Artificial Intelligence: A Modern Approach
3rd Edition
ISBN: 9780136042594
Author: Stuart Russell, Peter Norvig
Publisher: Prentice Hall
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Chapter 3, Problem 21E
Program Plan Intro
Breadth-first search:
- Breadth First Search (BFS), is the
algorithm that traverses or searches tree or graph data structures. - The search starts with the tree root, and then explores all the neighbor nodes at the present depth before moving to the nodes at the next depth level.
- The strategy used in this is quite opposite to depth-first search.
Depth First Search:
- Depth First Search (DFS), is the algorithm to traverse or search tree or graph data structures.
- The search starts with the root node, and then explores as far as possible along each branch before backtracking.
Uniform Cost Search:
- Uniform Cost Search (UCS) is the algorithm known to best for a search problem, and this does not include the use of heuristics.
- It solves any general graph for an optimal cost.
- Uniform cost search searches the branches which are more or less the same in cost.
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True or False (If your answer to the question is "False", explain why, and provide correction when possible).
(a) Let h(n) be the heuristics for the node n, h(m) be the heuristics for the node m, d(m,n) be the actual minimal cost from node m to n in a graph. A* satisfies the monotone restriction iff d(m,n)
Chapter 3 Solutions
Artificial Intelligence: A Modern Approach
Ch. 3 - Explain why problem formulation must follow goal...Ch. 3 - Prob. 2ECh. 3 - Prob. 3ECh. 3 - Prob. 4ECh. 3 - Prob. 5ECh. 3 - Prob. 6ECh. 3 - Prob. 8ECh. 3 - Prob. 9ECh. 3 - Prob. 10ECh. 3 - Prob. 11E
Ch. 3 - Prob. 12ECh. 3 - Prob. 13ECh. 3 - Prob. 14ECh. 3 - Prob. 15ECh. 3 - Prob. 16ECh. 3 - Prob. 17ECh. 3 - Prob. 18ECh. 3 - Prob. 20ECh. 3 - Prob. 21ECh. 3 - Prob. 22ECh. 3 - Trace the operation of A search applied to the...Ch. 3 - Prob. 24ECh. 3 - Prob. 25ECh. 3 - Prob. 26ECh. 3 - Prob. 27ECh. 3 - Prob. 28ECh. 3 - Prob. 29ECh. 3 - Prob. 31ECh. 3 - Prob. 32E
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Similar questions
- Exercise d. Coloring, with the oracle's help. (Textbook problem 4.2) Analogous to the previous problem, but a little trickier: suppose we have an oracle for the decision problem GRAPH k-COLORING. Show that by asking a polynomial number of questions, we can find a k-coloring if one exists. Hint: You want to iteratively compute a coloring, where partway through, some nodes have colors assigned already and others do not. You need to ask the oracle about a modified version of the original graph to learn if this partial coloring can be finished; if not, make a different choice when coloring the next node.arrow_forwardTrue or False (If your answer to the question is "False", explain why, and provide correction when possible). (a) Let h(n) be the heuristics for the node n, h(m) be the heuristics for the node m, d(m,n) be the actual minimal cost from node m to n in a graph. A* satisfies the monotone restriction iff d(m,n) <= |h(n)-h(m)|. (b) If an A* heuristics is admissible then it satisfies the monotone restriction. (c) Best-first search guarantees optimality in its returned solution. (d) Least-cost-first search guarantees optimality in its returned solution. (e) If all edges are with unit cost, then Breadth-first search guarantees optimality in its returned solution.arrow_forward5. (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…arrow_forward
- Question 8 Greedy best-fırst search is equivalent to A* search with all step costs set to 0. O True O False Question 9 If you had implemented Uniform Cost Search (the graph search version) in Programming Assignment 1, it would have found an optimal solution. (You may assume that the path costs are kept with the nodes on the frontier and explored lists and checked when comparing newly generated states to what has been seen before.) O True O False Question 10 A* search with an admissible heuristic always expands fewer nodes than depth-first search. O True O Falsearrow_forwardDo some outside research on depth-first traversal as it relates to traversing graphs. Then answer the following questions: a. Suppose you have an arbitrary connected graph G, shown in the image below. Use the vertex A as your starting point. Write out the order in which the algorithm could traverse the graph with a depth-first search, and explain your reasoning (there are multiple correct answers, hence the need for an explanation). b. Use a proof by induction to prove that when a depth-first traversal is performed, every vertex v in your graph G will have been visited at least one time. B D H E A G с I FLarrow_forward[Introduction to the Design and Analysis of Algorithms, 3rd Edition] Maxima search. A point (xi, yi) in the Cartesian plane is said to be dominated by point (xj , yj ) if xi ≤ xj and yi ≤ yj with at least one of the two inequalities being strict. Given a set of n points, one of them is said to be a maximum of the set if it is not dominated by any other point in the set. For example, in the figure below, all the maximum points of the set are circled. Design an efficient algorithm for finding all the maximum points of a given set of n points in the Cartesian plane. What is the time efficiency class of your algorithm?arrow_forward
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- Apply the Breadth first traversal algorithm to the undirected graph G given in Example and replicated here for convenience. The goal is to do a Breadth first search for the key 9.arrow_forwardProve that the following problem, given a set S of integers and a number t, is of the NP class. Is there a subset of S whose elements add up to t?Note: An issue with data structures and algorithmsarrow_forwardFor straight-line distance heuristic, draw the search tree after expansion of each node until the termination of the algorithm for: a) Greedy best-first search (label all node with their h values). What is the solution (list of visited cities) found by the algorithm? b) A* search (label all nodes with their f values). What is the solution (list of visited cities) found by the algorithm?arrow_forward
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