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How do I call upon the method in this program?

I'm trying to test out my program to see how it works, but I'm not sure how to call upon it in the main method. I've tried doing Assignment5Solution.findOrder() but it does not work. Any help with this issue would be greatly appreciated. The code is supposed to take the number of classes a student has to take along with the prerequisites for each course if there are any, and put the correct order of what classes the student should take.
package Assignment5;
import java.lang.reflect.Array;
import java.util.*;
/**
*
* #author harpe
*/
class Assignment5Solution {
public int[] findOrder(int numCourses, int[][] prerequisites) {
int E = prerequisites.length;
Graph G = new Graph(numCourses);
for (int i = 0; i < E; i++) {
G.addEdge(prerequisites[i][1], prerequisites[i][0]);
} // Graph is constructed
DFS d = new DFS(G); // depth first search
return d.reverseDFSorder();
}
public class DFS {
private boolean[] marked;
private int[] courseOrder; // i.e., reverse post order
private boolean hasCycle;
private int index; // index for the array courseOrder, index 0 is for the course taken first, …
private HashSet<Integer> callStack; // used to detect if there are cycles on the graph
DFS(Graph G) {
marked = new boolean[G.V()];
courseOrder = new int[G.V()];
index = courseOrder.length - 1; // index 0 of courseOrder will be course taken first, lastIndex will be taken last
callStack = new HashSet<Integer>(); // HashSet is a hash table, for O(1) search
for (int v = 0; v < G.V(); v++) { // to visit each node, including those on islands or isolated
if (!marked[v] && !hasCycle) {
dfs(G, v);
}
}
}
private void dfs(Graph G, int v) {
marked[v] = true;
callStack.add(v); // use HashSet to simulate callStack
for (int w : G.adj(v)) {
if (!marked[w]) {
dfs(G, w);
} else if (callStack.contains(w)) // search in HashSet is O(1)
{
hasCycle = true; // this is a cycle!
break;
}
}
callStack.remove(v);
courseOrder[index--] = v; // index starts from array length -1, decrease by 1 each time, and then ends at 0
}
public int[] reverseDFSorder() {
if (hasCycle) {
return new int[0]; // return an empty int array (with size 0)
}
return courseOrder;
}
} // end of class DFS
public class Graph {
private int V;
private List[] adj;
Graph(int V) // constructor
{
this.V = V;
adj = new List[V];
for (int i = 0; i < V; i++) {
adj[i] = new ArrayList<Integer>();
}
}
public void addEdge(int v, int w) {
adj[v].add(w);
}
public Iterable<Integer> adj(int v) {
return adj[v];
}
public int V() {
return V;
}
} // end of class Graph
} // end of class Solution

public int[] findOrder(int numCourses, int[][] prerequisites) {}
would need to be:
public static int[] findOrder(int numCourses, int[][] prerequisites) {}
The static keyword means you do not need to a declare an object of the class to use it. So you can use it using:
Assignment5Solution.findOrder(numCourses, prerequisites)
//numCourses and prerequisites can be any int and int[][] respectively.
EDIT: Another note too, depending on where your main method is you may need to make class Assignment5Solution a public class with:
public class Assignment5Solution {
It currently is package protected so it will only be able to be used if it is in the same package.
EDIT2:
If you want to use it as a nonstatic method you need to do something like this(change null and 0 to the real values):
Assignment5Solution test = new Assignment5Solution() {};
int numCourses = 0;
int [][] prereqs = null;
int[] reverseOrder = test.findOrder(numCourses, prereqs);

Set an element in an arraylist of a specific class

In my program I have a pair class:
class Pair {
public int ind = 0;
public String letter = "";
public Pair(int a, String b) {
ind = a; //index
letter = b;
}
}
how do I set the index (ind) of an element in an arraylist of Pairs? I have tried
RightMotor.ind.set(j, i);
and
LeftMotor.set(j, i).ind;
but they don't seem to work.

First you need to 'get' the Pair instance, like:
Pair pair = LeftMotor.get(i);
then you can change its fields:
pair.ind = j;
This can also be done in one line:
LeftMotor.get(i).ind = j;
Hint 1: this is not changing the index (position) of the instance in the list, LeftMotor.get(i) will still return the same element. i and ind are two completely disjunct values.
Hint 2: normally it is better to have private fields and have a method (setter) to change the fields (encapsulation):
class Pair {
private int ind = 0;
private String letter = "";
public Pair(int a, String b) {
ind = a; //index
letter = b;
}
public void setInd(int newInd) {
ind = newInd;
}
}
Hint 3: just to be clear, just because it is called ind it is not the index (position) of the list. It is a whole different question if you want to change the order of the elements in the list.

