Write a program that reads a connected graph from a file and displays

1. Write a program that reads a connected graph from a file and
displays its minimum spanning tree. The first line in the file
contains a number that indicates the number of vertices (n). The
vertices arc labeled as 0, L,..., n-1. Iiach subsequent line
describes the edges in the form of ul. vl, wl | u2. v2. w2
|....Iiach triplet in this form describes an edge and its weight.
Figure 29.24 shows an example of the file for the air-responding
graph. Note that we assume the graph is undirected. If the graph
has The vertices and edges of a weighted graph can be stored in
a file. an edge (u. v). it also lias an edge (v. u). Only one edge
is represented in the file. When you construct a grafih. both
edges need to be added. Your program should prompt the user to
enter the name ol the flic, read diita from the file,create an
ntfana: gof WelghtcdGraph, invoke g.printWalghtodEdgosO in
display all edges, invoke gatM1n1mjniSpann1ngTrooO to obtain
an ntfancc t rat of we-1igh t edCraph. MS I. invoke
troo.getTotalWeightO toi spfciythe weigln of the minimum
s|xtn>mig tree, and invoke trea.prlntTrcoO to display tlie tree.
Here is a sample run of the program:
Solution
import java.io.File;
import java.io.FileNotFoundException;
import java.util.ArrayList;
import java.util.List;
import java.util.PriorityQueue;

2. import java.util.Scanner;
public class Exercise09 {
public static void main(String[] args) throws
FileNotFoundException {
System.out.print("Enter a file name: ");
@SuppressWarnings("resource")
Scanner inputFileName = new Scanner(System.in);
String fileName = inputFileName.nextLine();
Scanner inputGraph = new Scanner(new File(fileName));
int numberOfVertices = inputGraph.nextInt();
inputGraph.nextLine();
System.out.println("The number of vertices is " +
numberOfVertices);
ArrayList<Integer> vertices = new ArrayList<>();
for (int i = 0; i < numberOfVertices; i++) {
vertices.add(i);
}
ArrayList<WeightedEdge> edges = new ArrayList<>();
while(inputGraph.hasNextLine()) {
String nextLine = inputGraph.nextLine();
nextLine = nextLine.replaceAll( ",", "");
nextLine = nextLine.replaceAll( "|", "");
Scanner inputVertic = new Scanner(nextLine);
while(inputVertic.hasNext()) {
int u = inputVertic.nextInt();

3. int v = inputVertic.nextInt();
double weight = inputVertic.nextDouble();
edges.add(new WeightedEdge(u, v, weight));
edges.add(new WeightedEdge(v, u, weight));
}
inputVertic.close();
}
inputGraph.close();
WeightedGraph<Integer> graph = new
WeightedGraph<>(edges, vertices);
graph.printWeightedEdges();
WeightedGraph<Integer>.MST tree =
graph.getMinimumSpanningTree();
System.out.println("Total weight is " +
tree.getTotalWeight());
tree.printTree();
}
static class WeightedGraph<V> extends AbstractGraph<V> {
// Priority adjacency lists
private List<PriorityQueue<WeightedEdge>> queues =
new ArrayList<PriorityQueue<WeightedEdge>>();
/** Construct a WeightedGraph from edges and vertices in
arrays */
public WeightedGraph() {

4. }
/** Construct a WeightedGraph from edges and vertices in
arrays */
public WeightedGraph(int[][] edges, V[] vertices) {
super(edges, vertices);
createQueues(edges, vertices.length);
}
/** Construct a WeightedGraph from edges and vertices in
List */
public WeightedGraph(int[][] edges, int
numberOfVertices) {
super(edges, numberOfVertices);
createQueues(edges, numberOfVertices);
}
/** Construct a WeightedGraph for vertices 0, 1, 2 and
edge list */
@SuppressWarnings({ "rawtypes", "unchecked" })
public WeightedGraph(List<WeightedEdge> edges,
List<V> vertices) {
super((List) edges, vertices);
createQueues(edges, vertices.size());
}
/** Construct a WeightedGraph from vertices 0, 1, and
edge array */
@SuppressWarnings({ "rawtypes", "unchecked" })

