Draw the expression tree for the expression: a b * (b c)/(d + e) + f ** g. Give the preorder and post-order traversal of the expression tree so obtained. Preorder and postorder traversals are recursively defined as follows:

Preorder Traversal

1.Visit the root

2. Visit left sub-tree in preorder traversal

3. Visit right sub-tree in preorder traversal

Post-Order Traversal

1. Visit left sub-tree in post-order traversal

2. Visit right sub-tree in post-order traversal

3. Visit the root

Notes:

(1) visit a node means writing the value inside the node.

(2) The operators have the following priorities of evaluation (highest to lowest)

(i) ( )

(ii) ** (exponentiation)

(iii) /, *

(iv) +, -

(3) Operations at the same level are evaluated from left to right, except exponentiation, which are evaluated from right to left.

For example, a b + c is (a b) + c and not a (b + c). a ** b ** c = a ** (b ** c) and not (a ** b) ** c.