6. Use the Breadth-First Spanning Tree Search Algorithm to find a spanning tree of K. Start from vertex h. Remember, we start with vertex h being labeled 0. b h g C e K6 a. Vertices that should be labeled as step 1: b. Vertices that should be labeled as step 2: c. Vertices that should be labeled as step 3: d. Edges that need to be removed to get a spanning tree: I
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- A mathematician applies Prim’s Algorithm to find a minimum spanning tree for the weighted graph starting at vertex D. The order of the edges picked so far is AD, AB, BE, and EF. The next edge selected when applying Prim’s Algorithm should be BF FG CG CE What is the total weight of the tree that uses the edges DE, CE, CG, FG and BF? 93 92 91 90 The tree described in problem #8 is a spanning True Falselines (93 sloc) 3.18 KB Raw Blame Given an undirected, connected and weighted graph G(V, E) with V number of vertices (which are numbered from 0 to V-1) and E number of edges. Find and print the Minimum Spanning Tree (MST) using Kruskal's algorithm. For printing MST follow the steps - 1. In one line, print an edge which is part of MST in the format - v1 v2 w where, v1 and v2 are the vertices of the edge which is included in MST and whose weight is w. And v1 <= v2 i.e. print the smaller vertex first while printing an edge. 2. Print V-1 edges in above format in different lines. Note : Order of different edges doesn't matter. Input Format : Line 1: Two Integers V and E (separated by space) Next E lines : Three integers ei, ej and wi, denoting that there exists an edge between vertex ei and vertex ej with weight wi (separated by space) Output Format : Print the MST, as described in the task. Constraints : 2 <=…Consider the following graph. Start from vertex x, use the Depth First Search (DFS) algorithm (described in the textbook) to compute the DFS tree(s). Show intermediate results similar to the textbook example and show the final DFS tree(s). It is assumed that in the adjacency list representation, all vertices are stored according to their alphabetical order. In other words, a vertex’s neighbors should be explored by their relative alphabetical order.
- Use breadth-first search starting at vertex S to construct a spanning tree of the graph below. If we tie-break alphabetically, what is the order of edges we construct our spanning tree? a. {S,T}, {S,V}, {S,W}, {T,X}, {V,Z}, {X,Y}, {U,Y} b. {S,V}, {S,T}, {S,W}, {V,Z}, {T,X}, {Y,Z}, {U,Y} c. {S,V}, {S,W}, {S,T}, {V,Z}, {T,X}, {Y,Z}, {U,Y} d. {S,T}, {S,W}, {S,V}, {T,X}, {V,Z}, {X,Y}, {U,Y}Use Prim's Algorithm starting at vertex SS to construct a minimum spanning tree of the graph below. If we tie-break alphabetically, what is the order of edges we construct our spanning tree? a. {S,T}, {S,V}, {V,Z}, {W,Z}, {Y,Z}, {W,X}, {U,Y} b. {S,T}, {S,W}, {W,Z}, {V,Z}, {Y,Z}, {W,X}, {U,Y} c. {S,T}, {V,Z}, {W,Z}, {Y,Z}, {S,V}, {W,X}, {U,Y} d. {S,T}, {S,V}, {S,W}, {V,Z}, {W,X}, {Y,Z}, {U,Y}THIS IS MY CODE HELP ME ACHIEVE POINTS OUTLINED BELOW : #include <stdio.h>#include <stdlib.h>#include <string.h>#include <float.h>#include "graph.h"#include "dijkstra.h" #define INFINITY DBL_MAX /* find shortest paths between source node id and all other nodes in graph. *//* upon success, returns an array containing a table of shortest paths. *//* return NULL if *graph is uninitialised or an error occurs. *//* each entry of the table array should be a Path *//* structure containing the path information for the shortest path between *//* the source node and every node in the graph. If no path exists to a *//* particular desination node, then next should be set to -1 and weight *//* to DBL_MAX in the Path structure for this node */Path *dijkstra(Graph *graph, int id, int *pnEntries){ int n; int i, j; int* nv = get_vertices(graph, &n); int *S = malloc(n * sizeof(int)); double *D = malloc(n * sizeof(double)); int *R = malloc(n…
- 12- A Graph consists of four vertices A, B, C and D. If we start from A, which vertex will be visited first of all by breadth-first search (BFS) algorithm? A C D BConsider the above rooted tree.1. Which vertex is the root?2. Which vertices are internal?3. Which vertices are leaves?4. Which vertices are children of j?5. Which vertex is the parent of h?6. Which vertices are siblings of o?7. Which vertices are ancestors of m?8. Which vertices are descendants of b?Use depth-first search starting at vertex SS to construct a spanning tree of the graph below. If we tie-break alphabetically, what is the order of edges we construct our spanning tree? a. {S,T}, {T,X}, {W,X}, {W,Z}, {V,Z}, {X,Y}, {U,Y} b. {S,T}, {S,V}, {V,Z}, {W,Z}, {W,X}, {T,X}, {X,Y}, {U,Y} c. {S,T}, {T,X}, {W,X}, {S,V}, {V,Z}, {Y,Z}, {U,Y} d. {S,T}, {T,X}, {W,X}, {W,Z}, {V,Z}, {Z,Y}, {U,Y}
- Question 4: Suppose you had a road network represented as a connected graph (vertices are intersections and edges are roads between intersections). How can you determine if closing a set of intersections results in the inability to travel between some remaining pair of intersections? Note: If an intersection is closed, all edges touching that vertex are closed too. You may assume we already know about depth first search, breadth first search, minimum spanning tree algorithms, and the shortest path algorithm from class, but you can’t assume anything else from class.Is the following statement true? Justify your answer. Let B be a binary tree. If for each of vertices (v) a data item is inserted into vertex (v) and they are bigger than the data item inserted in the left son of vertex (v) and smaller at the same time, than data item inserted in the right son of the vertex (v). B is a search tree. Definition of data item(data entry): Data item is one unit of data in a storage record.Minimum Spanning Tree of a graph includes all its nodes Both the lazy and eager versions of Prims Algorithm use priority queue of edges. Both the lazy version of Prims Algorithm and Kruskal’s algorithm uses priority queue of edges. A crossing edge connects vertices that are in the same partition.5.Minimum Spanning Tree of a graph includes all its edges.6.A crossing edge connects vertices that are in different partitions. 7.Breadth First Search Algorithm can be used for weighted graph traversal.8.Depth First Search Algorithm can be used for weighted graph traversal.9.A spanning tree of a graph is a tree but not a graph.10.Kruskal algorithm starts with an initial vertex v and always adds next smallest edge to the same tree that is connected to the initial vertex v. Which are the following true or false ?