Artificial Intelligence: A Modern Approach
3rd Edition
ISBN: 9780136042594
Author: Stuart Russell, Peter Norvig
Publisher: Prentice Hall
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Chapter 5, Problem 20E
a.
Explanation of Solution
Finite leaf values
- There is no pruning.
- In a max tree, the...
b.
Explanation of Solution
Pruning in expectimax tree
- There is no pruning.
- An unseen leaf might have a value arbitrarily highe...
c.
Explanation of Solution
Nonnegative leaf values
- There is no pruning.
- In a max tree, ...
d.
Explanation of Solution
Nonnegative leaf values
- There is no pruning.
- Nonnegative value...
e.
Explanation of Solution
Leaf values in a range
- There is pruning.
- If the first...
f.
Explanation of Solution
Leaf values in a range
- There is pruning.
- Suppose the first action at the root has value 0...
g.
Explanation of Solution
Outcomes of a chance
- Highest probability first...
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You are given a weighted tree T.(As a reminder, a tree T is a graph that is connected and contains no cycle.) Each node of the tree T has a weight, denoted by w(v). You want to select a subset of tree nodes, such that weight of the selected nodes is maximized, and if a node is selected, then none of its neighbors are selected.
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) <= |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.
Artificial Intelligence - Adversarial Search - a Game with uncertainty
1. In the following, a “max” tree consists only of max nodes, whereas an “expectimax” tree consistsof a max node at the root with alternating layers of chance and max nodes. At chance nodes, alloutcome probabilities are nonzero. The goal is to find the value of the root with a bounded-depthsearch. For each of following statements, either give an example or explain why this is impossible.
a) Assuming that leaf values are finite but unbounded, is pruning (as in α-β pruning) ever possiblein a max tree?b) Is pruning ever possible in an expectimax tree under the same conditions?c) If leaf values are all nonnegative, is pruning ever possible in a max tree? Give an example, orexplain why not.d) If leaf values are all nonnegative, is pruning ever possible in an expectimax tree? Give anexample, or explain why not.e) If leaf values are all in the range [0,1], is pruning ever possible in a max tree? Give an example,or explain…
Chapter 5 Solutions
Artificial Intelligence: A Modern Approach
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Similar questions
- 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)arrow_forwardProblem 6 Consider a data set that contains 4 Boolean attributes A, B, C, and D, and a Boolean class y. For the Boolean expression below (between the class the rest of the attributes), it is possible to construct a smaller decision tree that perfectly classifies the data without generating the complete tree (i.e., the number of leave nodes is less than 16). Then, draw such a tree. and y = A ^ BA C ^ Darrow_forwardDescribe in as few as one or as many as a few words as possible the differences between a decision tree and a random forest. In utilising the random forest technique, what are some ways that we may ensure that randomization will occur twice?arrow_forward
- True/False. Give a short explanation. i. Let T be a tree constructed by Dijkstra's algorithm for a weighted connected graph G. T is a spanning tree of G? ii. Let T be a tree constructed by Dijkstra's algorithm for a weighted connected graph G. T is a minimum spanning tree of G? iii. If an NP-complete problem can be solved in linear time, then all NP-complete problems can be solved in linear time. iv. If P # NP, there could be a polynomial-time algorithm for SAT.arrow_forwardYou use your favorite decision tree algorithm to learn a decision tree for binary classification. Your tree hasJ leaves indexed j = 1, . . . , J. Leaf j contains nj training examples, mj of which are positive. However,instead of predicting a label, you would like to use this tree to predict the probability P(Y = 1 | X) (whereY is the binary class and X are the input attributes). Therefore, you decide to have each leaf predict a realvalue pj ∈ [0, 1]. -What are the values pj that yield the largest log likelihood? Show your work.arrow_forwardInference in Bayesian networks is NP-hard in the worst case because it includes propositional logic inference as a special case. Write down a Bayesian network, where the nodes represent logical sentences, that implements modus ponens inference rule A ⇒ B, A infer B.arrow_forward
- Consider a graph G, where each of the edges have different weights. Let T1 be the minimum-weight spanning tree produced by Kruskal's Algorithm, and let T2 be the minimum-weight spanning tree produced by Prim's Algorithm. I claim that T1 and T2 must be identical spanning trees - i.e., the exact same set of edges must appear in both trees. Determine whether this claim is TRUE or FALSE. If your answer is TRUE, see if you can figure out why the claim is true. If your answer is FALSE, see if you can come up with a counterexample.arrow_forwardCorrect answer only. Else i will dislike. The guide of the maze shapes a tree with n rooms numbered from 1 to n and n−1 burrows associating them to such an extent that it is feasible to go between each pair of rooms through a few passages. The I-th room (1≤i≤n) has simulated intelligence hallucination rate. To go from the x-th space to the y-th room, there should exist a passage among x and y, and it takes max(|ax+ay|,|ax−ay|) energy. |z| means the outright worth of z. To forestall grave looters, the labyrinth can change the hallucination pace of any room in it. Chanek and Indiana would ask q inquiries. There are two kinds of inquiries to be finished: 1 u c — The figment pace of the x-th room is changed to c (1≤u≤n, 0≤|c|≤109). 2 u v — Chanek and Indiana ask you the base amount of energy expected to take the mysterious fortune at room v in case they are at first at room u (1≤u,v≤n). Help them, so you can get a part of the fortune! Input :The primary line contains two integers n and…arrow_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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