5. public WeightedGraph(List<WeightedEdge> edges, int
numberOfVertices) {
super((List) edges, numberOfVertices);
createQueues(edges, numberOfVertices);
}
/** Create priority adjacency lists from edge arrays */
private void createQueues(int[][] edges, int
numberOfVertices) {
for (int i = 0; i < numberOfVertices; i++) {
queues.add(new PriorityQueue<WeightedEdge>()); //
Create a queue
}
for (int i = 0; i < edges.length; i++) {
int u = edges[i][0];
int v = edges[i][1];
int weight = edges[i][2];
// Insert an edge into the queue
queues.get(u).offer(new WeightedEdge(u, v,
weight));
}
}
/** Create priority adjacency lists from edge lists */
private void createQueues(List<WeightedEdge> edges, int
numberOfVertices) {
for (int i = 0; i < numberOfVertices; i++) {

6. queues.add(new PriorityQueue<WeightedEdge>()); //
Create a queue
}
for (WeightedEdge edge : edges) {
queues.get(edge.u).offer(edge); // Insert an edge into
the queue
}
}
/** Display edges with weights */
public void printWeightedEdges() {
for (int i = 0; i < queues.size(); i++) {
System.out.print(getVertex(i) + " (" + i + "): ");
for (WeightedEdge edge : queues.get(i)) {
System.out.print("(" + edge.u + ", " + edge.v +
", "
+ edge.weight + ") ");
}
System.out.println();
}
}
/** Get the edges from the weighted graph */
public List<PriorityQueue<WeightedEdge>>
getWeightedEdges() {
return queues;
}

7. /** Clears the weighted graph */
public void clear() {
vertices.clear();
neighbors.clear();
queues.clear();
}
/** Add vertices to the weighted graph */
public void addVertex(V vertex) {
super.addVertex(vertex);
queues.add(new PriorityQueue<WeightedEdge>());
}
/** Add edges to the weighted graph */
public void addEdge(int u, int v, double weight) {
super.addEdge(u, v);
queues.get(u).add(new WeightedEdge(u, v, weight));
queues.get(v).add(new WeightedEdge(v, u, weight));
}
/** Get a minimum spanning tree rooted at vertex 0 */
public MST getMinimumSpanningTree() {
return getMinimumSpanningTree(0);
}
/** Get a minimum spanning tree rooted at a specified
vertex */
public MST getMinimumSpanningTree(int startingVertex)
{

8. List<Integer> T = new ArrayList<Integer>();
// T initially contains the startingVertex;
T.add(startingVertex);
int numberOfVertices = vertices.size(); // Number of
vertices
int[] parent = new int[numberOfVertices]; // Parent of a
vertex
// Initially set the parent of all vertices to -1
for (int i = 0; i < parent.length; i++)
parent[i] = -1;
double totalWeight = 0; // Total weight of the tree thus
far
// Clone the priority queue, so to keep the original queue
intact
List<PriorityQueue<WeightedEdge>> queues =
deepClone(this.queues);
// All vertices are found?
while (T.size() < numberOfVertices) {
// Search for the vertex with the smallest edge
adjacent to
// a vertex in T
int v = -1;
double smallestWeight = Double.MAX_VALUE;
for (int u : T) {
while (!queues.get(u).isEmpty()

9. && T.contains(queues.get(u).peek().v)) {
// Remove the edge from queues[u] if the
adjacent
// vertex of u is already in T
queues.get(u).remove();
}
if (queues.get(u).isEmpty()) {
continue; // Consider the next vertex in T
}
// Current smallest weight on an edge adjacent to u
WeightedEdge edge = queues.get(u).peek();
if (edge.weight < smallestWeight) {
v = edge.v;
smallestWeight = edge.weight;
// If v is added to the tree, u will be its parent
parent[v] = u;
}
} // End of for
if (v != -1)
T.add(v); // Add a new vertex to the tree
else
break; // The tree is not connected, a partial MST
is found
totalWeight += smallestWeight;
} // End of while

10. return new MST(startingVertex, parent, T, totalWeight);
}
/** Clone an array of queues */
private List<PriorityQueue<WeightedEdge>> deepClone(
List<PriorityQueue<WeightedEdge>> queues) {
List<PriorityQueue<WeightedEdge>> copiedQueues =
new ArrayList<PriorityQueue<WeightedEdge>>();
for (int i = 0; i < queues.size(); i++) {
copiedQueues.add(new
PriorityQueue<WeightedEdge>());
for (WeightedEdge e : queues.get(i)) {
copiedQueues.get(i).add(e);
}
}
return copiedQueues;
}
/** MST is an inner class in WeightedGraph */
public class MST extends Tree {
private double totalWeight; // Total weight of all edges
in the tree
public MST(int root, int[] parent, List<Integer>
searchOrder,
double totalWeight) {
super(root, parent, searchOrder);
this.totalWeight = totalWeight;

