CS 6601 Artificial Intelligence Spring 2023 Midterm Exam
Weight: 15% of your final grade
Duration of Exam: 27 Feb 2023, 8:00 AM (EDT) – 6 Mar 2022, 8:00 AM (EDT)
Before solving the exam, you should read the Ed posts for any updated information or clarifications on the exam.
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Make sure your answers follow the instructions given in the problem area. There is another quiz titled Midterm Exam Calculations if you wish to submit calculations. However, you will not be awarded any points for your calculations (only your nal answers are considered). The instructors reserve the right to assign partial credits based on your calculations.
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You must round all your final answers to 6 decimal places. Do not round intermediate results. You can use round(answer, 6) function in Python for help. You may not receive full credit if your answers are not given to the speci ed precision.
Points breakdown is provided below.
Q1 Q2 Q3 Q4 Q5 Q6
14 18 18 19 13 18
Search Part 1
Which of the following cost values for the new edge cost function nec(i, j) will allow you to perform Uniform Cost Search (UCS) with nec(i, j) and result in the same order of node generation and expansion as running UCS with edge cost ec(i, j)? Select all that apply
nec(i, j) = ec(i, j) + q; q>0
nec(i, j) = ec(i, j) * q; 0
None of the above
Given two admissible and consistent heuristics h1 and h2 which of the the following answers would be a de nition for a new admissible and consistent heuristic?
max(h1(x), h2(x)) h1(x) + h2(x) (h1(x) + h2(x)) / 2 abs(h1(x) + h2(x)) h1(x) – h2(x)
None of the above
Search Part 2
For the Search problems, assume the following:
1. Edge Cost ec(i, j) > 0 for every pair of neighboring nodes i and j. Consider this as the true cost of going from node i to node j.
2. ec(i, j) = ec(j, i)
3. Heuristic function h(x) is admissible and consistent. (h(x) is heuristic cost
from any node x to destination)
4. The variable q is a scalar constant.
3 3 points
For the given tree in Figure 1., which of the following cost values for the new edge cost function nec(i, j) will allow you to perform UCS with nec(i, j) and result in the same order of node expansion and path generation as Depth First Search? Note: Node exploration ties are broken left to right.
nec(i,j) = ec(i,j)
nec(i,j) = q; q<0 nec(i,j) = q; q>0 nec(i,j) = 1
nec(i,j) = -1
None of the above
Figure 1. ____________________________
Game Playing Part 1
John is a newly hired intern at Gtech Solutions, Inc. He has recently graduated with a BS degree in Computer Science with a GPA of 1.5 and his grasp on applications of Arti cial Intelligence are tenuous at best.
The senior manager at Gtech Solutions, Inc has asked John to assist him in developing a new gaming application which uses adversarial search to apply AI. John sees this as an opportunity to perform well and impress the manager, but he is struggling to understand the concepts of Iterative Deepening. Therefore, he needs help from a peer to explain it to him and help him in the development process.
You have agreed to help John learn some new skills and to perform well in the assigned task, that way John can become a more valuable contributor at Gtech Solutions, Inc. Please help by solving the following questions on Minimax & Alpha Beta pruning.
You remind John that the up arrow and down arrow indicate that it is the MAX and MIN player turn, respectively, and the numbers at the bottom show the payoff for the given terminal positions. And he can assume nodes are generated in the optimal order for alpha-beta pruning.
4 3 points
For the given tree in Figure 1., which of the following cost values for the new edge cost function nec(i, j) will allow you to perform UCS with nec(i, j) and result in the same order of node expansion and path generation as Breadth First Search? Note: Node exploration ties are broken left to right.
nec(i,j) = ec(i,j)
nec(i,j) = q; q<0 nec(i,j) = q; q>0 nec(i,j) = 1
nec(i,j) = -1
None of the above
5 4 points
Consider the graph given in Figure 2., with starting node A and goal node I. The edge costs represent the true cost to move between the adjacent nodes(Eg:c*fromEtoFis4)
In the table next to the graph, we have listed the values of heuristic functions h1(x) and h2(x). Use the dropdown’s below to indicate whether each is admissibility, and whether it is also consistent.
h1(x) is admissible h1(x) is consistent h2(x) is admissible h2(x) is consistent
6 2 points
What is the propagated value (at the root)?
