$5$A$)$ i$)$ Construct the Expression tree using the stack for the following and also describe the steps for

implementing the same and traverse the tree and provide the infix, postfix and prefix order traversal

of the constructed expression tree using stack for the following expressions.

$(\frac{5-z}{-}8{)}^{*}(4^2)$ also evaluate the expression tree when $z=20$

$(($true $V$ false$){?}^{{?}^{?}}$ false$)vv($true $V$ false$)$

$ab+$cde$+**$

$(2a+5b{)}^3{?}^{*}(x-7y{)}^4$

ii$)$ Construct the Binary search tree $($BST$)$ for the following and provide the Post$-$order, In$-$order, and

Pre$-$order traversal of the following:

a$)$ Given the post order A C E D B H I G F construct the BST and outline the In$-$order and Post order

tree traversal.

b$)$ Given the pre$-$order traversal order of the tree $20,16,5,18,17,19,60,85,70$ construct the BST

and provide the In$-$order and Post order tree traversal.

$5$B$)$ Outline the definition of sparse matrix. Implement the C$++$ User defined function to implement the

Sparse matrix addition and multiplication?

$5$C$)$ Write the user defined functions to merge the $2$ binary trees? What problems you will face if you

merge two binary trees of numerical elements which are represented using A single array.