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.

$1.$ Basic arithmetic operators: $+$ ; r$-,*,/$ along with the unary negation operator $-,$ i$.$e$.$

$-5$

$2.$ Unary scientific functions: sin$(),$ cos $(),$ tan$(),$ log$(),$ sart $()$

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

implement them.

Remarks

$1.$ 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

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

$3.$ Log$\_($b$\}($a$)$ is ordanry logarithm with base b$.$ Use th Log $()$ function in to implement log$\_\{$b$\}($a$)$ as log$($a$)/$log$($b$).$

$4.$ sqrt $()$ is square root.

$.$

$2^(3]$ stands for $2$ raising to the third power, which is equal to $3$

$6.$ Note that, according to our syntax, the curly braces $(\}$ are only used in logarithm$\text{'}$s subscript log$\_\{$b$\}($a$)$ and power's superscript $5.1^(2\}.$

$7.$ The operators' priorities are listed as follows.

$8.$ You do not need to check for invalid expressions $($like $2\mathrm{.}5+=3)$or invalid operations $($such as sqrt $(-5)).$

priority operators lowest $+,-$ mediumunary

high

$*,/$

highest sin$(),$ cos$(),$ tan$(),$ log$\_(7(),$ 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 string object $($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.