A Practical Introduction to Data Structures and Algorithm Analysis

Sec. 11.7 Exercises 419class KruskalElem implements Comparable {private int v, w, weight;public KruskalElem(int inweight, int inv, int inw){ weight = inweight; v = inv; w = inw; }public int v1() { return v; }public int v2() { return w; }public int key() { return weight; }public int compareTo(KruskalElem that) {if (weight < that.key()) return -1;else if (weight == that.key()) return 0;else return 1;}}static void Kruskal(Graph G) { // Kruskal’s MST algorithmParPtrTree A = new ParPtrTree(G.n()); // Equivalence arrayKruskalElem[] E = new KruskalElem[G.e()]; // Minheap arrayint edgecnt = 0; // Count of edgesfor (int i=0; i1; i++) { // Combine equiv classesKruskalElem temp = H.removemin(); // Next cheapestint v = temp.v1(); int u = temp.v2();if (A.differ(v, u)) { // If in different classesA.UNION(v, u);// Combine equiv classesAddEdgetoMST(v, u); // Add this edge to MSTnumMST--;// One less MST}}}Figure 11.24 An implementation for Kruskal’s algorithm.11.5 Wright a pseudocode algorithm to create a DFS tree for an undirected, connectedgraph starting at a specified vertex V.11.6 Show the BFS tree for the graph of Figure 11.25, starting at Vertex 1.11.7 Wright a pseudocode algorithm to create a BFS tree for an undirected, connectedgraph starting at a specified vertex V.11.8 The BFS topological sort algorithm can report the existence of a cycle if oneis encountered. Modify this algorithm to print the vertices possibly appearingin cycles (if there are any cycles).