In c$++$

Part $2\mathrm{.}1$: Implement evaluate for each Formula subclass

Each logical formula is represented as a tree. The tree in blue below is essentially what $pvv(q^{{?}^{?}}$notr$)$ looks like:

To evaluate any non$-$Var Formula to true or false, you can recursively evaluate its children and combine their result$($s$).$ For example, suppose you're evaluating $Or(x,y),$ where $x$ and $y$ are any Formula. To evaluate the entire $Or(x,y),$ you can evaluate $x$ and $y$ individually first $-$ then you can combine them together using II$,$ since that's what Or means!

The leaves in Formula trees are always Vars. A Var could stand for anything, so that is why we pass along the var$2$ Valmap $($shown in green$)$ when we call evaluate $-$ the user must pick ahead of time what each variable's value is$.$ You never change var $2$Val yourself during evaluation, and you keep passing the same var$2$Val map in each recursive call. Evaluating a Var is as simple as looking up its value in the map!

Implement the proper overridden evaluate method for each subclass of Formula.

Part $2$: SAT solve like there's no tomorrow

Make sure to watch the introduction video that explains everything! You won't need to write more than $50$ lines of code for this lab, but you'll have to think hard about every line.

SAT solving is the process of taking a Boolean formula and determining whether or not it is satisfiable $-$ that is$,$ whether it is possible to set the variables just right to make the formula be true. For example, the formula $pvv(q^{{?}^{?}}$notr$)$ is satisfiable because you could set $p=T,q=F,$ and $r=F$ and the formula would evaluate to $T.$

In this lab we want to find all the ways to make a formula satisfiable.

Take a look at logic.h and testLogic.cpp$,$ and notice how we're using subclasses of Formula to represent logical formulae. In particular, notice how I build the formula from above in testEval.