Artificial Intelligence: A Modern Approach
3rd Edition
ISBN: 9780136042594
Author: Stuart Russell, Peter Norvig
Publisher: Prentice Hall
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Chapter 3, Problem 28E
Program Plan Intro
Suboptimal solution:
- Suboptimal heuristic search
algorithms such as weighted A* and greedy best-first search are widely use to solve problems for which guaranteed optimal solutions are too expensive to obtain. - To guide their search, these algorithms rely on a heuristic function.
- These algorithms are used because, when constructing the heuristics, the optimal search can fail when considering the suboptimal search.
Explanation of Solution
Proof:
- As given in the problem, suppose
- Consider any node n on a path to an optimal goal. Here,
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Question 2:
Consider the 0/1 knapsack problem. Given Nobjects where each object is specified by a
weight and a profit, you are to put the objects in a bag of capacity C such that the sum of
weights of the items in the bag does not exceed Cand the profits of the items is maximized.
Note that you cannot use an item type more than once.
a. Using dynamic programming, write an algorithm that finds the maximum total
value according to the above constraints.
b. What is the complexity of your algorithm?
c. Show the dynamic programming table for the following data:
W= { 2 ,7 , 1} , P={ 3 ,15 , 2 } and C=8.
There are n ≥ 2 married couples who need to cross a river. They have a boat
that can hold no more than two people at a time. To complicate matters, all the husbands
are jealous and will not agree on any crossing procedure that would put a wife on the
same bank of the river with another woman's husband without the wife's husband being
there too, even if there are other people on the same bank. Can they cross the river under
such constraints? Solve the problem for n = 2.
Suppose a salesperson is planning a sales trip that includes n cities. Each city is
connected to some of the other cities by a road. To minimize travel time, the
salesperson wants to determine the shortest route that starts at the salesperson’s
home city, visits each of the cities once, and ends up at the home city.
This problem of finding the shortest route is called the Travelling Salesperson Problem
(TSP) and is a well-known problem that can be solved using Dynamic Programming.
Research about the TSP problem and find an algorithm based on Dynamic
Programming for that. Explain the approach, the algorithm, and its time complexity.
Use an example to explain the way the algorithm operates
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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