Artificial Intelligence: A Modern Approach
3rd Edition
ISBN: 9780136042594
Author: Stuart Russell, Peter Norvig
Publisher: Prentice Hall
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Expert Solution & Answer
Chapter 4, Problem 5E
Explanation of Solution
Determining the information and using it by the
- See figure S4.1 for the adapted algorithm. For states that OR-SEARCH finds a solution for it records the solution found.
- If it later visits state and the solution is immediately returns by that state.
- The user has to be careful when the OR-SEARCH algorithm fails to find the solution.
- As the user do not allow the cycles, the state can be solved by depending on the path to that solution...
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Students have asked these similar questions
In hill-climbing algorithms there are steps that make lots of progress and steps that make very little progress. For example, the first iteration on the input given might find a path through the augmentation graph through which a flow of 30 can be added. It might, however, find the path through which only a flow of 2 can be added. How bad might the running time be when the computation is unlucky enough to always take the worst legal step allowed by the algorithm? Start by taking the step that increases the flow by 2 for the input. Then continue to take the worst possible step. You could draw out each and every step, but it is better to use this opportunity to use loop invariants. What does the flow look like after i iterations? Repeat this process on the same graph except that the four edges forming the square now have capacities 1,000,000,000,000,000 and the crossover edge has capacity 1. (Also move t to c or give that last edge a large capacity.)1. What is the worst case number of…
Warshall's algorithm is applied on the following graph. Show the values of the table element "c to a"
for each step of the algorithm. Use -1 for infinity. Initially (at step 0) the table element is -1. (Table
elements are listed in alphabetical order from a to g, and this order is used for the steps of the
algorithm. Accordingly in the first step the paths going through a are used.)
a
...
1
2
2
2
(f
1
2
4
The Graph Data Structure is made up of nodes and edges. (A Tree Data Structure is a special kind of a
Graph Data Structure). A Graph may be represented by an Adjacency Matrix or an Adjacency List. Through
this exercise, you should be able to have a better grasp the Adjacency Matrix concept. You are expected to
read about the Adjacency Matrix concept as well as the Adjacency List concept.
Suppose the vertices A, B, C, D, E, F, G and H of a Graph are mapped to row and column
indices(0,1,2,3,4,5,6,and 7) of a matrix (i.e. 2-dimensional array) as shown in the following table.
Vertex of Graph
Index in the 2-D Array Adjacency Matrix
Representation of Graph
A
B
2
F
6.
H
7
Suppose further, that the following is an Adjacency Matrix representing the Graph.
3
4
5.
6.
7
0.
1
1
1
1
01
1
01
1.
3
14
1
1
1
6.
1
Exercise:
Show/Draw the Graph that is represented by the above Adjacency matrix. Upload the document that contains
your result. (Filename: AdjacencyMatrixExercise.pdf)
Notes:
-The nodes of the…
Chapter 4 Solutions
Artificial Intelligence: A Modern Approach
Knowledge Booster
Similar questions
- [7_B_1] Please answer this question step by steparrow_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_forward3. Kleinberg, Jon. Algorithm Design (p. 519, q. 28) Consider this version of the Independent Set Problem. You are given an undirected graph G and an integer k. We will call a set of nodes I "strongly independent" if, for any two nodes v, u € I, the edge (v, u) is not present in G, and neither is there a path of two edges from u to v. That is, there is no node w such that both (v, w) and (u, w) are present. The Strongly Independent Set problem is to decide whether G has a strongly independent set of size at least k. Show that the Strongly Independent Set Problem is NP-Complete.arrow_forward
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