Write a java program to implement the following algorithms for Binary Search Tree. $($Assume the tree

only contains integer keys$).$

TREE$-$INSERT $(T,z)$

$y=$ NIL

$x=$ T$.$root

while $x$ NIL

$y=x$

if $z.$ key $x=xx=xz*p=yy===z\frac{,}{\frac{?}{?}}T,(x,k)z,1x==k==x=z,3(x.$left,$k)(x.$right,$k)(x)(x)xx=xxxx=xx(T,x)xx(x,k)k.$ key

return TREE$-$SEARCH $(x.$left,$k)$

else return TREE$-$SEARCH $(x.$right,$k)$

TREE$-$Minimum $(x)$

TREE$-$MAXImum $(x)$

while $x.$right $$ NIL

$x=x.$ right

return $x$

while $x.$left $$ NIL

$x=x.$ left

return $x$

Write the following methods $in$ java and test them $in$ the main $()$ method.

BSTInsert $(T,x)$

TreeMinimum $(x)$

TreeMaximum $(x)$

TreeSearch $(x,k).$ key $,1ifx==$ NIL $ork==x.$ key

else $y.$ right $=z,3ifk.$ key

return TREE$-$SEARCH $(x.$left,$k)$

else return TREE$-$SEARCH $(x.$right,$k)$

TREE$-$Minimum $(x)$

TREE$-$MAXImum $(x)$

while $x.$right $$ NIL

$x=x.$ right

return $x$

while $x.$left $$ NIL

$x=x.$ left

return $x$

Write the following methods $in$ java and test them $in$ the main $()$ method.

BSTInsert $(T,x)$

TreeMinimum $(x)$

TreeMaximum $(x)$

TreeSearch $(x,k)$

$x=x.$left

else $x=x.$right

$z*p=y$

$ify==$ NIL

$T.$ root $=z\frac{,}{\frac{?}{?}}$ tree $T,$ TREe$-$SEARCH $(x,k)$

elseif $z.$ key $.$ key $,1ifx==$ NIL $ork==x.$ key

else $y.$ right $=z,3ifk.$ key

return TREE$-$SEARCH $(x.$left,$k)$

else return TREE$-$SEARCH $(x.$right,$k)$

TREE$-$Minimum $(x)$

TREE$-$MAXImum $(x)$

while $x.$right $$ NIL

$x=x.$ right

return $x$

while $x.$left $$ NIL

$x=x.$ left

return $x$

Write the following methods $in$ java and test them $in$ the main $()$ method.

BSTInsert $(T,x)$

TreeMinimum $(x)$

TreeMaximum $(x)$

TreeSearch $(x,k)$