/**
* Returns a new UDGraph with the same vertices as "this" UDGraph. The new graph has an edge (v,
* w) if and only if there is a path of length 2 from v to w in "this" graph. *** DO NOT CHANGE
* "this" GRAPH!!! ***
*
* @return the new UDGraph.
*/
public UDGraph length2Paths() {
UDGraph newGraph = new UDGraph(vertices);
for (int k = 0; k < vertices; k++) {
for (int i = 0; i < vertices; i++) {
for (int j = 0; j < vertices; j++) {
if (hasEdge(i, k) == true && hasEdge(k, j) == true) {
newGraph.addEdge(i, j);
}
}
}
}
return newGraph;
}
/**
* Returns a new UDGraph with the same vertices as "this" UDGraph. The new graph has an edge (v,
* w) if and only if there is a path of length "length" from v to w in "this" graph.
*
* @param length the length of paths used to construct the new graph.
* @return the new UDGraph.
*/
public UDGraph paths(int length) {
UDGraph newGraph = new UDGraph(vertices);
UDGraph storageGraph = new UDGraph(vertices);
int l = length;
if (l == 2) {
newGraph = this.length2Paths();
} else {
storageGraph = paths(l - 1);
for (int k = 0; k < vertices; k++) {
for (int i = 0; i < vertices; i++) {
if (storageGraph.hasEdge(i, k) == true) {
for (int j = 0; j < vertices; j++) {
if (hasEdge(k, j) == true) {
newGraph.addEdge(i, j);
}
}
}
}
}
}
return newGraph;
}
public static void main(String[] args) {
System.out.println("\n *** Lab 12: " + "Square the unweighted directed graph! *** \n");
// Create an 11-vertex graph.
System.out.println("Creating a graph with 11 vertices");
UDGraph graph = new UDGraph(11);
graph.addEdge(0, 8);
graph.addEdge(1, 0);
graph.addEdge(1, 3);
graph.addEdge(2, 0);
graph.addEdge(3, 2);
graph.addEdge(3, 5);
graph.addEdge(4, 2);
graph.addEdge(4, 5);
graph.addEdge(5, 7);
graph.addEdge(5, 9);
graph.addEdge(6, 4);
graph.addEdge(6, 7);
graph.addEdge(8, 4);
graph.addEdge(8, 6);
graph.addEdge(8, 10);
graph.addEdge(9, 1);
graph.addEdge(10, 6);
boolean goodJob = true;
String t1String =
"11 vertices and 17 edges\n. . . . . . . . t . .\n"
+ "t . . t . . . . . . .\nt . . . . . . . . . .\n. . t . . t . . . . .\n"
+ ". . t . . t . . . . .\n. . . . . . . t . t .\n. . . . t . . t . . .\n"
+ ". . . . . . . . . . .\n. . . . t . t . . . t\n. t . . . . . . . . .\n"
+ ". . . . . . t . . . .\n";
System.out.println("\nThe original graph is\n" + graph);
if (!t1String.equals(graph.toString())) {
System.out.println("Error: the original graph should be\n" + t1String);
goodJob = false;
}
// Do length-2 paths work?
String t2String =
"11 vertices and 25 edges\n. . . . t . t . . . t\n"
+ ". . t . . t . . t . .\n. . . . . . . . t . .\nt . . . . . . t . t .\n"
+ "t . . . . . . t . t .\n. t . . . . . . . . .\n. . t . . t . . . . .\n"
+ ". . . . . . . . . . .\n. . t . t t t t . . .\nt . . t . . . . . . .\n"
+ ". . . . t . . t . . .\n";
System.out.println("Testing length-2 paths.");
System.out.println("The graph of length-2 paths is\n" + graph.length2Paths());
if (!t2String.equals(graph.length2Paths().toString())) {
System.out.println("Error: the length-2 path graph should be\n" + t2String);
goodJob = false;
}
// Do length-3 paths work?
String t3String =
"11 vertices and 34 edges\n. . t . t t t t . . .\n"
+ "t . . . t . t t . t t\n. . . . t . t . . . t\n. t . . . . . . t . .\n"
+ ". t . . . . . . t . .\nt . . t . . . . . . .\nt . . . . . . t . t .\n"
+ ". . . . . . . . . . .\nt . t . t t . t . t .\n. . t . . t . . t . .\n"
+ ". . t . . t . . . . .\n";
System.out.println("Testing length-3 paths.");
System.out.println("The graph of length-3 paths is\n" + graph.paths(3));
if (!t3String.equals(graph.paths(3).toString())) {
System.out.println("Error: the length-3 path graph should be\n" + t3String);
goodJob = false;
}
// Do length-4 paths work?
String t4String =
"11 vertices and 49 edges\nt . t . t t . t . t .\n"
+ ". t t . t t t t t . .\n. . t . t t t t . . .\nt . . t t . t . . . t\n"
+ "t . . t t . t . . . t\n. . t . . t . . t . .\n. t . . . . . . t . .\n"
+ ". . . . . . . . . . .\nt t t . . t . t t t .\nt . . . t . t t . t t\n"
+ "t . . . . . . t . t .\n";
System.out.println("Testing length-4 paths.");
System.out.println("The graph of length-4 paths is\n" + graph.paths(4));
if (!t4String.equals(graph.paths(4).toString())) {
System.out.println("Error: the length-4 path graph should be\n" + t4String);
goodJob = false;
}
// Do length-5 paths work?
String t5String =
"11 vertices and 63 edges\nt t t . . t . t t t .\n"
+ "t . t t t t t t . t t\nt . t . t t . t . t .\n. . t . t t t t t . .\n"
+ ". . t . t t t t t . .\nt . . . t . t t . t t\nt . . t t . t . . . t\n"
+ ". . . . . . . . . . .\nt t . t t . t t t t t\n. t t . t t t t t . .\n"
+ ". t . . . . . . t . .\n";
System.out.println("Testing length-5 paths.");
System.out.println("The graph of length-5 paths is\n" + graph.paths(5));
if (!t5String.equals(graph.paths(5).toString())) {
System.out.println("Error: the length-5 path graph should be\n" + t5String);
goodJob = false;
}
if (goodJob) {
System.out.println(" *** Good Job! *** \n");
}
}