$**************************************$

$//***$You must use all the given methods without changing their signature.$**$

$//***$However$,$ you may add new methods using the given ones if necessary.$***$

$//*************************************************************************$

public class PegSolitaireBoardProfVersion $\{$

protected char$[][]$ pegBoard;

private static final int UP $=1$;

private static final int DOWN $=2$;

private static final int LEFT $=3$;

private static final int RIGHT $=4$;

$//$ Initializes the board at its starting position

$//[\text{'}\text{'},\text{'}\text{'},\text{'}$X$\text{'},\text{'}$X$\text{'},\text{'}$X$\text{'},\text{'}\text{'},\text{'}\text{'}],$

$//[\text{'}\text{'},\text{'}\text{'},\text{'}$X$\text{'},\text{'}$X$\text{'},\text{'}$X$\text{'},\text{'}\text{'},\text{'}\text{'}],$

$//[\text{'}$X$\text{'},\text{'}$X$\text{'},\text{'}$X$\text{'},\text{'}$X$\text{'},\text{'}$X$\text{'},\text{'}$X$\text{'},\text{'}$X$\text{'}],$

$//[\text{'}$X$\text{'},\text{'}$X$\text{'},\text{'}$X$\text{'},\text{'}$O$\text{'},\text{'}$X$\text{'},\text{'}$X$\text{'},\text{'}$X$\text{'}],$

$//[\text{'}$X$\text{'},\text{'}$X$\text{'},\text{'}$X$\text{'},\text{'}$X$\text{'},\text{'}$X$\text{'},\text{'}$X$\text{'},\text{'}$X$\text{'}],$

$//[\text{'}\text{'},\text{'}\text{'},\text{'}$X$\text{'},\text{'}$X$\text{'},\text{'}$X$\text{'},\text{'}\text{'},\text{'}\text{'}],$

$//[\text{'}\text{'},\text{'}\text{'},\text{'}$X$\text{'},\text{'}$X$\text{'},\text{'}$X$\text{'},\text{'}\text{'},\text{'}\text{'}]$

public PegSolitaireBoardProfVersion$()\{$

this.pegBoard $=$ new char$[7][7]$;

for $($int i $=0$; i $<mtext\; id="EditorElement\_3028609"></mtext><mn\; id="EditorElement\_3028610">7</mn>$; i$++)\{$

for $($int j $=0$; j $<mtext\; id="EditorElement\_3028645"></mtext><mn\; id="EditorElement\_3028646">7</mn>$; j$++)\{$

if $($i $<mtext\; id="EditorElement\_3028671"></mtext><mn\; id="EditorElement\_3028672">2</mn>$ && j $<mtext\; id="EditorElement\_3028680"></mtext><mn\; id="EditorElement\_3028681">2</mn><mi\; id="EditorElement\_3028682">)</mi><mtext\; id="EditorElement\_3028683"></mtext><mi\; id="EditorElement\_3028684">\{</mi>$

this.pegBoard$[$i$][$j$]=\text{'}\text{'}$;

$\}$ else if $($i $<mtext\; id="EditorElement\_3028745"></mtext><mn\; id="EditorElement\_3028746">2</mn>$ && j $>4)\{$

this.pegBoard$[$i$][$j$]=\text{'}\text{'}$;

$\}$ else if $($i $>4$ && j $<mtext\; id="EditorElement\_3028828"></mtext><mn\; id="EditorElement\_3028829">2</mn><mi\; id="EditorElement\_3028830">)</mi><mtext\; id="EditorElement\_3028831"></mtext><mi\; id="EditorElement\_3028832">\{</mi>$

this.pegBoard$[$i$][$j$]=\text{'}\text{'}$;

$\}$ else if $($i $>4$ && j $>4)\{$

this.pegBoard$[$i$][$j$]=\text{'}\text{'}$;

$\}$ else if $($i $==3$ && j $==3)\{$

this.pegBoard$[$i$][$j$]=\text{'}$O$\text{'}$;

$\}$ else $\{$

this.pegBoard$[$i$][$j$]=\text{'}$X$\text{'}$;

$\}$

$\}$

$\}$

$\}$

$//$ moves the $\text{'}$X$\text{'}$s and $\text{'}$O$\text{'}$s to the corresponding positions after the jump happens

private boolean moveForward$($int x$,$ int y$,$ int direction$)\{$

$//$ Implement moveForward here

$//*********$The error will go away once you implement and returns a boolean

$//$ value$*********$

return false;