You want to make those instance variables private, then getters/setters to access/modify them. This allows you to safely and securely manipulate the data with a reduced chance of bleedover (which can crash your program or cause unintended consequences).
Within your class:
class Pair {
private int ind = 0;
private String letter = "";
public Pair(int index, String letter) {
ind = index;
letter = letter;
}
public int getIndex() {
return index;
}
public void setIndex(int index) {
this.index = index;
}
public String getLetter() {
return this.letter;
}
public void setLetter(String letter) {
this.letter = letter;
}
public void setIndexAndLetter(int index, String letter) {
this.index = index;
this.letter = letter;
}
}
Elsewhere in your program:
Pair rightMotor = new Pair(1, "a");
Pair leftMotor = new Pair(2, "b");
Pair middleMotor = new Pair(0, "");
rightMotor.setInd(3);
leftMotor.setLetter("d");
middleMotor.setIndAndLetter(rightMotor.getInd() + leftMotor.getInd(), "z");

You have to create a Pair instance using the Pair constructor before adding it to the ArrayList:
RightMotor.add(new Pair(i,j)); // assuming i is an int and j is a String
If you want to replace the Pair stored in a given index use:
RightMotor.set(index,new Pair(i,j));
If you want to change an existing Pair stored in the ArrayList:
RightMotor.get(index).setInd(newValue);
This will require a setter method in your Pair class:
public void setInd (int i) {
ind = i;
}

So I think that you could solve this in a couple of different ways... however I think I know what you are trying to do.... I feel like you are trying to keep the ArrayList and the Pair index synchronized... either way you will need a helper method to accomplish this. I agree with hendripd that you should use private variables and utilize the getters and setters. However this is my solution.
Pair:
public class Pair implements Comparable<Pair> {
private int index = 0;
private String letter = "";
public Pair(int index, String letter) {
this.index = index;
this.letter = letter;
}
public Pair(Pair pair) {
this.index = pair.getIndex();
this.letter = pair.getLetter();
}
#Override
public int compareTo(Pair pair) {
if (this.index > pair.index) {
return 1;
} else if (this.index < pair.index) {
return -1;
} else {
return 0;
}
}
#Override
public String toString() {
return this.index + " " + this.letter;
}
public int getIndex() {
return this.index;
}
public String getLetter() {
return this.letter;
}
public void setIndex(int index) {
this.index = index;
}
public void setLetter(String letter) {
this.letter = letter;
}
}
Main:
import java.util.ArrayList;
import java.util.Collections;
public class Main {
public static ArrayList<Pair> rightMotor;
public static void main(String[] args) {
rightMotor = new ArrayList<Pair>();
rightMotor.add(new Pair(0, "a"));
rightMotor.add(new Pair(1, "b"));
setIndex(rightMotor, 0, 1);
// If you choose to go with the second option utilizing Comparable<Pair>
// Collections.sort(rightMotor);
for (Pair pair : rightMotor) {
System.out.println(pair.toString());
}
}
public static void setIndex(ArrayList<Pair> motor, int oldIndex, int newIndex) {
Pair tempPair = new Pair(motor.get(oldIndex));
if (oldIndex < newIndex) {
for (int i = oldIndex; i < newIndex; i++) {
motor.set(i, motor.get(i + 1));
motor.get(i).setIndex(i);
}
} else if (oldIndex > newIndex) {
for (int i = oldIndex; i > newIndex; i--) {
motor.set(i, motor.get(i - 1));
motor.get(i).setIndex(i);
}
}
tempPair.setIndex(newIndex);
motor.set(newIndex, tempPair);
}
}
Note that the Pair class implements comparable... you could use Collections.Sort(rightMotor) which then you would only need to fix the indexes of the instances... i.e.
public static void setIndex(ArrayList<Pair> motor, int oldIndex, int newIndex) {
motor.get(oldIndex).setIndex(newIndex);
if (oldIndex < newIndex) {
for (int i = oldIndex; i < newIndex; i++) {
motor.get(i + 1).setIndex(i);
}
} else if (oldIndex > newIndex) {
for (int i = oldIndex; i > newIndex; i--) {
motor.get(i - 1).setIndex(i);
}
}
}
Or... you can use the original one I posted which also handles the sorting at the same time. This keeps your Arraylist in numerical order by index either way.
Test casing:
rightMotor.add(new Pair(0, "a"));
rightMotor.add(new Pair(1, "b"));
rightMotor.add(new Pair(2, "c"));
rightMotor.add(new Pair(3, "d"));
rightMotor.add(new Pair(4, "e"));
rightMotor.add(new Pair(5, "f"));
setIndex(rightMotor, 0, 1);
setIndex(rightMotor, 3, 1);
setIndex(rightMotor, 4, 3);
outputs this result:
0 b
1 d
2 a
3 e
4 c
5 f

