Write a program that builds a binary expression tree (BXT) from a given postfix expression, displays the expression in prefix form and evaluates it. Follow these steps in solving this problem:

• draw a BXT for each of the four given expressions; use the tree to write the expression in prefix form and evaluate it.

• fill in the five functions in the program shell "bxt.java" shown below

• copy the shell "bxt.java" and complete the program

• run your program on these four postfix expressions
  • 12+
  • 12+4*
  • 432*+7-
  • 82+591-+*

Extensions

• Display the expression in fully parenthesized infix form instead of prefix form.

• Enter the postfix expression using variables rather than numbers and ask for the values of the variables when the expression is evaluated.

• Expand the program to include other binary operations.