$\}$

$//$ moves the $\text{'}$X$\text{'}$s and $\text{'}$O$\text{'}$s back to their initial position before the jump

$//$ occurred

private void moveBackward$($int x$,$ int y$,$ int direction$)\{$

$//$ Implement moveBackward here

$\}$

private void addPeg$($int x$,$ int y$)\{$

pegBoard$[$x$][$y$]=\text{'}$X$\text{'}$;

$\}$

private void removePeg$($int x$,$ int y$)\{$

pegBoard$[$x$][$y$]=\text{'}$O$\text{'}$;

$\}$

$//$ check if the jump is valid

$//$ checks if the result of the jump will be out of bounds

$//$ checks that the $\text{'}$X$\text{'}$ performing the jump has one more $\text{'}$X$\text{'}$ in between itself

$//$ and the $\text{'}$O$\text{'}$

private boolean checkMove$($int x$,$ int y$,$ int newX, int newY$)\{$

$//$ Implement checkMove here

$//*********$The error will go away once you implement and returns a boolean

$//$ value$*********$

return false;

$\}$

$//$ getNewX and getNewY get the x and y coordinates of the position where the $\text{'}$X$\text{'}$

$//$ will occupy after the jump

private int getNewX$($int x$,$ int direction$)\{$

int newX $=$ x;

switch $($direction$)\{$

case RIGHT:

newX $=$ newX $+2$;

break;

case LEFT:

newX $=$ newX $-2$;

$\}$

return newX;

$\}$

private int getNewY$($int y$,$ int direction$)\{$

int newY $=$ y;

switch $($direction$)\{$

case UP:

newY $=$ newY $+2$;

break;

case DOWN:

newY $=$ newY $-2$;

$\}$

return newY;

$\}$

private void print$()\{$

$//$ Implement print here

$\}$

$//$ recursive and backtracking algorithm to compute all the possible moves

$//$ loops through the rows and columns of the matrix and tests if a jump in each

$//$ of the $4$ directions is a valid move

$//$ if it is a valid move it will perform the move and update the board and store

$//$ it into the array at the corresponding move count

$//$ base case occurs if the move count is equal to $31$ AND the centre position is

$//$ still filled with an $\text{'}$X$\text{'},$ otherwise it calls the recursive method and moves

$//$ on to the next move

$//$ if the base case is not reached, than the backtracking method is called and

$//$ tries a new jump direction

public boolean findSolution$($int move$)\{$

$//$ Implement findSolution here

$//*********$The error will go away once you implement and returns a boolean

$//$ value$*********$

return false;

$\}$

$\}$

considering this code, help me implement the peg solitaire so the solution can look like this:$-$

$/[\text{'}\text{'},\text{'}\text{'},\text{'}0\text{'},\text{'}0\text{'},\text{'}0\text{'},\text{'}\text{'},\text{'}\text{'}],$

$//[\text{'}\text{'},\text{'}\text{'},\text{'}0\text{'},\text{'}0\text{'},\text{'}0\text{'},\text{'}\text{'},\text{'}\text{'}],$

$//[\text{'}0\text{'},\text{'}0\text{'},\text{'}0\text{'},\text{'}0\text{'},\text{'}0\text{'},\text{'}0\text{'},\text{'}0\text{'}],$

$//[\text{'}0\text{'},\text{'}0\text{'},\text{'}0\text{'},\text{'}$X$\text{'},\text{'}0\text{'},\text{'}0\text{'},\text{'}0\text{'}],$

$//[\text{'}0\text{'},\text{'}0\text{'},\text{'}0\text{'},\text{'}0\text{'},\text{'}0\text{'},\text{'}0\text{'},\text{'}0\text{'}],$

$//[\text{'}\text{'},\text{'}\text{'},\text{'}0\text{'},\text{'}0\text{'},\text{'}0\text{'},\text{'}\text{'},\text{'}\text{'}],$

$//[\text{'}\text{'},\text{'}\text{'},\text{'}0\text{'},\text{'}0\text{'},\text{'}0\text{'},\text{'}\text{'},\text{'}\text{'}]$