Implement the Automaton class in the header file using the functions in the given spec sheet.Implementation Specifications & Notes

$\_-$num$\_$parents is the number of parents this Automaton considers $(1,3$ or $5),$

Automaton: :$\_$extreme$\_$bit

Automaton: :Automaton$($size$\_$t num$\_$parents, size$\_$t rule$)$

Set $\_$extreme$\_$bit to $0.$

Note you can $($but don't have to$)$ do all of this via a member initialization list. Thanks to the compiler flags we'r using, you'll probably

bool Automaton: : set$\_$rule$($size$\_$t rule$)$

You can assume $($or rather, you should ensure because you're also coding the constructor$)$ that when this method is invoked, the $\_$num$\_$parents member of the current object will already be set. Check its value, and if it is greater than permitted by MAX$\_$PARENTS, return false.

Furthermore, you should also return false if the rule value is greater than the maximum permitted by the $\_\_$num$\_$parents value. What is that value? How many rules does a particular number of parents allow?

Return false also if there is an even number of parents.

In short, this function will ensure that the Automaton object is valid, and return fal. constructor$)$ if it is not. The constructor, in turn, can set the $\_$is$\_$valid attribute.

Otherwise, fill in the $\_$rules vector of the current object with the appropriate values for the given rule and return true. You can also assume $($or$,$ again, ensure$)$ that the vector would already have been sized correctly in the constructor.

bool Automaton: : equals$($const Automaton& that$)$

This function should return true if the $**$ this Automaton is equal to that Automaton

They are both invalid.

bool Automaton: :make$\_$next$\_$gen$($const std: :vector&$&$=1\{1\}$:$\text{'}{2}^0=1n$