complete the coding portions for $1$c$,1$d$,2$a$,$ and $2$b$.$ you may need to download or lookup the games.py or agents.py in amia$-$python code.

Problem $1.(30$ points$)$

For problem $1,$ you will put answers in your writeup for a $-$ c$.$ Also make alterations to the given python module.

a$.$ Run the ps$3.$py code. You will be prompted to play tic$-$tac$-$toe against a minimax agent. Common wisdom suggests that the best first move is the center square. The agent doesn$$t begin by playing in the center square. Why do you think the agent plays where it does instead of the center? Give an explanation $(4-5$ sentences$)$ in your writeup.

b$.$ Alter the ps$3.$py code$$s main function so that it calls problem $1$b instead of problem $1$a$.$ You will be prompted to play connect$-4$ against an alpha$-$beta with cutoff agent that is using a silly evaluation function. See if you can defeat the agent in a few games. Describe $(3-4$ sentences$)$ what your plan to defeat it every time. Explain briefly $(2-3$ sentences$)$ why your plan works.

c$.$ In the function c$4$ good eval, write a new evaluation function. Using this function, write code in problem $1$c that will play an alpha$-$beta agent with depth cutoff $4$ using your evaluation function against a random agent. Play once as X and once as O$.($Note: For this problem and also $1($d$)$ and also $2($b$),$ it may help to write a version of your eval function to evaluate as $$X$$ and another version of your eval function to evaluate as $$O$.$ This is fine.$)$ Have the function return a tuple $($nx$,$ no$),$ where nx is the number of games that your agent wins as X$,$ and no is the number of games that your agent wins as O$.$ So if you win both games, you return $(1,1).$

Describe $(2-3$ sentences$)$ your evaluation function in your writeup and explain $(2-3$ sentences$)$ why you think it should do well. If your agent doesn$$t usually win against a random agent, then you probably did something wrong.

d$.$ In the function problem $1$d$,$ run $8$ games of an alpha$-$beta$-$cutoff agent using my evaluation function versus an alpha$-$beta$-$cutoff agent using your evaluation function, with each agent playing $4$ times as X and $4$ times as O$.$ Run four of games at depth limit $2$ for both agents, then four games at depth limit $3$ for both agents. Return a tuple $($nx$,$ no$),$ where nx is the number of games that your agent wins as X$,$ and no is the number of games that your agent wins as O$.$ So if you win all $8$ games, you return $(4,4).$

sys$.$path.append$(\text{'}$aima$-$python'$)$

from games import $*$

import math

def c$4\_$silly$\_$eval$($state$)$:

$\text{'}\text{'}\text{'}$Example of a silly evaluation function:

Each X piece is worth points based on its column number $(1$ through $6)$

Each O piece is worth points based in its $-$column number

$\text{'}\text{'}!$

ev $=0$

for col in range$(1,7)$:

for row in range$(1,8)$:

if state.board.get$(($row$,$col$))==\text{'}$X$\text{'}$:

ev $+=($col $*0\mathrm{.}01)$

elif state.board.get$(($row$,$ col$))==\text{'}0\text{'}$:

ev $-=($col $*0\mathrm{.}01)$

return ev

def c$4\_$good$\_$eval$($state$)$:

$\text{'}\text{'}\text{'}$Write your answer to $1$c in this function!

$\text{'}\text{'}!$

return $0$

def ab$\_$cutoff$\_$player$($game$,$ state$)$:

return alpha$\_$beta$\_$cutoff$\_$search$($state$,$ game, d$=2,$ eval$\_$fn$=$c$4\_$silly$\_$eval$)$

class PS$3$:

def init$($self$)$:

pass

def problem$\_1$a$($self$)$:

tt $=$ TicTacToe$()$

tt$.$play$\_$game$($alpha$\_$beta$\_$player,query$\_$player$)$

def problem$\_1$b$($self$)$:

c$4=$ ConnectFour$()$

c$4.$play$\_$game$($ab$\_$cutoff$\_$player, query$\_$player$)$

def problem$\_1$c$($self$)$:

write your code for problem $1$c here

return $0,0$

def problem$\_1$d$($self$)$:

write your code for problem $1$d here

return $0,0$

def problem$\_2$b$($self$)$:

write your code for problem $2$d here

return $0,0$

def main$()$:

ps$3=$ PS$3()$

An example for you to follow to get you started on Games

print$(\text{'}$Example Problem, playing Tic Tac Toe:$\text{'})$

print$(\text{'}=====================================\text{'})$

ps$3.$problem$\_1$a$()$

print$(\text{'}$Example Problem, playing Connect $4$ against my silly eval:$\text{'})$

print$(\text{'}========================================================\text{'})$

uncomment to get it to run problem$2$

#ps$3.$problem$\_1$b$()$

if name $==$ 'main':

main$()$

class Gomoku$($TicTacToe$)$:

$"""$Also known as Five in a row."""

def init$($self$,$ h$=15,$ v$=16,$ k$=5)$:

TicTacToe.init$($self$,$ h$,$ v$,$ k$)$