Artificial Intelligence: A Modern Approach
3rd Edition
ISBN: 9780136042594
Author: Stuart Russell, Peter Norvig
Publisher: Prentice Hall
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Chapter 5, Problem 14E
Explanation of Solution
Alpha beta pruning
- The exact statement is that the
algorithms examines bm/2 + bm/2 − 1 nodes at level m...
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Chapter 5 Solutions
Artificial Intelligence: A Modern Approach
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- Given P(D|M) , P(M) ,and P(D′|M) , solve the following1. Using the main tree, prove all probabilities on the reverse tree.2. If P(D|M) = 0.3, P(M) = 0.1 ,and P(D′|M) = 0.65 find P(D)arrow_forward2. Exact Median Complexity Show that (2, 2, 3) ≤ 6 by finding a decision tree for median with height six.arrow_forwardConsider the following problem for path finding where S is the source, G is the Goal and O are obstacles. We can only move horizontally and vertically (not diagonally). We will not re-visit an already visited cell. - Simulate the application of Breadth-first search tree to find all paths from S to G. Provide the order of visit for each node. - Simulate the application of Depth-first search tree to find all paths from S to G. Provide the order of visit for each node. S O G Oarrow_forward
- Consider the vacuum-world problem defined as shown in the following figure-1. a. Which of the algorithms defined in this chapter would be appropriate for this problem? Should the algorithm use tree search or graph search? b. Apply your chosen algorithm to compute an optimal sequence of actions for a 3×3 world whose initial state has dirt in the three top squares and the agent in the center. c. Construct a search agent for the vacuum world, and evaluate its performance in a set of 3×3 worlds with probability 0.2 of dirt in each square. Include the search cost as well as path cost in the performance measure, using a reasonable exchange rate. d. Compare your best search agent with a simple randomized reflex agent that sucks if there is dirt and otherwise moves randomly. e. Consider what would happen if the world were enlarged to n × n. How does the performance of the search agent and of the reflex agent vary with n?arrow_forwardWrite an MST and EdgeWeightedGraph client check() that usesthe following cut optimality conditions implied by Proposition J to verify that a proposed set of edges is in fact an MST: A set of edges is an MST if it is a spanning tree andevery edge is a minimum-weight edge in the cut defined by removing that edge fromthe tree. What is the order of growth of the running time of your method?arrow_forwardSuppose a candidate solution p, where p is a phenotype consisting of 4 vertices. Suppose that minimum fitness occurs when no pair of vertices in p are connected, and maximum fitness occurs when all pairs of vertices in p are connected. Write a pseudocode on how to calculate the fitness F of p.arrow_forward
- Implement The dynamic programming algorithm for the leveled graph problem. pre-cond: G is a weighted directed layered graph, and s and t are nodes. post-cond: optSol is a path with minimum total weight from s tot, and optCost is its weight, and optNum is the number of possible optimal solutions.arrow_forwardgiven 2n-1+1 subsets obtained by a set S with n elements. Project an optimal algorithm that tests the given subsets to se if there are 2 subsets A and B, where A Union B is equal to S.arrow_forwardShow all the steps of Kruskal''s minimum cost spanning tree algorithm for a complete graph of 6 vertices where the weight of the edge between the distinct vertices i and j is |i-j-1|, for 1 <= i, j <= 6.arrow_forward
- Suppose we have the following undirected graph, and we know that the two bolded edges (B-E and G-E) constitute the global minimum cut of the graph. 1. If we run the Karger’s algorithm for just one time to find the global minimum cut, what is the probability for the algorithm to find the minimum cut correctly? Please show your reasoning process. 2. How many times do we need to run the Karger’s algorithm if we want to guarantee that the probability of success is greater than or equal to 0.95, by “success” we mean that there is at least one time the Karger’s algorithm correctly found the minimum cut. Please show your reasoning process. [You do not have to work out the exact value of a logarithm]arrow_forwardDetermine whether the two bipartite graphs below have a perfect matching. Justifyyour answer, either by showing a perfect matching or using Hall’s theorem to prove that it doesnot exist.arrow_forwardConsider the following greedy algorithm to solve the Traveling Salesman Problem: Start from any vertex (city). At any vertex, always select, among its neighbouring cities that have not been visited, the vertex that is the closest. Show that this algorithm does not always produce an optimal solution by giving a counter example. Note that by the definition of the TSP, the graph you provide must be a weighted and complete graph.arrow_forward
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