Assume the graph is represented by two linear arrays corresponding to the end vertices of edges. Write and explain the algorithm to find a spanning tree of the graph with an example.
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- Path Search in A Maze A two dimensional array of red and green entries represents a maze. Green entries are passable and red entries are blocked (like a wall). Two special green entries en and ex denote the entrance and exit of the maze. Abstract the problem as a graph.2. Q1) You are given an undirected connected planar graph. There are 10 vertices and 7 faces in the graph. What is the number of edges in the graph? Note that: A graph is said to be planar if it can be drawn in a plane so that no edge cross. Q2) In how many ways can we pick any number of balls from a pack of three different balls? Q3) The distance between 2 points A and B is 1320Km. Two cars start moving towards each other with 50 Km/hr and 60 Km/hr. After how many hours do they meet?Task 3. Adjacency List using linked list. Your program must ask the number of vertices and then the list of vertices to store. Afterwards, the adjacent vertices to each of the vertex to store the information. You may consider the following simple graph to test your program. a b d e
- 1. Write a program (WAP) to create an undirected graph using adjacency matrix representation.Number of nodes and edges should be taken from the user. After creating the graph, performfollowing operations: (i) Search a node. Take the node number from the user. If the node is found then print its associatededges.(ii) Insert a node in the graph.(iii) Insert an edge in the graph. Take the node numbers from the user between which the edge is tobe inserted.(iv) Delete a node from the graph. Take the node number to be deleted from the user.(v) Apply DFS on the graph and print the graph traversal.(vi) Apply BFS on the graph and print the graph traversal.2. Solve the above problem using adjacency list representation.1. Let Sn denote a directed graph with n vertices, numbered from 1 to n, in which there are edges from vertex 1 to all other vertices, and from all other vertices back to vertex 1, but no other edges. Write the Python adjacency list representation for S6.Exercise # 2 - Detecting Cycle between List of N Airports The following graph is an example from Rosen (2011). It shows the flights and distances between some of the major airports in the United States. Dallas 200 1300 200 Austin Washington Denver 1400 Atlanta 160 800 800 Chicago Houston Write a function that takes a list of N airports and checks if they form a cycle of size N. {A cycle is a directed path that starts and ends at the same vertex. Before writing code, make sure you can identify cycles yourself} >> check_cycles (G, ['Austin','Houston', 'Atlanta','Washington','Dallas'l) Yes >>> check_cycles (G, ['Austin', 'Houston','Atlanta','Washington']) No 600 600 780 0000 000L 006
- 3. Refer to the graph G below. w i h e G Map out all of the following graphs: a) walk b) path c) circuit d) сycle e) triangle6. Write a java Program to implement Breadth First Search traversal of Graph.Enter the number of vertices in graph us 4.Python Graph Algorithms: Minimum Spanning Trees Note: There are helper functions (see 'required' below), and some of them (like Kruskal's Algorithm, WeightedQuickUnion, and such) can help answering this problem. Problem: Suppose you are an engineer working on designing a road network for a new town. The town has many residential areas and commercial centers that need to be connected efficiently. You decided to represent the town as a connected, undirected graph where each vertex represents a location, and each edge represents a road connecting two locations. The weight of each edge represents the distance between the two locations. To ensure the road network is efficient, you need to find the minimum spanning tree of the graph. However, due to budget constraints, you can only construct roads with a maximum distance limit. You need to determine for how many pairs of locations, the minimum spanning tree of the graph remains the same when the maximum distance limit of a road is increased…
- Prim's C++ algorithm. If you provide the software the number of vertices and adjacency matrix of a graph, it will use Prim's method to discover the shortest path across the graph.1. BFS (Breadth First Search) and DFS (Depth First Search) algorithms on graphs. a. Represent the following graph in computer. D b. Implement BFS in Java and calculate the BFS result on the above graph using your code. The source (or starting point) is A. c. Implement DFS in Java and calculate the DFS result on the above graph using your code. The source (or starting point) is A. d. What is the time complexity of your BFS algorithm and why? What is the time complexity of your DFS algorithm and why?DATA STRUCTURES AND ALGORITHMS C++ Write an algorithm which provides a path from a specific source to destination node in a graph withminimum stops. Draw a directed graph from the following adjacency list. Simulate/dry run your algorithm on it and provide step-by-step updates of values in used data structure(s) considering “A” as source and “J” asdestination.