The assignment should be submitted via Blackboard. NOTE: LATE SUBMISSIONS WILL NOT BE ACCEPTED.
Instructions
Some questions and subsections are for CSE 5360. CSE 4308
students can answer these questions for extra credit.
The answers can be typed as a document or handwritten and
scanned.
Name files as
assignment3_<net-id>.<format>
Accepted document format is .pdf.
If you are using Word, OpenOffice or LibreOffice, make
sure
to
save as .pdf.
If you are using LaTEX, compile into a .pdf file.
Please do not submit
.txt files.
If
you are scanning handwritten documents make sure to scan it at a
minimum of 600dpi and save as a .pdf or .png file. Do not
insert images in word document and submit.
If there are multiple files in your submission, zip them
together as assignment3_<net-id>.zip and submit the .zip
file.
Problem 1
Max: [4308: 20 Points,
5360: 15 Points]
X
O
O
X
X
O
Figure 1. A tic-tac-toe board state.
Consider the tic-tac-toe board state shown in Figure 1. Draw
the full
minimax search tree starting from this state, and ending in terminal
nodes. Show the utility value for each terminal and non-terminal node.
Also show which move the Minimax algorithm decides to play.
Utility values are +1 if X wins, 0 for a tie, and -1 if O wins. Assume
that X makes the next move (X is the MAX player).
Problem 2
Max: [4308: 20 Points,
5360: 15 Points]
Figure 2. A game search tree.
a. (4308: 15 points, 5360: 10 points)
In the game search tree of Figure 2, indicate what nodes will be pruned
using alpha-beta search, and what the estimated utility values are for
the rest of the nodes. Assume that, when given a choice, alpha-beta
search expands nodes in a left-to-right order. Also, assume the MAX
player plays first. Finally incidcate which action the Minmax algorithm
will pick to exectute.
b. (4308: 5 points, 5360: 5 points) This question is also on
the game search tree
of Figure 2. Suppose we are given some additional knowledge about the
game: the maximum utility value is 10, i.e., it is not mathematically
possible for the MAX player to get an outcome greater than 10. How can
this knowledge be used to further improve the efficiency of alpha-beta
search? Indicate the nodes that will be pruned using this improvement.
Again, assume that, when given a choice, alpha-beta search expands
nodes in a left-to-right order, and that the MAX player plays first.
Problem 3
Max: [4308: 20 Points,
5360: 20 Points]
Figure 3: Yet another game search tree
Consider
the MINIMAX tree above. Suppose that we are the MAX player, and we
follow the MINIMAX algorithm to play a full game against an opponent.
However,we
do not know what algorithm the opponent uses.
Under
these conditions, what is the best possible outcome of playing the full
game for the MAX player? What is the worst possible outcome for the MAX
player? Justify your answer.
NOTE:
the question is not asking you about what MINIMAX will compute for the
start node. It is asking you what is the best and worst outcome of acomplete
gameunder
the assumptions stated above.
Problem 4
Max: [4308: 15 Points,
5360: 10 Points]
Figure 4: An Expectiminmax tree.
Find
the value of every non-terminal node in the expectiminmax tree given
above. Also indicate which action will be performed by the algoirithm
The following outline map needs to be colored.
Your
job is to color the various sections such that no two sections
sharing a border have the same color. You are allowed to use the colors
(Red, Green, Blue).
Figure 5: Map to be colored.
Part a: Draw
the Constraint Graph for this problem. Can you use this information to
simplify the problem?
Part b:
Assuming you are using Backtracking search to solve this problem and
that you are using both MRV and Degree heuristic to select the
variable, Which variable will be selected at each level of the search
tree [You do not need to draw the tree. Just let me know which variable
will be selected and why (MRV and degree values)]. Note: Multiple
possible answers. You only have to give one.
Part c: EC (10 points): Give one valid solution to this
problem.
Problem 6 (Extra Credit for 4308, Required for 5360)
Max: [4308: 20 Points EC,
5360: 20 Points]
Suppose that you want to implement an algorithm tht will compete on a
two-player deterministic game of perfect information. Your opponent is
a supercomputer called DeepGreen. DeepGreen does not use Minimax. You
are given a library function DeepGreenMove(S), that takes any state S
as an argument, and returns the move that DeepGreen will choose for
that state S (more precisely, DeepGreenMove (S) returns the state
resulting from the opponent's move).
Write
an algorithm in pseudocode (following the style of the Minimax
pseudocode) that will always make an optimal decision given the
knowledge we have about DeepGreen. You are free to use the library
function DeepGreenMove(S) in your pseudocode. How does this compare to
Minimax wrt optimality of solution and the number of states explored.