11. }
public double getTotalWeight() {
return totalWeight;
}
}
/** Find single source shortest paths */
public ShortestPathTree getShortestPath(int sourceVertex)
{
// T stores the vertices whose path found so far
List<Integer> T = new ArrayList<Integer>();
// T initially contains the sourceVertex;
T.add(sourceVertex);
// vertices is defined in AbstractGraph
int numberOfVertices = vertices.size();
// parent[v] stores the previous vertex of v in the path
int[] parent = new int[numberOfVertices];
parent[sourceVertex] = -1; // The parent of source is set
to -1
// cost[v] stores the cost of the path from v to the source
double[] cost = new double[numberOfVertices];
for (int i = 0; i < cost.length; i++) {
cost[i] = Double.MAX_VALUE; // Initial cost set to
infinity
}
cost[sourceVertex] = 0; // Cost of source is 0

12. // Get a copy of queues
List<PriorityQueue<WeightedEdge>> queues =
deepClone(this.queues);
// Expand T
while (T.size() < numberOfVertices) {
int v = -1; // Vertex to be determined
double smallestCost = Double.MAX_VALUE; // Set
to infinity
for (int u : T) {
while (!queues.get(u).isEmpty()
&& T.contains(queues.get(u).peek().v)) {
queues.get(u).remove(); // Remove the vertex in
queue
// for u
}
if (queues.get(u).isEmpty()) {
// All vertices adjacent to u are in T
continue;
}
WeightedEdge e = queues.get(u).peek();
if (cost[u] + e.weight < smallestCost) {
v = e.v;
smallestCost = cost[u] + e.weight;
// If v is added to the tree, u will be its parent
parent[v] = u;

13. }
} // End of for
T.add(v); // Add a new vertex to T
cost[v] = smallestCost;
} // End of while
// Create a ShortestPathTree
return new ShortestPathTree(sourceVertex, parent, T,
cost);
}
/** ShortestPathTree is an inner class in WeightedGraph */
public class ShortestPathTree extends Tree {
private double[] cost; // cost[v] is the cost from v to
source
/** Construct a path */
public ShortestPathTree(int source, int[] parent,
List<Integer> searchOrder, double[] cost) {
super(source, parent, searchOrder);
this.cost = cost;
}
/** Return the cost for a path from the root to vertex v
*/
public double getCost(int v) {
return cost[v];
}
/** Print paths from all vertices to the source */

14. public void printAllPaths() {
System.out.println("All shortest paths from "
+ vertices.get(getRoot()) + " are:");
for (int i = 0; i < cost.length; i++) {
printPath(i); // Print a path from i to the source
System.out.println("(cost: " + cost[i] + ")"); //
Path cost
}
}
}
}
static class WeightedEdge extends AbstractGraph.Edge
implements Comparable<WeightedEdge> {
public double weight; // The weight on edge (u, v)
/** Create a weighted edge on (u, v) */
public WeightedEdge(int u, int v, double weight) {
super(u, v);
this.weight = weight;
}
/** Compare two edges on weights */
public int compareTo(WeightedEdge edge) {
if (weight > edge.weight) {
return 1;
} else if (weight == edge.weight) {
return 0;

15. } else {
return -1;
}
}
@Override
public boolean equals(Object obj) {
if (obj instanceof WeightedEdge) {
WeightedEdge that = (WeightedEdge)obj;
return (u == that.u) && (v == that.v) && (weight ==
that.weight);
} else {
return false;
}
}
@Override
public String toString() {
return "(" + u + ", " + v + ", " + weight + ")";
}
}
static abstract class AbstractGraph<V> implements Graph<V>
{
protected List<V> vertices = new ArrayList<V>(); // Store
vertices

16. protected List<List<Integer>> neighbors = new
ArrayList<List<Integer>>(); // Adjacency
// lists
/** Construct an empty graph */
protected AbstractGraph() {
}
/** Construct a graph from edges and vertices stored in
arrays */
protected AbstractGraph(int[][] edges, V[] vertices) {
for (int i = 0; i < vertices.length; i++)
this.vertices.add(vertices[i]);
createAdjacencyLists(edges, vertices.length);
}
/** Construct a graph from edges and vertices stored in
List */
protected AbstractGraph(List<Edge> edges, List<V>
vertices) {
for (int i = 0; i < vertices.size(); i++)
this.vertices.add(vertices.get(i));
createAdjacencyLists(edges, vertices.size());
}
/** Construct a graph for integer vertices 0, 1, 2 and edge
list */
@SuppressWarnings("unchecked")
protected AbstractGraph(List<Edge> edges, int