"Class, interface or enum expected" error in Java

I'm working on this code to build a maze using disjoint set data structure in Java. I'm getting an error("class, interface or enum expected") starting //Building maze using Disjoint Set data structure to end. Can anyone please help me out?
//Implementation of Disjoint Set
public class DisjSet {
private int[] set;
private int[] sizes;
private int size;
public DisjSet(int size) {
this.set = new int[size];
for (int i = 0; i < size; i++) { this.set[i] = i; }
this.sizes = new int[size];
for (int i = 0; i < size; i++) { this.sizes[i] = 1; }
this.size = size;
}
public int find(int item) {
int root = item;
// find the root
while (set[root] != root) {
root = set[root];
}
// now shorten the paths
int curr = item;
while (set[curr] != root) {
set[curr] = root;
}
return root;
}
public int join(int item1, int item2) {
int group1 = find(item1);
int group2 = find(item2);
--size;
if (sizes[group1] > sizes[group2]) {
set[group2] = group1;
sizes[group1] += sizes[group2];
return group1;
} else {
set[group1] = group2;
sizes[group2] += sizes[group1];
return group2;
}
}
}
//Building maze using Disjoint Set data structure
Maze createRandomMaze(int rows, int columns) {
Maze maze = new Maze(rows, columns);
// create all walls
List<Wall> walls = maze.getAllInnerWalls();
// remove all the walls you can
DisjSet diset = new DisjSet(rows*columns);
while (diset.size() > 1) {
int wallIndex = random.nextInt(walls.size());
int cell1 = walls.get(wallIndex).cell1;
int cell2 = walls.get(wallIndex).cell2;
if (diset.find(cell1) != diset.find(cell2)) {
// we can remove the wall
maze.removeWall(walls.get(wallIndex));
diset.join(cell1, cell2);
}
walls.remove(wallIndex);
}
return maze;
}

These:
Maze createRandomMaze(int rows, int columns) {
Maze maze = new Maze(rows, columns);
// create all walls
List<Wall> walls = maze.getAllInnerWalls();
// remove all the walls you can
DisjSet diset = new DisjSet(rows*columns);
while (diset.size() > 1) {
int wallIndex = random.nextInt(walls.size());
int cell1 = walls.get(wallIndex).cell1;
int cell2 = walls.get(wallIndex).cell2;
if (diset.find(cell1) != diset.find(cell2)) {
// we can remove the wall
maze.removeWall(walls.get(wallIndex));
diset.join(cell1, cell2);
}
walls.remove(wallIndex);
}
return maze;
should be put inside a method, only declarations are allowed at class level.
If you have a main method, already, move the above code there. If you don't, declare a main method:
public static void main(String[] args) {
// put the above code here...
}
Now when you run your code, the main method will be called and the above lines will be run.