7 2 points
How many nodes (terminal) will be pruned when the Alpha-Beta algorithm is
8 2 points
Use your mouse, to drag the nodes that would not be generated or explored during Alpha-Beta pruning, and to drag the nodes which would be generated or explored, into the correct category
Not generated or explored Generated or explored
Possible answers
True True True True
Game Playing Part 2
In this problem, you will use the maxn algorithm for three player games (as provided in the Korf readings) in which the sum of the three players�� utilities are equal to 15 and each utility >=0. The leaf utilities are written as tuples (U_A, U_B, U_C), with the rst, second, and third component indicating the utility of that leaf to A, B, and C respectively. In this generalized setting, A seeks to maximize U_A, the rst component, while B seeks to maximize U_B, the second component, and C seeks to maximize U_C, the third component.
9 4 points
What is the nal value propagated at the top?
(U_A: , U_B: , U_C: )
10 4 points
What are the nal bounds calculated with the Alpha-beta algorithm at the top node?
11 2 points
Shallow pruning is a generalized version of alpha-beta pruning on non-cooperative, perfect-information games with more than two players. You may nd more
information about shallow pruning in canvas->File->Readings. What is the total number of nodes (both leaf and inner nodes) in the tree that would get pruned?
Game Playing Part 3
Answer the following questions about Alpha-Beta Pruning:
= >= <= = >= <= <= = >=
Alpha-Beta Pruning can alter the computed minimax value at the root of the tree
When doing alpha-beta pruning on a game tree which is traversed from left to right, the leftmost branch will never be pruned.
True False
Instructions
In classic Sudoku, the objective is to ll a 9 �� 9 grid with digits so that each column, each row, and each of the nine 3 �� 3 subgrids that compose the grid contain all of the digits from 1 to 9. For this problem we will be using a simpli ed version of Sudoku where the objective will be to ll a 4 x 4 grid with digits so that each column, each row, and each of the four 2 �� 2 subgrids that compose the grid contain all of the digits from 1 to 4.
Optimization Part 1
Example of a 4×4 grid with subgrids enumerated, along with its solution grid:
Some of the grid cells are initially filled with values to restrict the problem space, the solver must correctly populate the solution for the subgrids and the grid rows and columns.
Each 2×2 subgrid must contain the numbers 1 through 4, and each row and each column of the grid must contain the numbers 1 through 4. Look carefully at the solution grid.
We will use two algorithms to solve the puzzle, Genetic Algorithms and Simulated Annealing. We will use the initial state from the example above as our starting point for each problem
PART 1A. GENETIC ALGORITHM:
To begin, we randomly populate the remaining cells of 4 grids (cloned from examples initial state) with the numbers 1-4
For our GA we de ne a tness function as: FF = #Max errors – # of errors
The number of errors is the sum (# of errors in each row + # of errors in each column + # of errors in each 2 x 2 subgrid). For example, if a row of the grid has the values [3, 4, 3, 2] then the number of errors in this row is 1 because there is 1 duplicate value. e.g.,
Based on the information above answer the following questions:
14 2 points
What is the maximum number of errors for an empty 4 x 4 board?
15 4 points
Fill out the Table below. The two values in bold have already been lled in for you. The probability of a board being chosen is proportional to its tness score.
Parents Fitness Score A
Probability 0.255319
16 4 points
Next you will be performing a Breeding Step. The units we will use for breeding are the top and bottom subgrids.
For example the child created by breeding A with B, A|B, would be formed like this.
In our problem case A has been chosen to breed with D and B to breed with C. Each child is written as Parent1|Parent2. This child is composed of the two upper subgrids of Parent1 and the two lower subgrids of Parent2. Some of the values have already been lled in for you.
Parent Child Fitness
Probability
B B|C 0.25
17 1 point
We could proceed in this fashion, breeding parents to produce children who will then breed to produce further children and so on. Assuming that we only
choose the offspring that reproduce from the current generation, is the solution reachable for this board without a mutation step?
Optimization Part 2
For this part we must an Energy Function (E) and a starting Temperature (T0).
The Energy Function is as the sum of the number of distinct elements in each row, column, and subgrid multiplied by -1.