17. numberOfVertices) {
for (int i = 0; i < numberOfVertices; i++)
vertices.add((V) (new Integer(i))); // vertices is {0,
1, ...}
createAdjacencyLists(edges, numberOfVertices);
}
/** Construct a graph from integer vertices 0, 1, and edge
array */
@SuppressWarnings("unchecked")
protected AbstractGraph(int[][] edges, int
numberOfVertices) {
for (int i = 0; i < numberOfVertices; i++)
vertices.add((V) (new Integer(i))); // vertices is {0,
1, ...}
createAdjacencyLists(edges, numberOfVertices);
}
/** Create adjacency lists for each vertex */
private void createAdjacencyLists(int[][] edges, int
numberOfVertices) {
// Create a linked list
for (int i = 0; i < numberOfVertices; i++) {
neighbors.add(new ArrayList<Integer>());
}
for (int i = 0; i < edges.length; i++) {
int u = edges[i][0];

18. int v = edges[i][1];
neighbors.get(u).add(v);
}
}
/** Create adjacency lists for each vertex */
private void createAdjacencyLists(List<Edge> edges, i nt
numberOfVertices) {
// Create a linked list for each vertex
for (int i = 0; i < numberOfVertices; i++) {
neighbors.add(new ArrayList<Integer>());
}
for (Edge edge : edges) {
neighbors.get(edge.u).add(edge.v);
}
}
public boolean isCyclic() {
for (int i = 0; i < vertices.size(); i++) {
if(isCyclic(i)) {
return true;
}
}
return false;
}

19. private boolean isCyclic(int v) {
List<Integer> searchOrder = new ArrayList<Integer>();
int[] parent = new int[vertices.size()];
for (int i = 0; i < parent.length; i++) {
parent[i] = -1;
}
boolean[] isVisited = new boolean[vertices.size()];
return isCyclic(v, v, parent, searchOrder, isVisited);
}
private boolean isCyclic(int first, int v, int[] parent,
List<Integer> searchOrder, boolean[] isVisited) {
searchOrder.add(v);
isVisited[v] = true;
for (int i : neighbors.get(v)) {
if (!isVisited[i]) {
parent[i] = v;
int[] newParent = java.util.Arrays.copyOf(parent,
parent.length);
boolean[] newIsVisited =
java.util.Arrays.copyOf(isVisited, parent.length);
@SuppressWarnings("unchecked")
List<Integer> newSearchOrder = (List<Integer>)
((ArrayList<Integer>)searchOrder).clone();
if(isCyclic(first, i, newParent, newSearchOrder,
newIsVisited)) {

20. return true;
}
} else if(first == i) {
if(searchOrder.size() > 2) {
return true;
}
}
}
return false;
}
@Override
/** Return the number of vertices in the graph */
public int getSize() {
return vertices.size();
}
@Override
/** Return the vertices in the graph */
public List<V> getVertices() {
return vertices;
}
@Override
/** Return the object for the specified vertex */
public V getVertex(int index) {
return vertices.get(index);

21. }
@Override
/** Return the index for the specified vertex object */
public int getIndex(V v) {
return vertices.indexOf(v) ;
}
@Override
/** Return the neighbors of the specified vertex */
public List<Integer> getNeighbors(int index) {
return neighbors.get(index);
}
@Override
/** Return the degree for a specified vertex */
public int getDegree(int v) {
return neighbors.get(v).size();
}
@Override
/** Print the edges */
public void printEdges() {
for (int u = 0; u < neighbors.size(); u++) {
System.out.print(getVertex(u) + " (" + u + "): ");
for (int j = 0; j < neighbors.get(u).size(); j++) {
System.out.print("(" + u + ", " +
neighbors.get(u).get(j)
+ ") ");

22. }
System.out.println();
}
}
@Override
/** Clear graph */
public void clear() {
vertices.clear();
neighbors.clear();
}
@Override
/** Add a vertex to the graph */
public void addVertex(V vertex) {
vertices.add(vertex);
neighbors.add(new ArrayList<Integer>());
}
@Override
/** Add an edge to the graph */
public void addEdge(int u, int v) {
neighbors.get(u).add(v);
neighbors.get(v).add(u);
}
/** Edge inner class inside the AbstractGraph class */
public static class Edge {
public int u; // Starting vertex of the edge

