Write a program in cppthat accepts a string that is a space$-$delimited integer arithmetic expression in postfix notation. Use a stack to compute the value.

Example:

The input string $54+310*+$ is equivalent to the infix expression $(5+4)+(3*10)$

The answer is $39.$

The algorithm is:

Take the leftmost token from the string

If it is numeric $($which may include a unary operator$),$ push that token onto the stack

If it is a binary operation, pop the vector twice, apply the operation, and push the result

When the input string is empty, the stack will contain one entry: the final answer

Here$$s how the given string gets processed:

String Stack

$54+310*+$

$4+310*+5$

$+310*+$ a $45$

$310*+9$

$10*+39$

$*+1039$

$+309$

$39$

The final answer, $39,$ is the only element in the stack after all tokens in the string have been consumed.

This problem has an extra twist. The string contains characters, so $10$ isn$$t a ten, but is the char $1$ followed by the char $0.$ You will need to convert string representations of integers $($signed and unsigned$)$ into their integer values. You$$ll also need to handle unary $-$ and $+.$

We also have to worry about the three non$-$commuting operators $/\%.$ We will evaluate the postfix string $45-$ as $4-5$ and, likewise, will evaluate $45/$ as $4/5$ and $45\%$ as $4\%5.$

The program should continue to accept and process input strings until the user enters a zero as input. There$$s no need to check for validity; all input will be well$-$formed postfix expressions.