Energy Function = – ( sum of number of distinct elements in each row + sum of the number of distinct elements in each column + sum of number of distinct elements in each subgrid)
Here is an example board and the calculation for its Energy Function.
In the four rows there are 3, 2, 4 and 3 distinct elements respectively. In the four columns there are 3, 3, 3, and 3 distinct elements respectively. In the four subgrids there are 3, 3, 4, and 3 distinct elements respectively. The value of the Energy Function is then
Instructions
Simulated Annealing: For this part you will be using Simulated Annealing. We will be using the same initial example grid from part 1.
Programming Help
Energy Function = – (3 + 2 + 4 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 4 + 3) = – 37 Based on this information answer the following questions:
At what minimum value of the Energy Function should the algorithm stop?
The starting Temperature for our simulated annealing is set to T0 = 0.5.
The algorithm starts in the board state A from the section on Genetic Algorithms. In the first iteration of the algorithm we compare A to the state A�� shown below.
The in the table is the difference in Energy Function(defined above) between the A and state i.e. the Energy Function of A�� – Energy Function of A. The probability for the transition is defined as e-��E/T. Please fill in the blank in the table for probability and answer the questions below.
Board State T Probability
Based on the probability entered above:
You decide to roll a fair six sided die to decide if you want to transition to this state or not. If the probability you found for A�� is greater than the probability of you rolling that number or greater then you will transition to A��. Suppose you rolled a 5
Do you transition to A’? Yes
How does changing the initial temperature affect the algorithm? Choose all that apply
SettingtheinitialtemperaturetoT0 =1.0willincreaserandomnessanddecreasetheprobabilityofchoosingworseboardstates SettingtheinitialtemperaturetoT0 =1.0willdecreaserandomnessandincreasetheprobabilityofchoosingworseboardstates SettingtheinitialtemperaturetoT0 =0.05willincreaserandomnessandincreasetheprobabilityofchoosingworseboardstates SettingtheinitialtemperaturetoT0 =0.05willdecreaserandomnessanddecreasetheprobabilityofchoosingworseboardstates
Constraint Satisfaction Problem Part 1
The Midtown School of Science and Technology��s Academic Decathlon team is preparing for another run to nationals this year! As the coach for the team, you are in charge of organizing team meetings and ensuring that the team prepares effectively for the upcoming competition. Of course that means understanding the unique relationships between the 6 team members: Betty, Flash, Liz, MJ, Ned, and Peter
You��ve found a nice spot for the meetings in classroom 404, a round table with 6 seats. You can see a diagram of the table below with the seats numbered 1 through 6. Note that the chairs are identical
Your students are high schoolers with complicated relationships, so it��s expected that they have some strong feelings about where they are willing to sit. You��ve been observing them for a while and this is what you know so far:
Ned is Peter’s best friend and will only sit next to Peter
Liz and Flash are teammates for the ECON category and must sit next to each other MJ appears to be spying on Peter and must sit either next to, or across from Peter
It��s time for the rst team meeting of 2023! Use what you have learned to solve these CSPs.
How many valid seating solutions are there for the 5 remaining students if Liz sits in seat 1 for the rst meeting?
Peter arrives and sees Liz at the table alone, sitting in seat 1. He sits down next to Liz (seat 2 or 6) and strikes up a conversation. Is the following statement true? Peter will have to move once the entire team arrives.
True False
The first meeting goes well and the team now reconvenes for a second meeting. The same restrictions carry over from the first meeting and once again Liz (who always arrives early) arrives first and sits down in seat 1.
This time MJ arrives second. If we were to seat MJ second (after Liz) based on the metric of Least Constraining Value with respect to our variable ��Peter��, what seat(s) can we choose to assign to MJ? Select all that apply
MJ wants to spy on Peter so she smartly decides not to sit down until Peter arrives. As she waits, Ned suddenly shows up and sits down next to Liz in seat 2. Is there a valid seating solution for the team without moving Liz or Ned? If so, assign each team member a valid seat. If not, choose ��none�� for each of the seats (excluding Liz and Ned)
Seat1:Liz Seat2:Ned
Seat 3: Seat 4: Seat 5: Seat 6:
程序代写 CS代考 加QQ: 749389476
Everything is going great as we prepare for the third meeting! Or at least until today. Apparently Peter tripped and spilled juice on Flash during lunch today… Peter and Flash will not sit next to each other today. The same restrictions carry over from the rst meeting and once again Liz arrives rst and sits down in seat 1.