Altering the value of k in kNN algorithm - Java

I have applied the KNN algorithm for classifying handwritten digits. the digits are in vector format initially 8*8, and stretched to form a vector 1*64..
As it stands my code applies the kNN algorithm but only using k = 1. I'm not entirely sure how to alter the value k after attempting a couple of things I kept getting thrown errors. If anyone could help push me in the right direction it would be really appreciated. The training dataset can be found here and the validation set here.
ImageMatrix.java
import java.util.*;
public class ImageMatrix {
private int[] data;
private int classCode;
private int curData;
public ImageMatrix(int[] data, int classCode) {
assert data.length == 64; //maximum array length of 64
this.data = data;
this.classCode = classCode;
}
public String toString() {
return "Class Code: " + classCode + " Data :" + Arrays.toString(data) + "\n"; //outputs readable
}
public int[] getData() {
return data;
}
public int getClassCode() {
return classCode;
}
public int getCurData() {
return curData;
}
}
ImageMatrixDB.java
import java.util.*;
import java.io.*;
import java.util.ArrayList;
public class ImageMatrixDB implements Iterable<ImageMatrix> {
private List<ImageMatrix> list = new ArrayList<ImageMatrix>();
public ImageMatrixDB load(String f) throws IOException {
try (
FileReader fr = new FileReader(f);
BufferedReader br = new BufferedReader(fr)) {
String line = null;
while((line = br.readLine()) != null) {
int lastComma = line.lastIndexOf(',');
int classCode = Integer.parseInt(line.substring(1 + lastComma));
int[] data = Arrays.stream(line.substring(0, lastComma).split(","))
.mapToInt(Integer::parseInt)
.toArray();
ImageMatrix matrix = new ImageMatrix(data, classCode); // Classcode->100% when 0 -> 0% when 1 - 9..
list.add(matrix);
}
}
return this;
}
public void printResults(){ //output results
for(ImageMatrix matrix: list){
System.out.println(matrix);
}
}
public Iterator<ImageMatrix> iterator() {
return this.list.iterator();
}
/// kNN implementation ///
public static int distance(int[] a, int[] b) {
int sum = 0;
for(int i = 0; i < a.length; i++) {
sum += (a[i] - b[i]) * (a[i] - b[i]);
}
return (int)Math.sqrt(sum);
}
public static int classify(ImageMatrixDB trainingSet, int[] curData) {
int label = 0, bestDistance = Integer.MAX_VALUE;
for(ImageMatrix matrix: trainingSet) {
int dist = distance(matrix.getData(), curData);
if(dist < bestDistance) {
bestDistance = dist;
label = matrix.getClassCode();
}
}
return label;
}
public int size() {
return list.size(); //returns size of the list
}
public static void main(String[] argv) throws IOException {
ImageMatrixDB trainingSet = new ImageMatrixDB();
ImageMatrixDB validationSet = new ImageMatrixDB();
trainingSet.load("cw2DataSet1.csv");
validationSet.load("cw2DataSet2.csv");
int numCorrect = 0;
for(ImageMatrix matrix:validationSet) {
if(classify(trainingSet, matrix.getData()) == matrix.getClassCode()) numCorrect++;
} //285 correct
System.out.println("Accuracy: " + (double)numCorrect / validationSet.size() * 100 + "%");
System.out.println();
}

In the for loop of classify you are trying to find the training example that is closest to a test point. You need to switch that with a code that finds K of the training points that is the closest to the test data. Then you should call getClassCode for each of those K points and find the majority(i.e. the most frequent) of the class codes among them. classify will then return the major class code you found.
You may break the ties (i.e. having 2+ most frequent class codes assigned to equal number of training data) in any way that suits your need.
I am really inexperienced in Java, but just by looking around the language reference, I came up with the implementation below.
public static int classify(ImageMatrixDB trainingSet, int[] curData, int k) {
int label = 0, bestDistance = Integer.MAX_VALUE;
int[][] distances = new int[trainingSet.size()][2];
int i=0;
// Place distances in an array to be sorted
for(ImageMatrix matrix: trainingSet) {
distances[i][0] = distance(matrix.getData(), curData);
distances[i][1] = matrix.getClassCode();
i++;
}
Arrays.sort(distances, (int[] lhs, int[] rhs) -> lhs[0]-rhs[0]);
// Find frequencies of each class code
i = 0;
Map<Integer,Integer> majorityMap;
majorityMap = new HashMap<Integer,Integer>();
while(i < k) {
if( majorityMap.containsKey( distances[i][1] ) ) {
int currentValue = majorityMap.get(distances[i][1]);
majorityMap.put(distances[i][1], currentValue + 1);
}
else {
majorityMap.put(distances[i][1], 1);
}
++i;
}
// Find the class code with the highest frequency
int maxVal = -1;
for (Entry<Integer, Integer> entry: majorityMap.entrySet()) {
int entryVal = entry.getValue();
if(entryVal > maxVal) {
maxVal = entryVal;
label = entry.getKey();
}
}
return label;
}
All you need to do is adding K as a parameter. Keep in mind, however, that the code above does not handle ties in a particular way.

Checking for odd cycles in an undirected graph

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.