You have to implement two function in C++ using Adjacency matrix
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- Write a Java program to find the Adjacency Matrix Representation using Directed Graph. а. Insert new nodes and directed edge between two nodes b. Display the representationYou need to implement Prim's algorithm for mst creation. Your function is going to take a vector<vector<int>> or equivalent representing a graph and it will return another vector<vector<int>> or equivalent representing the chosen edges for the minimum spanning tree.In this problem you will design an algorithm that takes as input a directed acyclic graph G = (V,E) and two vertices s and t, and returns the number of simple paths from s tot in G. For example, the directed acyclic graph below contains exactly four simple paths from vertex p to vertex v: pov, poryv, posryv, and psryv. Notice: your algorithm needs only to count the simple paths, not list them. m y W Design a recursive backtracking (brute-force) algorithm that determines the number of paths from s to t. Write down the pseudocode of your algorithm and prove its correctness, i.e., convince us that it works beyond any doubt. (Hint: using induction.).
- Write pseudocode to find all pairs shortest paths using the technique used in Bellman-Ford's algorithm so that it will produce the same matrices like Floyd-Warshall algorithm produces. Also provide the algorithm to print the paths for a source vertex and a destination vertex. Describe the properties of the algorithm you provide and the run time for your algorithm in detail.If we need a lot of adding and removing edges to a graph, it is better to represent the graph as O Adjacency matrix O Adjacency list5. Consider a directed graph G with n nodes. Write a function findUnreachableNode that takes a node and prints all the nodes that are unreachable from the given node. You can use either adjacency list or adjacency matrix to solve this problem. Function Signature: findUnreachableNode (int node) For example: In the following graph, findUnreachableNode (0) will return 4, 6, 7 as they are unreachable from node 0. 1 7 4 Good luck!!!
- Write a function that returns true (1) if there is an edge between two vertices u and v in an adjacency-listed directed graph.We need two methods for topological sorting—a method to determine if avertex has no successors and a method for removing a vertex from a graph.Write the method for determining no successors first.We are given an undirected connected graph G = (V, E) and vertices s and t.Initially, there is a robot at position s and we want to move this robot to position t by moving it along theedges of the graph; at any time step, we can move the robot to one of the neighboring vertices and the robotwill reach that vertex in the next time step.However, we have a problem: at every time step, a subset of vertices of this graph undergo maintenance andif the robot is on one of these vertices at this time step, it will be destroyed (!). Luckily, we are given theschedule of the maintenance for the next T time steps in an array M [1 : T ], where each M [i] is a linked-listof the vertices that undergo maintenance at time step i.Design an algorithm that finds a route for the robot to go from s to t in at most T seconds so that at notime i, the robot is on one of the maintained vertices, or output that this is not possible. The runtime ofyour algorithm should ideally be O((n + m) ·T ) but you will…
- Write a function that returns true (1) if there is an edge between two vertices u and v in an adjacency-list directed graph.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…The Graph Data Structure is made up of nodes and edges. (A Tree Data Structure is a special kind of a Graph Data Structure). A Graph may be represented by an Adjacency Matrix or an Adjacency List. Through this exercise, you should be able to have a better grasp the Adjacency Matrix concept. You are expected to read about the Adjacency Matrix concept as well as the Adjacency List concept. Suppose the vertices A, B, C, D, E, F, G and H of a Graph are mapped to row and column indices(0,1,2,3,4,5,6,and 7) of a matrix (i.e. 2-dimensional array) as shown in the following table. Vertex of Graph Index in the 2-D Array Adjacency Matrix Representation of Graph A B 2 F 6. H 7 Suppose further, that the following is an Adjacency Matrix representing the Graph. 3 4 5. 6. 7 0. 1 1 1 1 01 1 01 1. 3 14 1 1 1 6. 1 Exercise: Show/Draw the Graph that is represented by the above Adjacency matrix. Upload the document that contains your result. (Filename: AdjacencyMatrixExercise.pdf) Notes: -The nodes of the…