Everyone (except Liz who is always early) arrives together to the meeting. If we use Minimum Remaining Value as our metric, who should we assign a seat to rst? Select all that apply
Flash MJ Ned Peter
Whoops! We completely forgot that at the last meeting, Ned and Betty volunteered to be teammates for the math section and so Ned and Betty must sit next to each other.
Given this new information, if we use Minimum Remaining Value as our metric, who should we assign a seat to rst now? Select all that apply
Betty Flash MJ Ned Peter
Ned, a little nervous because he completely forgot that the team was doing mock exams today, chokes on his water and starts coughing like crazy. Flash thinks Ned has COVID and now will not sit next to or across from Ned.
Given this new information, how many valid seatings of the team are there for this third meeting, with Liz in seat 1?
It��s competition day! The team arrives at the competition opening ceremony and everyone walks into the auditorium. It��s a lively atmosphere with all the other teams present in their school colors. You lead the team to your assigned row of 7 seats. Since it��s not a study session nor the actual competition, teammates working on the same section do not have to sit next to each other.
Based on this, here are the following restrictions:
Ned is Peter��s best friend and will only sit next to Peter.
MJ appears to be spying on Peter and must sit next to Peter. Flash is still mad at Peter and will not sit next to Peter.
Flash still suspects Ned has COVID and will not sit next to Ned. Flash likes to talk and wants to sit next to more than one person
How many valid seating solutions are there for the team?
Code Help
30 3 points
If we use Degree Heuristic as our metric, who should we assign a seat to rst? Select all that apply
Betty Flash MJ
Ned Peter Yourself
31 0 points
Phew! Pat yourself on the back, you��ve done it! You��ve led a bunch of high schoolers to Academic Decathlon nationals! Now everything is out of your hands and you can nally go sightseeing in DC, perhaps you��ll go check out the Cherry Blossoms that are rumored to be blooming soon… Unfortunately you��re interrupted by a guy dressed in a fancy suit and square rimmed glasses. He introduces himself as Tony and says he needs to talk to Peter. Since the opening ceremony hasn��t started yet, you give Peter a nod and go back to looking at your DC for Dummies guidebook. Suddenly something crashes through the roof of the auditorium and onto the stage and all hell breaks loose…
Don’t pick me, this is scary, and incorrect
Spidey senses tingling! is the right answer
Instructions
Round all of your answers to 6 decimal places, when in doubt use the python function round(answer, 6)
Probability Part 1, The Shell Game
Having fruitfully absorbed the Artificial Intelligence course material, your AI startup “bayes.AI.n solutions”, has had a successful IPO which has left you with money to burn. Since a deep understanding of probability was key to your success in artificial intelligence, you now enjoy traveling the globe to various casinos and applying this knowledge to games of chance.
At the Casino de Monte-Carlo located in Monte Carlo (which you affectionately refer to as ��Casino MCMC��), located in Monaco, they have a variety of games where players try to guess the location of hidden money underneath cups.
The first dealer, Ada, runs a game with the following rules:
1. Ada uses 3 cups placed upside down, lined up in a row, numbered 1, 2, and 3 from left to right (from the player��s perspective)
2. Ada secretly places $1000 underneath one of the cups
3. The player pays $500 fee to play per game (not returned, win or lose)
4. The player guesses which cup the money is under
5. The dealer reveals which cup the money was under
5A. If the player guessed correctly, they win the $1,000 (this is a net winning of $500 to the player, after subtracting the $500 entry fee).
5B. If the player guessed incorrectly, they win nothing and are out the $500 entry fee
Over the course of several days, you notice that the money is not always placed in a uniform distribution after the first game of the day!
You notice the following pattern:
For the first game of each day, the placement of the money has a uniform distribution, i.e., there is an equal probability for the money to be under any of the cups
For subsequent games,
A. If the player wins, Ada will hide the money under one of the two cups not chosen by the player with a uniform random distribution
B. If the player loses, Ada will hide the money under cup 2 if the money was previously under cup 1, otherwise the money is hid under cup 1
You enter the Casino de Monte-Carlo as it is opening, and Ada is just about to start the game. You recognize the first player as someone who always just picks the leftmost cup (Cup 1) no matter what, and will play all day with this dealer.
