Description

Evaluating Mathematical Epressions : due $2024/1/1$ Mon $($at $11$:$59$pm$)$

A Mathematical epression is something like the following$2+(5*(3\mathrm{.}1^\{3\mathrm{.}3\}+$ sin$(6\mathrm{.}1)))/$ log$\_\{3\}(15)*2,$ in which there is a mixture of arithmetic expression, trigonometric, and logarithmic functions. Here is a list of those $12$ functions.

Basic arithmetic operators: $+,-,*,/$ along with the unary negation operator $-,$ i$.$e$.-5$

Unary scientific functions: sin$(),$ cos$(),$ tan$(),$ log$(),$ sqrt$()$

Binary scientific functions: log$\_\{$b$\}($a$)$ and $2^\{3\}.$ You should use the corresponding math functions in to implement them.

Remarks

Unary negation $-$: note that $-5^\{2\}$ must be interpreted as $-(5^\{2\})$ instead of $(-5)^\{2\}.$ The unary operator $-$ acts on any double and turns its value negative.

log$()$ stands for natural logarithm, i$.$e$.$ with base e $=2\mathrm{.}718....$

log$\_\{$b$\}($a$)$ is ordanry logarithm with base b$.$ Use the log$()$ function in to implement log$\_\{$b$\}($a$)$ as log$($a$)/$log$($b$).$

sqrt$()$ is square root.

$2^\{3\}$ stands for $2$ raising to the third power, which is equal to $8$

Note that, according to our syntax, the curly braces $\{\}$ are only used in logarithm$\text{'}$s subscript log$\_\{$b$\}($a$)$ and power's superscript $5\mathrm{.}1^\{2\}.$

The operators' priorities are listed as follows.

You do not need to check for invalid expressions $($like $2\mathrm{.}5+=3)$or invalid operations $($such as sqrt$(-5)).$

priority operators

lowest $+,-$

medium unary $-$

high $*,/$

highest sin$(),$ cos$(),$ tan$(),$ log$\_\{\}(),$ log$(),$ sqrt$(),^\{\}$

If two operators have the same priority, they should be evaluated in from left to right.

Write a class Expression that holds the value of a Mathematical epression and it has $($at least$)$ two member functions input$()$ and eval$(),$ in which the latter evaluates the expression. You may add members you like, as long as you keep all data members private or protected. We strongly suggest you use the getline$()$ function to read the whole expression as a stringobject $($remember to include $).$ Do not use cin $>>$ str; as it will stop on whitespaces. Use getline$($cin$,$ str$)$; instead to read the whole line $($in which str is a string object$).$ The main function is given as follows. Do not change main$()$ otherwise you may lose penalty points.

int main $()\{//$ DO NOT CHANGE MAIN!!

Expression exp$1$;

exp$1.$input$()$;

exp$1.$eval$()$;

exp$1.$output$()$;

return $0$;

$\}$

Try to explore the power of C$++$ and make your program as flexible as possible, i$.$e$.$ if new functions like sinh or tanh are added in the future, you do not need to modify too much of your work to support them.

Hint

You may need to use two stacks to do this assignment. One for storing the operands, and the other for storing the operators. You can use the standard library templates to do that. Include to use their templates. You also need to include and libraries.

Grading & Submission

Same as Assignment #$2.70\%$ correctness and $30\%$ style. Submit your sourcecode $($with detailed comments$)$ on both OJ and eLearn.

Input $1$

$2+(5*(3\mathrm{.}1^\{3\mathrm{.}3\}+$ sin$(6\mathrm{.}1)))/$ log$\_\{3\}(15)*2$

Output $1$

$170\mathrm{.}961$

Input $2$

$-87\mathrm{.}38+$ sqrt$(\mathrm{.}23^\{1\mathrm{.}4\}+91\mathrm{.}13)*3\mathrm{.}456+$tan$(98\mathrm{.}23)$

Output $2$

$-53\mathrm{.}2482$