Artificial Intelligence: A Modern Approach
3rd Edition
ISBN: 9780136042594
Author: Stuart Russell, Peter Norvig
Publisher: Prentice Hall
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Chapter 3, Problem 32E
Program Plan Intro
8-puzzle problem:
- In the below figures, the start state and goal state of the 8-puzzle problem is shown.
- The start state consists the unordered tiles and the goal state consists of ordered tiles.
- There are two heuristics are implemented. That are,
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Suggest a heuristic of your own to solve the 8-puzzle problem using A* algorithm and starting from the initial state
1 3 5 to the goal state 1 2 3
4 2 - 4 5 6
7 8 6 7 8 -
Answer the given question with a proper explanation and step-by-step solution.
You are asked to pick up a project on building highways to connect all cities in the country. The cost of building a highway between two cites i and j is c(i, j) > 0. If you were in charge from the beginning, this would have been a minimum spanning tree problem and could be solve easily with the algorithms covered in class. Since you pick it up halfway, however, some suboptimal choices have already been made by your predecessor. In other words, highways were already built between some pairs of cities. Design an algorithm to find a cost minimizing set of highways to built subject to the choices already made.
Do not copy others.
Search and learn three existing algorithms that use the dynamic programming strategy, in addition to those that we have discussed the class (“rod-cutting” and “matrix-chain”). For each algorithm, concisely and clearly describe:
1. The problem statement
2. The recursive structure in the solution.
3. Why does the recursion-based idea not work well ?
4. Why does dynamic programming work ?
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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- Start from any random state of the 8 puzzle problem. State the goal state for your problem. Then simulate the possible states that a stochastic hill climbing search and a first choice hill climbing search might take from the given state using manhattan distance heuristic. N.B. for stochastic hill climbing you can try to find the solution 2 times.arrow_forwardThis question is related from analysis of algorithms subject kindly solved it correctlyarrow_forwardBecause even though we may not understand them, algorithms can help us solve problems.arrow_forward
- For relatively small values of n, algorithms with larger orders can be more efficient than algorithms with smaller orders. Use a graphing calculator or computer to answer this question. For what values of n is an algorithm that requires n operations more efficient than an algorithm that requires [50 log2(n)] operations? (Assume n is an integer such that n > 1.) n?arrow_forwardBoth Dijkstra and Prim's algorithms are so fundamental in understanding the areas of greedy algorithms and Graph theory. Because of that, they are taught in literally every algorithms and graph theory class. So it is very important for you to have a complete and clear understanding of these algorithms. Also, understanding these two algorithms open the door to solving other similar problems. There are many articles and references available out there for the topics. You may do your own research as much as you can but you should come out with your own words to explain how they work in detail along with a few slides to summarize them. Please be mindful of the spirit of ELI5 and try to prove it in simple English.arrow_forwardConsider the “recursion tree” and “subproblem graph” for our two algorithms. The case n = 4 is illustrated below. For the case n = 4, the recursion tree has 16 vertices and 15 edges, while the subproblem graph has 5 vertices and 10 edges. For the case n = 10, determine the number of vertices and edges in the recursion tree, as well as the number of vertices and edges in the subproblem graph. Clearly justify your answers.arrow_forward
- Start from any random state of the 8 puzzle problem. State the goal state for your problem. Then simulate the possible states that a stochastic hill climbing search and a first choice hill climbing search might take from the given state using manhattan distance heuristicarrow_forwardSuppose you are using a search algorithm to solve the 15-puzzle problem (i.e., the 4x4 version of the sliding-block puzzle we discussed in class). What are the benefits and drawbacks of using a depth first search? What are the benefits and drawbacks of using a breadth first search?arrow_forwardExplain and model the Tower of Hanoi game using recursion concepts. Show step by step the moves that are needed (number of moves) to solve the game with four discs and check it with the formula obtained from the mathematical modeling of the problem.arrow_forward
- Modeling the spread of a virus like COVID-19 using recursion. Let N = total population (assumed constant, disregarding deaths, births, immigration, and emigration). S n = number who are susceptible to the disease at time n (n is in weeks). I n = number who are infected (and contagious) at time n. R n = number who are recovered (and not contagiuous) at time n. The total population is divided between these three groups: N = S n + I n + R n There are several hidden assumptions here that may or may not apply to COVID-19, such as a recovered person is assumed to not be able to get the disease a second time, at least within the time window being examined. On week 0 (the start), you assume a certain small number of people have the infection (just to get things going). Everyone else is initially susceptible, and no one is recovered. There are two constants of interest: Let period = time period that it takes for an infected person to recover (recover meaning they become not infectious to…arrow_forwardREAD AND SOLVE VERY CAREFULLY WITH PYTHONthanks in advance Given a jungle matrix N*M:jungle = [[1, 0, 0, 0],[1, 1, 0, 1],[0, 1, 0, 0],[1, 1, 1, 1,]]Where 0 means the block is dead end and 1 means the block can be used in the path from source to destination. Task: (Use Python)Starting at position (0, 0), the goal is to reach position (N-1, M-1).Your program needs to build and output the solution matrix, a 4*4 matrix with 1’s in positions used to get from the starting position (0,0) to the ending position (N-1, M-1) with the following constraints:- You can only move one space at a time.- You can only move in two directions: forward and down.- You can only pass thru spaces on the jungle matrix marked ‘1’If you cannot reach the ending position, print a message that you’re trapped in the jungle Algorithm:If destination is reached print the solution matrixElse Mark current cell in the solution matrix Move forward horizontally and recursively check if this leads to…arrow_forwardWhy do we care most about worst case Big-O analysis for algorithms?arrow_forward
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