South Dakota State University Chapter 3 Artificial Intelligence Exercises Artificial intelligence exercise assignment Link for exercise assignment (textboo

South Dakota State University Chapter 3 Artificial Intelligence Exercises Artificial intelligence exercise assignment Link for exercise assignment (textbook): https://www.cs.ubc.ca/~poole/aibook/2e/html/ArtInt2e.Ch3.S11.html Need to answer question #3 and question #4 in this exercises. Exercise 3.
Consider the problem of finding a path in the grid shown
in Figure 3.14 from the position
s to the position g. A piece can move on the
grid horizontally or vertically, one square at a time. No step may be made into a
forbidden shaded area.
Figure 3.14: A grid-searching problem
(a) On the grid shown in Figure 3.14, number the nodes expanded (in
order) for a depth-first search from
s to g, given that the order of the
operators is up, left, right, and down. Assume there is cycle pruning. What
is the first path found?
(b) On a copy of the same grid, number the nodes expanded, in order, for
a greedy best-first search from
s to g. Manhattan distance should be used
as the evaluation function. The Manhattan distance between two points is
the distance in the
x-direction plus the distance in the y-direction. It
corresponds to the distance traveled along city streets arranged in a grid.
Assume multiple-path pruning. What is the first path found?
(c) On a copy of the same grid, number the nodes expanded, in order, for
a heuristic depth-first search from
s to g, given Manhattan distance as the
evaluation function. Assume cycle pruning. What is the path found?
(d) Number the nodes in order for an
A* search, with multiple-path
pruning, for the same grid. What is the path found?
(e) Show how to solve the same problem using dynamic programming.
Give the cost_to_goal value for each node, and show which path is found.
(f) Based on this experience, discuss which algorithms are best suited for
this problem.
(g) Suppose that the grid extended infinitely in all directions. That is, there
is no boundary, but s,
g, and the blocks are in the same positions relative
to each other. Which methods would no longer find a path? Which would
be the best method, and why?
Exercise 4.
This question investigates using graph searching to design video
presentations. Suppose there exists a database of video segments, together
with their length in seconds and the topics covered, set up as follows:
Segment Length
Topics covered
seg0
10
[welcome]
seg1
30
[skiing, views]
seg2
50
[welcome, artificial_intelligence, robots]
seg3
40
[graphics, dragons]
seg4
50
[skiing, robots]
Represent a node as a pair:
?To_Cover,Segs?,
where Segs is a list of segments that must be in the presentation, and To_Cover is
a list of topics that also must be covered. Assume that none of the segments
in
Segs cover any of the topics in To_Cover.
The neighbors of a node are obtained by first selecting a topic from
To_Cover. There
is a neighbor for each segment that covers the selected topic. [Part of this exercise is
to think about the exact structure of these neighbors.]
For example, given the aforementioned database of segments, the neighbors of the
node
?[welcome,robots],[]? assuming that welcome was selected, are ?[],[seg2]?
and ?[robots],[seg0]?
Thus, each arc adds exactly one segment but can cover one or more topics. Suppose
that the cost of the arc is equal to the time of the segment added.
The goal is to design a presentation that covers all of the topics in
MustCover. The
starting node is
?MustCover,[]? and the goal nodes are of the
form ?[],Presentation?. The cost of the path from a start node to a goal node is the
time of the presentation. Thus, an optimal presentation is a shortest presentation that
covers all of the topics in
MustCover.
(a) Suppose that the goal is to cover the
topics
[welcome,skiing,robots] and the algorithm always select the
leftmost topic to find the neighbors for each node. Draw the search space
expanded for a lowest-cost-first search until the first solution is found.
This should show all nodes expanded, which node is a goal node, and the
frontier when the goal was found.
(b) Give a non-trivial heuristic function
that
h that is admissible. [Note
h(n)=0 for all n is the trivial heuristic function.] Does it satisfy the
monotone restriction for a heuristic function?
Textbook: https://www.cs.ubc.ca/~poole/aibook/2e/html/ArtInt2e.Ch3.S11.html for reference.

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