8. В 11 Suppose Dijkstra's algorithm is being run from vertex A and vertices A and C are in the shortest path cloud so far, with the graph and d[] values as shown. What vertex would be added next? D + After adding that vertex and relaxing across the edges coming out of it, what would the value of d[F] be? What is the worst-case runtime of Dijkstra's algorithm on a connected graph with N vertices and M edges? What auxiliary data structure is normally used to find the next vertex to add to the shortest path tree? 3. 2.

8. В 11 Suppose Dijkstra's algorithm is being run from vertex A and vertices A and C are in the shortest path cloud so far, with the graph and d[] values as shown. What vertex would be added next? D + After adding that vertex and relaxing across the edges coming out of it, what would the value of d[F] be? What is the worst-case runtime of Dijkstra's algorithm on a connected graph with N vertices and M edges? What auxiliary data structure is normally used to find the next vertex to add to the shortest path tree? 3. 2.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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In order to test connectivity, Python code uses the function Connectivity Undirected, which then calls the BFS algorithm, which returns a list of visited vertices and sorts them as shown below. The connectivity is then calculated by comparing this list to every node in the network in the main function. Be aware that in order to match the visited vertices with the sorted array of vertices, we must first sort the visited vertices. However, ordering can be avoided if sets are used in place of lists.
Fill in the blank Dijkstra's algorithm works because, on every shortest path p from a source vertex u to a target vertex v, there is a (predecessor) vertex w in p immediately before v such that removing v from p yields the shortest path from u to w. In other words, the path through the previous vertex is also the shortest path. Thus, choosing an edge from the previous vertex that brings us to v with the __ cost always yields the shortest path to v.
Let G be an undirected graph whose vertices are the integers 1 through 8, and let the adjacent vertices of each vertex be given by the table below: look at the picture sent Assume that, in a traversal of G, the adjacent vertices of a given vertex are returned in the same order as they are listed in the table above. Which statement of the following is correct? group of answer choices a) The sequence of vertices visited using a DFS traversal starting at vertex 1: 1, 2, 3, 4, 6, 5, 7, 8. b) The sequence of vertices visited using a BFS traversal starting at vertex 1: 1, 2, 3, 4, 6, 5, 7, 8. c) Both sequences are wrong. d) Both sequences are correct.
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}
Create an API and implementation that solves the multisource shortest-paths problem on edge-weighted digraphs with positive edge weights using Dijkstra's algorithm: Find a shortest-paths forest that permits the construction of a function that provides to clients the shortest path from any source to any vertex. This is done given a set of sources. Hint: Initialize the priority queue with all sources and set their distTo[] entries to 0 or add a fake vertex with a zero-weight edge to each source.
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…
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}
Create an API and implementation that solves the multisource shortest-paths problem on edge-weighted digraphs with positive edge weights using Dijkstra's algorithm: Find a shortest-paths forest given a set of sources, allowing the implementation of a method that returns to clients the shortest path from any source to each vertex. Add a dummy vertex with a zero-weight edge to each source, or start the priority queue with all sources and set their distTo[] entries to 0.
Given the following set of vertices V and set of edges E. V = {p, q, r, s, t, u} E = {(p,q), (q,r), (r, s), (t,p), (q,t), (r, t), (t,u)} Which of the following is correct? Select one: A.There are 7 vertices B.There are 7 edges. C.The degree at vertex p is 7 D.The total degree of all vertices is 7
Create an API and implementation that solves the multisource shortest-paths problem on edge-weighted digraphs with positive edge weights using Dijkstra's algorithm: Find a shortest-paths forest given a collection of sources, allowing the creation of a method that delivers to clients the shortest path from every source to any vertex. Add a dummy vertex with a zero-weight edge to each source, or start the priority queue with all sources and set their distTo[] entries to 0.
In a lecture the professor said that for every minimum spanning tree T of G there is an execution of the algorithm of Kruskal which delivers T as a result. ( Input is G). The algorithm he was supposedly talking about is: Kruskal() Precondition. N = (G, cost) is a connected network with n = |V| node and m = |E| ≥ n − 1 edges.All edges of E are uncolored. postcondition: All edges are colored. The green-colored edges together with V form one MST by N. Grand Step 1: Sort the edges of E in increasing weight: e1 , e2, . . . , em Grand step 2: For t = 0.1, . . . , m − 1 execute: Apply Kruskal's coloring rule to the et+1 edge i dont really understand this statement or how it is done. can someone explain me what he meant?
Provide a class to assess DAGs for mathematical expressions. Use a vertex-indexed array to store values for every vertex. Suppose that values for leaves have already been determined. Explain a family of mathematical expressions where the expression tree's size is exponentially bigger than the matching DAG's size (so the running time of your programme for the DAG is proportional to the logarithm of the running time for the tree).