)].setPrev(i); //then "pi"[v] <- vertex i
DFSVisit(v, (Integer)adjList.get(j), VOandBE); //DFS-Visit(v)
}
}
VOandBE[0].add(v[i].getId());
v[i].setColor("black");
time++;
v[i].setFTime(time);
return VOandBE;
}
public static void main(String[] args) {
try {
// --Read First Line of Input File
// --Find Number of Vertices
FileReader file1 = new FileReader("W:\\Documents\\NetBeansProjects\\algorithms311\\src\\algorithms311\\" + GRAPH);
BufferedReader bReaderNumEdges = new BufferedReader(file1);
String numVertS = bReaderNumEdges.readLine();
int numVert = Integer.parseInt(numVertS);
System.out.println(numVert + " vertices");
// --Make Vertices
Vertex vertex[] = new Vertex[numVert];
for(int k = 0; k <= numVert - 1; k++) {
vertex[k] = new Vertex(k);
}
// --Adj Lists
FileReader file2 = new FileReader("W:\\Documents\\NetBeansProjects\\algorithms311\\src\\algorithms311\\" + GRAPH);
BufferedReader bReaderEdges = new BufferedReader(file2);
bReaderEdges.readLine(); //skip first line, that's how many vertices there are
String edge;
while((edge = bReaderEdges.readLine()) != null) {
StringTokenizer ST = new StringTokenizer(edge);
int vArr[] = new int[2];
for(int j = 0; ST.hasMoreTokens(); j++) {
vArr[j] = Integer.parseInt(ST.nextToken());
}
vertex[vArr[0]-1].addAdj(vArr[1]-1);
vertex[vArr[1]-1].addAdj(vArr[0]-1);
}
for(int i = 0; i < vertex.length; i++) {
System.out.println(vertex[i] + ", adj nodes: " + vertex[i].getAdjList());
}
LinkedList[] l = new LinkedList[2];
l = DFS(vertex);
System.out.println("");
System.out.println("Visited Nodes: " + l[0]);
System.out.println("");
System.out.print("Back Edges: ");
for(int i = 0; i < l[1].size(); i++) {
int[] q = (int[])(l[1].get(i));
System.out.println("[" + q[0] + "," + q[1] + "] ");
}
for(int i = 0; i < l[1].size(); i++) { //iterate through the list of back edges
int[] q = (int[])(l[1].get(i)); // q = pair of vertices that make up a back edge
int u = q[0]; // edge (u,v)
int v = q[1];
LinkedList cycle = new LinkedList();
if(l[0].indexOf(u) < l[0].indexOf(v)) { //check if u is before v
for(int z = l[0].indexOf(u); z <= l[0].indexOf(v); z++) { //if it is, look for u first; from u to v
cycle.add(l[0].get(z));
}
}
else if(l[0].indexOf(v) < l[0].indexOf(u)) {
for(int z = l[0].indexOf(v); z <= l[0].indexOf(u); z++) { //if it is, look for u first; from u to v
cycle.add(l[0].get(z));
}
}
System.out.println("");
System.out.println("Cycle detected! : " + cycle);
if((cycle.size() & 1) != 0) {
System.out.println("Cycle is odd, graph is not 2-colorable!");
}
else {
System.out.println("Cycle is even, we're okay!");
}
}
}
catch (IOException e) {
System.out.println("AHHHH");
e.printStackTrace();
}
}
}
The issue is most likely the recursive calls in DFSVisit. If you don't want to go with the 'easy' answer of increasing Java's stack size when you call the JVM, you may want to consider rewriting DFSVisit to use an iterative algorithm instead of recursive. While Depth First Search is more easily defined in a recursive manner, there are iterative approaches to the algorithm that can be used.
For example: this blog post
The stack is a region in memory that is used for storing execution context and passing parameters. Every time your code invokes a method, a little bit of stack is used, and the stack pointer is increased to point to the next available location. When the method returns, the stack pointer is decreased and the portion of the stack is freed up.
If an application uses recursion heavily, the stack quickly becomes a bottleneck, because if there is no limit to the recursion depth, there is no limit to the amount of stack needed. So you have two options: increase the Java stack (-Xss JVM parameter, and this will only help until you hit the new limit) or change your algorithm so that the recursion depth is not as deep.
I am not sure if you were looking for a generic answer, but from a brief glance at your code it appears that your problem is recursion.
If you're sure your algorithm is correct and the depth of recursive calls you're making isn't accidental, then solutions without changing your algorithm are:
add to the JVM command line e.g. -Xss128m to set a 128 MB stack size (not a good solution in multi-threaded programs as it sets the default stack size for every thread not just the particular thread running your task);
run your task in its own thread, which you can initialise with a stack size specific to just that thread (and set the stack size within the program itself)-- see my example in the discussion of fixing StackOverflowError, but essentially the stack size is a parameter to the Thread() constructor;
don't use recursive calls at all-- instead, mimic the recursive calls using an explicit Stack or Queue object (this arguably gives you a bit more control).