Using Hill-climbing search, transform the initial-state 8-puzzle to goal-sate Initial-state Goal-sate Define h as the Sum of distances of each tile from its goal position, Expand the state with minimum h at each step; the state with the minimum h will be in memory.
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Using Hill-climbing search, transform the initial-state 8-puzzle to goal-sate
Initial-state Goal-sate
Define h as the Sum of distances of each tile from its goal position,
Expand the state with minimum h at each step; the state with the minimum h will be in memory.
Step by step
Solved in 2 steps with 2 images
- In this question you will explore Graph Colouring algorithms. Given a graph G, we say that G is k-colourable if every vertex of G can be assigned one of k colours so that for every pair u, v of adjacent vertices, u and v are assigned different colours. The chromatic number of a graph G, denoted by χ(G), is the smallest integer k for which graph G is k-colorable. To show that χ(G) = k, you must show that the graph is k-colourable and that the graph is not (k − 1)-colourable. Question: It is NP-complete to determine whether an arbitrary graph has chromatic number k, where k ≥ 3. However, determining whether an arbitrary graph has chromatic number 2 is in P. Given a graph G on n vertices, create an algorithm that will return TRUE if χ(G) = 2 and FALSE if χ(G) 6= 2. Clearly explain how your algorithm works, why it guarantees the correct output, and determine the running time of your algorithm.The clique problem is finding cliques in a diagram. A clique is a set of vertices that are adjacent to each other. The 4-clique is a set of four knots all connected. So, in this example of the 4-clique problem, we have a graph with 7 vertices. A brute force algorithm searched all possible combinations of four vertices and found a set that formed a clique. If you want to understand more about it, the problem (and if possible read on). Note that the clique problem is NP-complete, so deterministic search is not practical for large graph sizes. This makes it an ideal candidate for evolutionary exploration. In this problem, we have to assume that we are given the problem of implementing the 4-clique problem as an evolutionary algorithm for an arbitrary graph with an arbitrary number of vertices (an n-vertex graph). If 4 cliques are found, the algorithm succeeds. 1. Provide an algebraic expression, in terms of n, for the size of the phenotypic search space (the number of possible…5. (This question goes slightly beyond what was covered in the lectures, but you can solve it by combining algorithms that we have described.) A directed graph is said to be strongly connected if every vertex is reachable from every other vertex; i.e., for every pair of vertices u, v, there is a directed path from u to v and a directed path from v to u. A strong component of a graph is then a maximal subgraph that is strongly connected. That is all vertices in a strong component can reach each other, and any other vertex in the directed graph either cannot reach the strong component or cannot be reached from the component. (Note that we are considering directed graphs, so for a pair of vertices u and v there could be a path from u to v, but no path path from v back to u; in that case, u and v are not in the same strong component, even though they are connected by a path in one direction.) Given a vertex v in a directed graph D, design an algorithm for com- puting the strong connected…
- 2. An undirected graph G can be partitioned into connected components, where two nodes are in the same connected component if and only if there is a path connecting them. Design and analyze an efficient algorithm that computes the connected components of a graph G given in adjacency list format. Be sure to give a correctness argument and detailed time analysis. You can use algorithms from class as a sub-procedure, but be sure to use the claims proven about them carefully. A good algorithm has time approximately 0(n + m) where the graph has n nodes and m edges.Review the 8-puzzle problem. Consider that the initial state is 1 3 48 27 6 5and the goal state is1 2 38 47 6 5Apply the breath-first-search method to obtain the path from the initial state to the goal state. Youneed to show the corresponding search tree. As soon as you find the goal state, you can stop the searchprocess.3) The graph k-coloring problem is stated as follows: Given an undirected graph G= (V,E) with N vertices and M edges and an integer k. Assign to each vertex v in V a color c(v) such that 136. 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 falseConsider a graph and implement Breadth-first search, Uniform-cost search, Depth-first search, Depth-limited search, Iterative deepening depth-first search and Bidirectional search using your favorite programming language. Also draw and visualize the solution.3) The graph k-coloring problem is stated as follows: Given an undirected graph G = (V,E) with N vertices and M edges and an integer k. Assign to each vertex v in Va color c(v) such that 1< c(v)Artificial Intelligence - Adversarial Search 1. Consider the following three variants of minimax search: the simple version, alpha-beta search, anddepth-limited search, and consider the games of tic-tac-toe and chess. For the chess game, supposethat the Threefold Repetition Rule and the Fifty-Move Rule, and the similar rules if any, are notconsidered, i.e., the game will not terminate if the same position occurs multiple times. For eachcombination of minimax variant and game, answer the following question: can that minimax variantpossibly never terminate, in computing the best next move? Justify your answer.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. (1) Abstract the problem as a graph; (2) Design an efficient algorithm (pseudo code) to find a shortest path from en to ex if it exists and then print out the path. Analyze the complexity of your algorithm.6. In Java create an algorithm for an undirected graph with n vertices and m edges that...- Takes as a parameter some integer k- Returns the maximum induced subgraph where each vertex of that subgraph has a degree greater than or equal to k (or returns null if no such subgraph exists)- Operates in O(n + m) timeSEE MORE QUESTIONSRecommended textbooks for youDatabase System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill EducationStarting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSONDigital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSONC How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSONDatabase Systems: Design, Implementation, & Manag…Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage LearningProgrammable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill EducationDatabase System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill EducationStarting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSONDigital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSONC How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSONDatabase Systems: Design, Implementation, & Manag…Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage LearningProgrammable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education