$($Due November $6)$ Write a program that, given an arithmetic expression,

first transforms it to a postfix form, and then

computes its value $($by using the stack$-$based algorithms that we recalled in class$).$

You can assume that the expression contains no variables, only numbers, and all the numbers are one$-$digit numbers, i$.$e$.,$ each of these numbers is either $0,$ or $1,$ or $2,$dots, or $9.$ For example, your program should correctly process expressions like $2+3**4,$ but there is no need to process expressions like $11+22.$ For simplicity, assume that the only arithmetic operations are addition $+,$ subtraction $-,$ and multiplication $*,$ and that there are no parentheses.

Comments:

as with all programming assignments for this class, submit a file containing the code, and a file containing an example of what this program generates on each step;

ideally, use Java, but if you want to write it in some other programming language, check with the TA that it is OK; usually, C or $C++$ are OK $.$