JAVA Code Required* You are given a convex polygon of n vertices P1, P2, ..., Pn (in counter-clock or clock order). Each vertex is assigned with a weight wi. Find a subset of vertices that includes vertex 1. 1 =i1
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- Dynamic Programming - Finding the Best Delivery Route Problem: Assume that you work for a pizza bakery as a delivery boy/girl. You are responsible for delivering pizzas prepared based on online orders. You collect orders once an hour, then start delivering. You would like to determine the route where you deliver all pizzas in minimum time. You can illustrate this problem as follows: The bakery and customers are vertices and all of them are connected (there is no pair of vertices that are not connected with an edge. The weight of edges is the time that you need to take to travel between vertices. The edges are two-way (your graph is undirected). Please solve this problem using the DP technique. Show five steps of DP.3. a) How can you store the following graph in a computer memory? 5 3 1 3 3 0 2 -2 12 4 7 2 b) Determine the shortest path from vertex '0' to vertex '2' of the above-mentioned graph. c) Illustrate 'Depth First Search' for the above-mentioned graph.5. * Show that there is an algorithm to decide if a graph has a vertex cover of size k, with running time O(kn +20(k)). Hint: use the FPT algorithm discussed in class and the results of the previous problem.
- Lets say you are currently at vertex f, after you have relaxed all of the outgoing edges, what would be the distance of vertex g? 7 А.) 7 В.) 3 f 5 10 С.) 10 h D.) 21 6.lert dont submit AI generated answer. Write a program that reads a weighted graph.The program must print on the screen the distance matrix and the "PI" matrix of the shortest paths obtained by the Floyd-Warshall algorithm. Input: Receives n and m; n is the total number of vertices and m the total number of arcs.Next, m lines, each line with a trio of integers, corresponding to the beginning and end of the arc, followed by the weight of the arc.(Vertices are identified from 0 to n-1.) Output: Prints the distances and shortest paths obtained by the Floyd-Warshall algorithm. Exemple: Input: 5 9 0 1 3 0 2 8 0 4 -4 1 3 1 1 4 7 2 1 4 3 0 2 3 2 -5 4 3 6 Output: [[ 0 1 -3 2 -4] [ 3 0 -4 1 -1] [ 7 4 0 5 3] [ 2 -1 -5 0 -2] [ 8 5 1 6 0]] [[-1 2 3 4 0] [ 3 -1 3 1 0] [ 3 2 -1 1 0] [ 3 2 3 -1 0] [ 3 2 3 4 -1]]To help jog your memory, here are some definitions: Vertex Cover: given an undirected unweighted graph G = (V, E), a vertex cover Cy of G is a subset of vertices such that for every edge e = (u, v) = E, at least one of u or v must be in the vertex cover Cy. Set Cover: given a universe of elements U and a collection of sets S = {S₁, ..., Sm}, a set cover is any (sub)collection C's whose union equals U. In the minimum vertex cover problem, we are given an undirected unweighted graph G = (V, E), and are asked to find the smallest vertex cover. For example, in the following graph, {A, E, C, D} is a vertex cover, but not a minimum vertex cover. The minimum vertex covers are {B, E, C} and {A, E, C}. A B E с F D Then, recall in the minimum set cover problem, we are given a set U and a collection S = {S₁, ..., Sm} of subsets of U, and are asked to find the smallest set cover. For example, given U := {a, b, c, d}, S₁ := {a, b,c}, S₂ = = {b,c}, and S3 := {c, d), a solution to the problem is C's…
- Given the directed weighted graph class by adjacency matrix, develop java method to calculate and print the out-edges of each node in the following Graph. 50 10 40 20 60 E. 30 Output: -- Print the number of connected vertices of the Graph А: 2 B: 3 C: 0 D: 1 Е: 0Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. You are given an undirected chart with n vertices and m edges. Additionally, you are given an integer k. Find either a faction of size k or a non-void subset of vertices to such an extent that every vertex of this subset has essentially k neighbors in the subset. In case there are no such inner circles and subsets report about it. A subset of vertices is known as a faction of size k if its size is k and there exists an edge between each two vertices from the subset. A vertex is known as a neighbor of the other vertex if there exists an edge between them. Input The primary line contains a solitary integer t (1≤t≤105) — the number of experiments. The following lines contain portrayals of experiments. The principal line of the depiction of each experiment contains three integers n, m, k (1≤n,m,k≤105, k≤n). Every one of the following m lines contains two integers u,v…: The adjacency matrix that represents the following graph is 3 1. 4.
- 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…Specifications: You will create an implementation of this algorithm. Your driver program should provide a graph and a source vertex in the graph. Your implementation should use Dijkstra's Algorithm to determine the shortest path using adjacency matrix representation. Specifically, given a graph and a source vertex in the graph, find the shortest paths from source to all vertices in the given graph, using Dijkstra's Algorithm.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