Based on the information above answer the following questions.
32 3 points
What is the probability for each cup to be covering the $1000 in the
second game? P(Cup 1):
P(Cup 2): P(Cup 3):
33 1 point
What is the probability that the money will be under Cup 2 during the third
34 1 point
What is the probability that the player will win the third game?
35 1 point
What is the probability the player will win at least two of the rst three games?
You have the chance to play this game two times with the same dealer tomorrow, starting with the rst game. If you play the optimal strategy (you maximize your chance of winning each game), how much net money in dollars do you expect to gain (positive number) or lose (negative number) in those two games, including both the costs and winnings from each game? Enter the number only (no dollar signs)
Suppose you are playing, and you initially pick the yellow cup, and Andrey reveals a blue cup (4) with no money underneath. What is the probability of the money being underneath each remaining cup?
Cup 1: Cup 2: Cup 3:
Suppose you are playing, and you initially pick a blue cup (cup 2), and Andrey reveals another blue cup (cup 4) without the money. What is the probability the money is underneath each unrevealed cup?
Cup 1: Cup 2: Cup 3:
Based on what you know you need to make 3 choices on this game. Whether or not it is pro table to play, and if you do play to make money, what is the optimal strategy. Should you play?
Pay the $3000 to play
Do not play
Based on what you know you need to make 3 choices on this game. Whether or not it is pro table to play, and if you do play to make money, what is the optimal strategy. What strategy should you use when choosing a cup?
Initially select the yellow cup Initially select any blue cup
I am not playing
Based on what you know you need to make 3 choices on this game. Whether or not it is pro table to play, and if you do play to make money, what is the optimal strategy. What strategy should you use when Andrey reveals an empty blue cup?
Trade in your cup and pay the additional fee to switch cup(s) Always keep your initial selection, and do not switch
I am not playing
Instructions
Round all of your answers to 6 decimal places, when in doubt use the python function round(answer, 6)
Probability Part 2, Andrey’s Table
You move on to another game, a variant run by the dealer named Andrey. In this game, Andrey uses four upside-down cups: a yellow cup marked cup 1, and three blue cups marked cups 2 through 4.
A player must pay a $3,000 entry fee to play (not returned, win or lose)
You recognize that before the game begins Andrey secretly places $10,000 underneath one of the cups, with the following distribution: A 0.4 probability under the yellow cup (1), and a .2 probability under each of the blue cups (2, 3, 4).
The player chooses one of the cup.
Andrey then reveals one of blue cups that did not have the money underneath it. (Not the cup chosen by the player)
The rules of the game depend on whether the player initially chose the yellow cup or one of the blue cups.
1. If the 1.
2. If the 1.
player had chosen the yellow cup:
The player can choose to remain with yellow cup for no further investment
Or pay an additional fee of $3000 to trade the unrevealed yellow cup for both of the remaining blue cups
The player wins the hidden $10,000 if the money is underneath one of their nal chosen cups (the yellow cup if they didn��t switch, or blue cup if they did)
player chose a blue cup:
The player can remain with their initially chosen blue cup for no further investment
Or pay an additional fee of $1500 to trade their blue cup for the yellow cup (the player cannot switch to the blue cup)
The player wins the hidden $10,000 if the money is underneath their nal chosen cup (the yellow cup if they switched, or their original blue cup)
Given the information above, answer the following questions.
Bayes Nets Part 1
It is 2067, and 5 years of failing crops has brought widespread famine. Cooper, a retired NASA pilot, has taken up farming to help the famine-relief effort. Awaking early and heading out to do his chores he is startled to nd a gravitational anomaly appearing in his daughter Murph’s bedroom. Everything in her room is standing at an angle. Using his Lacoste-Starner gravitymeter he detects a (GPS) coordinate pattern. He maps the origin on his phone, and follows it to a NASA facility, he knows it conducted top-secret research led by Dr. Brand.
