Please help me quickly Question OneFor the following graph, Apply Dijkstra Algorithm to find the length of thehortest path:a. What is the shortest path from A to E? what is its lengthb. What is the shortest path from D to C? what is its lengthQuestion TwoGiven the Tree below. Answer the following questions:The root node?1012b.The siblings of node 7?C.The ancestors of node 5?d.The descendants of node 15?e.The internal vertices?f.The leaf nodes?259

1) Since no edge weight is given i am assuming it default 1 Question One(a) Shortest path from A to…

Answered: Question One For the following graph,…

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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Draw a tree with 14 vertices Draw a directed acyclic graph with 6 vertices and 14 edges Suppose that your computer only has enough memory to store 40000 entries. Which best graph data structure(s) – you can choose more than 1 -- should you use to store a simple undirected graph with 200 vertices, 19900 edges, and the existence of edge(u,v) is frequently asked? - Adjacency Matrix - Adjacency List - Edge List
Given a graph that is a tree (connected and acyclic). (1) Pick any vertex v. (II) Compute the shortest path from v to every other vertex. Let w be the vertex with the largest shortest path distance. (III) Compute the shortest path from w to every other vertex. Let x be the vertex with the largest shortest path distance. Consider the path p from w to x. Which of the following are true a. p is the longest path in the graph b. p is the shortest path in the graph c. p can be calculated in time linear in the number of edges/vertices a,c a,b a,b,c b.c
Solve the problem in the image below:
you need to write the solutions in python and provide a brief explanation of your codes and the efficiency analysis with comments. 3. Consider a loop tree which is an undirected wighted graph formed by taking a binary tree and adding an edge from exactly one of the leaves to another node in the tree as follows: Letnbe the number of vertices in a loop tree. How long does it take Prim's or Kruskal's algorithms to find the minimum spanning tree in terms ofn? Devise a more efficient algorithm that takes an nxn adjacency weighted matrix as input, and finds the minimum spanning tree of a loop tree. 三 input1 - Not Defteri Dosya Düzenle 1078000000 700650060 800006400 060000000 050000021 006000000 004000000 060020000 000010000 output1 - Not Defteri Dosya Düzenle Görünü p 14873265 三 input2 - Not Defteri Dosya Düzenle Görünüm0210000200344010000000300000040005604005000000
b) Apply an algorithm to find the minimum spanning tree. To solve this problem, you need to transfer the unweighted graph into weighted graph and you can do it by using your mobile number (11 digits). Just assign the digits sequentially (left to right) to the edges of binary tree segment (means black color edges). And for rest of the edges, you may write 1 as their weights.
a. For the graph below, give the order in which Dijkstra’s Algorithm would visit each vertex, starting from vertex A. 3 2 B F A G 4 ( E 4 D H 4 b. Change one of the weights in the graph so that the shortest paths tree returned by Dijkstra's is not correct. Hint: we showed in class that Dijkstra’s returns the correct SPT as long as all edges are non- negative. Set the weight of the edge connecting vertex . and vertex to c. Suppose we use the following heuristic: h(A) = 2 h(B) = 2 h(C) = 20 h(D) = 2 h(E) = 6 h(F) = 2 h(G) = 0 2 %3D h(H) %3D Recall that A* is just Dijkstra’s algorithm, except that vertices are given a priority equal to the sum of their Dijkstra priority (distance from the source) plus the heuristic distance, and also that we quit when the target is visited. Give the path (not order visited) that A* returns from A to G, you may not need all of the blanks: _A_ 2.
Y3
Let G be a connected graph with n vertices and m edges.Which of the following statements are true?(i) G is a tree if and only if n = m+1.(ii) G is a tree if and only if m = n+1.(iii) G is a tree if and only if the addition of any edgeto G will produce a unique cycle.(iv) G is a tree if and only if G contains at least onepath b etween any two vertices.(v) If G is connected, then G is a tree if and only if Gcontains at most one path between any two vertices.(vi) A connected subgraph of a tree is always a tree.
Let n be 22 . Let T be a binary rooted tree with n vertices. (a) What is the least number of levels that T can have? Explain your answer. (b) What is the greatest number of levels that T can have? Explain your answer. Please answer both a and b. I will provide you positive response. Thanks
Please help me with this algorithm. The algorithm should be in psuedocode format. Thank you. Consider a situation in which you are provided some minimum spanning tree Twhich was formed from the vertices and edges contained in the graph G = (V, E).Now, suppose that I provided you with some edge (u, v) such that u, v ∈ G.V andδ(u, v) = w(u, v) (they are directly connected). We can say that a new graph G'can be formed such that G' = (V, E ∪ (u, v)). Design an algorithm that constructs T'from G' in O(V + E) time in the worst case(it may be bounded below this, but it cannot be bounded higher).
I A E H F В G Suppose you run a topological sort on the shown graph starting at vertex B. Use the rule that when DFS has a choice of nodes to visit, it visits them in alphabetical order. What's the first vertex in the resulting topological order? What is the second? What is the third? What is the fourth?
10

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