23. public int v; // Ending vertex of the edge
/** Construct an edge for (u, v) */
public Edge(int u, int v) {
this.u = u;
this.v = v;
}
}
@Override
/** Obtain a DFS tree starting from vertex v */
/** To be discussed in Section 27.6 */
public Tree dfs(int v) {
List<Integer> searchOrder = new ArrayList<Integer>();
int[] parent = new int[vertices.size()];
for (int i = 0; i < parent.length; i++)
parent[i] = -1; // Initialize parent[i] to -1
// Mark visited vertices
boolean[] isVisited = new boolean[vertices.size()];
// Recursively search
dfs(v, parent, searchOrder, isVisited);
// Return a search tree
return new Tree(v, parent, searchOrder);
}
/** Recursive method for DFS search */
private void dfs(int v, int[] parent, List<Integer>
searchOrder,

24. boolean[] isVisited) {
// Store the visited vertex
searchOrder.add(v);
isVisited[v] = true; // Vertex v visited
for (int i : neighbors.get(v)) {
if (!isVisited[i]) {
parent[i] = v; // The parent of vertex i is v
dfs(i, parent, searchOrder, isVisited); // Recursive
search
}
}
}
@Override
/** Starting bfs search from vertex v */
/** To be discussed in Section 27.7 */
public Tree bfs(int v) {
List<Integer> searchOrder = new ArrayList<Integer>();
int[] parent = new int[vertices.size()];
for (int i = 0; i < parent.length; i++)
parent[i] = -1; // Initialize parent[i] to -1
java.util.LinkedList<Integer> queue = new
java.util.LinkedList<Integer>(); // list
//
used
// as

25. // a
//
queue
boolean[] isVisited = new boolean[vertices.size()];
queue.offer(v); // Enqueue v
isVisited[v] = true; // Mark it visited
while (!queue.isEmpty()) {
int u = queue.poll(); // Dequeue to u
searchOrder.add(u); // u searched
for (int w : neighbors.get(u)) {
if (!isVisited[w]) {
queue.offer(w); // Enqueue w
parent[w] = u; // The parent of w is u
isVisited[w] = true; // Mark it visited
}
}
}
return new Tree(v, parent, searchOrder);
}
/** Tree inner class inside the AbstractGraph class */
/** To be discussed in Section 27.5 */
public class Tree {
private int root; // The root of the tree
private int[] parent; // Store the parent of each vertex
private List<Integer> searchOrder; // Store the search

26. order
/** Construct a tree with root, parent, and searchOrder
*/
public Tree(int root, int[] parent, List<Integer>
searchOrder) {
this.root = root;
this.parent = parent;
this.searchOrder = searchOrder;
}
/** Return the root of the tree */
public int getRoot() {
return root;
}
/** Return the parent of vertex v */
public int getParent(int v) {
return parent[v];
}
/** Return an array representing search order */
public List<Integer> getSearchOrder() {
return searchOrder;
}
/** Return number of vertices found */
public int getNumberOfVerticesFound() {
return searchOrder.size();
}

27. /** Return the path of vertices from a vertex to the root
*/
public List<V> getPath(int index) {
ArrayList<V> path = new ArrayList<V>();
do {
path.add(vertices.get(index));
index = parent[index];
} while (index != -1);
return path;
}
/** Print a path from the root to vertex v */
public void printPath(int index) {
List<V> path = getPath(index);
System.out.print("A path from " + vertices.get(root)
+ " to "
+ vertices.get(index) + ": ");
for (int i = path.size() - 1; i >= 0; i--)
System.out.print(path.get(i) + " ");
}
/** Print the whole tree */
public void printTree() {
System.out.println("Root is: " + vertices.get(root));
System.out.print("Edges: ");
for (int i = 0; i < parent.length; i++) {
if (parent[i] != -1) {

28. // Display an edge
System.out.print("(" + vertices.get(parent[i])
+ ", "
+ vertices.get(i) + ") ");
}
}
System.out.println();
}
}
}
interface Graph<V> {
/** Return the number of vertices in the graph */
public int getSize();
/** Return the vertices in the graph */
public java.util.List<V> getVertices();
/** Return the object for the specified vertex index */
public V getVertex(int index);
/** Return the index for the specified vertex object */
public int getIndex(V v);
/** Return the neighbors of vertex with the specified index
*/
public java.util.List<Integer> getNeighbors(int index);
/** Return the degree for a specified vertex */
public int getDegree(int v);
/** Print the edges */

29. public void printEdges();
/** Clear graph */
public void clear();
/** Add a vertex to the graph */
public void addVertex(V vertex);
/** Add an edge to the graph */
public void addEdge(int u, int v);
/** Obtain a depth-first search tree */
public AbstractGraph<V>.Tree dfs(int v);
/** Obtain a breadth-first search tree */
public AbstractGraph<V>.Tree bfs(int v);
}
}