He meets with Dr. Brand who explains that while NASA was shut down by the government, a team has continued a mission of discovering habitable planets. They have also been working on a secret formula to overcomes the magnitude of gravitational force crucial for the missions return to earth. Dr. Brand asks if Cooper would pilot a test- ight using the formula which he believes is humanity’s last hope. Cooper reluctantly agrees, even though he worries about leaving Murph behind.
The ight will use a wormhole near Saturn, and apply some of the new eld equations from the secret formula to navigate the shortcut to another galaxy. Their mission is to explore three planets [Planet 1 chosen to explore(E1), Planet 2 chosen (E2), Planet 3(E3)], orbiting the other side of the black hole called Gargantua
He and Amelia (senior scientist) will need to nd out whether any of the three planets are habitable (HP1, HP2, HP3). Upon landing on planet 1, a massive tidal wave oods the ship’s engines (engines wet (EW)), forcing Cooper and Amelia to wait signi cantly longer than planned for them to dry out. Checking the earth time, they see that 23 earth years have passed due to the time dilation caused by the planet’s proximity to Gargantua.
In the meanwhile on Earth, Murph has become a renowned scientist and is working with Dr. Brand whose health is failing. Dr. Brand discloses (BD) that he gave up working on the secret formula years ago, as they need critical information from inside the black hole. He fears that he has doomed humanity to extinction. Murph tries to relay a message to Cooper, but it is too late for the message to reach in time (MT). The crew had already departed for planet 2.
On planet 2, the crew nds a previous NASA explorer, Dr. Mann, alive. They ask him about potential for habitation there. Mann secretly reveals to Cooper that it is not habitable, but hoped that NASA would send a mission to rescue him. Cooper shares with Mann that they only have enough resources for one person to go back home. Mann struggles with Cooper in an attempt to sabotage the mission (SB) and take the spacecraft home. Cooper overcomes Dr. Mann and restrains him.
Cooper decides to attempt to use the gravity of Gargantua as a slingshot to planet 3 so that Amelia can explore planet 3. Back on Earth, Murph works tirelessly to solve Dr. Brand’s equation. Cooper and Amelia begin the journey to E3, it is not working as planned due to weight and fuel. Cooper decides to sacri ce himself by exiting the ship and falls into the black hole. He somehow nds himself inside a ve-dimensional tesseract composed of time-slices from including one he recognizes from Murph’s bedroom. He realizes that this dimension space was created by future humans with the ability to time-travel, Cooper discovers how he can communicate with Murph (CM) from inside the black hole, using gravity.
Murph recognizes a pattern is being transmitted through the gravitational anomaly, she uses pattern recognition to decode the information and discovers it is her father (FA). Using the decoded information she discovers some of it will help solve Brand’s gravity-equation (EQ). Cooper is transported from the tesseract by the future beings, and taken to a space station near Saturn where he will eventually reunite with Murph (RM).
Amelia nds that planet 3 is habitable and begins to set up a new habitat for earths inhabitants. Over the next hundred years, humanity is saved (HS).
Story summary
1. (GPS) {T,F}: Cooper deducing the gravitational anomaly to be a GPS coordinate pattern. 2. (E1) {T,F}: planet 1 is chosen and explored.
3. (E2) {T,F}: planet 2 is chosen and explored.
4. (E3) {T,F}: planet 3 is chosen and explored.
5. (HP1) {T,F}: planet 1 is a habitable planet.
6. (HP2) {T,F}: planet 2 is a habitable planet.
7. (HP3) {T,F}: planet 3 is a habitable planet.
8. (EW) {T,F}: The ship��s engine becomes ooded by water.
9. (BD) {T,F}: Dr. Brand discloses to Murph that he had given up solving the formula.
10. (MT) {T,F}: Murph��s message reaches Cooper in time.
11. (SB) {Complete, Partial, None}: Dr Mann sabotages the mission.
12. (CM) {T,F}: Cooper successfully communicating with Murph from the tesseract
13. (FA) {T,F}: Murph recognizing the gravity abnormalities as communication
14. (EQ) {T,F}: Murph solving Dr. Brand��s formula.
15. (RM) {T,F}: Cooper reuniting with Murph.
16. (HS) {T,F}: Humanity is saved from extinction.
The hyper-intelligent future beings, who created the tesseract for Cooper inside the singularity, we