21.2-4Suppose that all edge weights in a graph are integers in the range from 1 to [V]. How fast canyou make Kruskal's algorithm run? What if the edge weights are integers in the range from 1 toW for some constant W?Kruskal's algorithmKruskal's algorithm finds a safe edge to add to the growing forest by finding, of all the edges that connect any two trees in the forest, an edge (u, v) with the lowest weight. LetC₁ and C₂ denote the two trees that are connected by (u, v). Since (u, v) must be a light edge connecting C₁ to some other tree, Corollary 21.2 implies that (u, v) is a safe edgefor C₁. Kruskal's algorithm qualifies as a greedy algorithm because at each step it adds to the forest an edge with the lowest possible weight.9(1)11141114781010(K)a1114(1)117.7.610(04(m) a117.68Figure 21.4, continued Further steps in the execution of Kruskal's algorithm.b1411114176101021

Finding the Cheapest Connections: Understanding Kruskal's AlgorithmImagine you're building a…

Answered: 21.2-4 Suppose that all edge weights in…

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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Java programming homework Need help with question c 14.52
Exercise 12.9 Given a weighted (connected) undirected graph G = (V, E, w), with m =n+ 0(1) edges (i.e., the number of edges is at most the number of vertices plus some constant), give an O(n)-time algorithm to compute the minimum spanning tree of G. Prove the correctness and the running time of your algorithm. (Hint: Think of how one can eliminate an edge from being in the MST.)
16.8 Explain why it is necessary that the Edge class “show through” the Graph interface. (Hint: Consider implementations of the Iterator constructed by the edges method.)16.9 Compare and contrast the performance of the adjacency list and adjacency matrix implementations of graphs
C++ Given a directed graph. The task is to find a shortest path from vertex 0to a target vertex v. You may adapt Breadth First Traversal of thisgraph starting from 0 to achieve this goal.Note: One can move from node u to node v only if there's an edge from u to v and find the BFS traversal of the graph starting from the 0th vertex, from left to right according to the graph. Also, you should only take nodes directly or indirectly connected from Node 0 in consideration. ExampleInput:6 8 20 10 41 20 33 54 55 23 1Output:0 1 2 Use the driver code typed out below. // { Driver Code Starts #include <bits/stdc++.h>using namespace std; // } Driver Code Endsclass Solution { public: // Function to return a path vector consisting of vertex ids from vertex 0 to target vector shortestPath(int V, vector adj[], int target) { // Enter code here! }}; // { Driver Code Starts.int main() { int tc; cin >> tc; while (tc--) { int V, E, target; cin >> V >> E >> target; vector…
using vertex 'A' as the starting vertex, perform BFS traversal on the graph, and collect the visited nodes in a list. Break ties alphabetically (i.e., the adjacent nodes from node E should be tried in the order A, B, C, D, H). Note: write a single vertex at one text field, e.g., A, without any space and quotation marks.
b3
Undirected graph is given with the list of edges. Build an adjacency matrix. Print the number of ones in adjacency matrix. Graph can contain multiple edges and loops. Input First line contains number of vertices n. Each of the next line contains one edge. Read the edges till the end of file. Output Build an adjacency matrix. Print the number of ones in adjacency matrix. Sample input 3 1 2 23 22 32 Sample output 5
36. Let G be a simple graph on n vertices and has k components. Then the number m of edges of G satisfies n-k ≤m if G is a null graph. This statement is A. sometimes true B. always true C. never true D. Neither true nor false
Definition: We define a path in a graph to be short if it contains ≤ 100 edges. Note that we are looking at the number of edges, not the number of vertices. The Problem: •INPUT – An unweighted DAG G = (V, E) – Two specific vertices s, t ∈V •OUTPUT: the number of different short paths in G from s to t. You don’t have to output the actual paths; you just have to figure out how many of them there are. Show a dynamic programming algorithm that solves the above problem in O(|E|) time. You only need to write pseudocode, nothing else. NOTE: a reminder that you can assume in this class that all arithmetic operations (multiplication, addition, etc.) take O(1) time, even if the numbers are very big.
B D F. E G H Suppose we run the Floyd-Warshall transitive closure algorithm on this graph. What is one edge that will be added in the first pass, paths through A? (For an edge from A to B, for example, you would write AB. If there is none, write NONE.) | What is one edge that will be added in the second pass? What is one edge that will be added in the third pass? What is the runtime of Floyd-Warshall on a graph with N vertices and M edges?
Is the following statement true or false? a. Performing one rotation always preserves the AVL property. b. For any two functions f and g, we always have either f = O(g) or g = O(f). c. We run the breadth-first search algorithm (BFS) on a undirected graph G such that all edges have the same weight. BFS returns the shortest path from a source vertex s to any other vertex.
If there is an Euler path that starts at AA and ends at some other vertex, give it. Otherwise enter DNE.This should be a list of letters, from A to the other vertex: e.g. ACBDEAD (if that were even possible!). Path: Since this is a planar graph, the number of regions - arcs + nodes equals what number?

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