Java Programming : $1.$ Implement a binary tree node class similar to the following:

Class BinaryNode$\{$

DataType key;

BinaryNode left;

BinaryNode right;

$\}$

$2.$ Implement a program that reads in a postfix expression $($every operator is preceded by exactly two operands$),$ using integers as operands and basic mathematics operators $(+,-,*$ and $/),$ and constructs an expression tree out of binary nodes for this expression.

The program should utilize a stack to build the tree, using the following logic:

$$ Read one symbol at a time from an input expression

$$ If the symbol is an operand, create a one$-$node tree and push it to stack

$$ If the symbol is an operator

$$ Create a new node for the symbol

$$ Pop two trees T$1($popped first$)$ and T$2$ from the stack

$$ Form a new tree: root$($symbol$),$ left $($T$2),$ right $($T$1)$

$$ Push the new tree to stack

$3.$ Implement the three traversal methods: pre$-$order traversal, in$-$order traversal and post$-$order traversal. When $$visiting$$ a node, each method should print the node$$s value.

Void pre$-$order$-$traverse $($node v$)$ Void in$-$order$-$traverse $($node v$)$

$\{\{$

visit $($work at$)$ v; if$($v$.$left $!=$ null$)$

for$($ each child u of v$)$ in$-$order$-$traverse$($v$.$left$)$

pre$-$order$-$traverse$($u$)$; visit $($work at$)$ v;

$\}$ if$($v$.$right $!=$ null$)$

in$-$order$-$traverse$($v$.$right$)$

Void post$-$order$-$traverse $($node v$)\}$

$\{$

for$($ each child u of v$)$

post$-$order$-$traverse$($u$)$;

visit $($work at$)$ v;

$\}$

$4.$ Test all of your code using two postfix expressions, each with at least $12$ symbols

a$.$ First use your code from Task $2$ to read the postfix expression and return the tree

b$.$ Then run each of these three traversal methods on the tree, to print out the prefix, infix and postfix expression correspondingly.