Develop the element type that will represent each board position.Develop the element type that will represent each board position. In addition to

representing the state of the TicTacToe board, you will also need an integer to store

the evaluation of the position in Step $2\mathrm{.}3$ below. I recommend something as simple

as the TicTacToePosition shown here. I chose to represent the board as a

String of nine characters, each position either a blank, an $\text{'}x\text{'}$ or an $\text{'}O\text{'}.$

The root of your tree will be the blank board. There are $9$ children from

here. That is$,$ the human player can select to place their $x$ in any position $0$

through $8.$ Create these children. From there, each of these positions has

at most $8$ counter moves for $0.$ This continues down until there are no

moves left. We will ignore symmetries.

There are at most $9!+$dots$1!(986,409)$ board configurations. Our tree will

need to be order $9$ and this will result in many empty positions. You should

start your tree out with the capacity set at a staggering $500,000,000$ places! This may require more heap memory

than your Java installation is used to$.$ Therefore, you may need to use the option: $-xm2048M$ to increase your

memory usage. Instructions on using this option are dependent on the IDE you use.

To perform this step, you may want to study and adapt the pre$-$order traversal algorithm. Remember not to

generate moves for positions that are already occupied.

If this is as far as you get, you will want to prove that your solution works. Print out the first $100$ positions in the

array. Perhaps you could use code like the following $($adapted to any data types$/$classes you have used$).$ Put this

code in the main method of a class called GenTree.java.

for $($int $i=0$; $i<mn\; id="EditorElement\_29241">1</mn><mn\; id="EditorElement\_29242">0</mn><mn\; id="EditorElement\_29243">0</mn>$; $i++)\{$

TicTacToePosition $t=$ gameTree $*$ get$($i$)$;

if $(t=$ null$)$

System.out.printf$("\%2$d$)\%$s

$",$ i$,$ gameTree.get$($i$).$board$)$;

else

System.out.printf$("\%2$d$)$ Empty

$",$ i$)$;

$\}$