Reference no: EM13844478

Given a valid postfix expression, create the corresponding expression tree.

Traverse this tree in inorder, preorder and postorder fashion (all three methods, both recursively and iteratively).

 The program must support (at least) the following in the postfix expression:

Binary operators: ^ - Exponentiation (Highest precedence) /, * - Division, Multiplication +, - - Addition, Subtraction (Lowest precedence)
Operands:

The operands are all variables, which is represented by a single lowercase English character. (a - z) Input - Output Format The only line of the input contains a valid postfix expression. (There will not be any space anywhere in the expression) Do the inorder, preorder and postorder ( recursively).

Output the result of each traversal on a fresh line. For the inorder traversals, use proper parentheses also (i.e., each operator, together with its operands must be enclosed in parentheses).

Sample Input/Output abc*+ Inorder: (a+(b*c)) Preorder: +a*bc Postorder: abc*+ m Inorder: m Preorder: m Postorder: m abcd^*+e- Inorder: ((a+(b*(c^d)))-e) Preorder: -+a*b^cde Postorder: abcd^*+e-