Shape functions $(20$ pts$)[$Difficulty: Easy$]$ These functions serve to introduce the concept of polymorphism and object$-$oriented programming. You will be programming two types of objects that represent shapes. The rectangle$\_$t type represents a rectangle shape with a width and length. The triangle$\_$t type represents an equilateral triangle with a length. Both types are based on a base shape$\_$t type that corresponds to the base class in an object$-$oriented language.

Polymorphism is the concept that a pointer to a base object can refer to objects of different sub$-$types. For example, a shape$\_$t pointer can refer to a rectangle$\_$t or a triangle$\_$t$.$ Object$-$oriented languages handle this automatically, but in a non$-$object$-$oriented language like C$,$ we must emulate this behavior ourselves. This is done by having the shape$\_$t struct located at the beginning of the rectangle$\_$t and triangle$\_$t structs $($as shown in pointer.h$).$ Thus, casting a rectangle$\_$t pointer to a shape$\_$t pointer is valid since the beginning of rectangle$\_$t is a shape$\_$t struct $($note this is an actual struct, not a pointer to the struct$).$

To support virtual functions $($i$.$e$.,$ shape functions that can either refer to rectangle functions or triangle functions$),$ we use what's known as a virtual function pointer table that contains function pointers that refer to the correct functions. For example, rectangle$\_$t will have function pointers within the shape$\_$t portion that point to rectangle functions, and triangle$\_$t will have function pointers within the shape$\_$t portion that point to triangle functions. Thus, a shape can call the appropriate function by using the virtual function pointer table. For example, the provided shape$\_$area function uses the table to call the appropriate area function for the shape.

Your role in this part of the assignment is to $1)$ understand how the shapes are manipulated, and $2)$ implement a set of functions that emulate object$-$oriented programming in C$.$ The first four functions implement the area and perimeter calculations for rectangles and triangles. The next two functions illustrate the initialization of each shape. The last two functions illustrate how to compare generic shapes, which may either be rectangles, triangles, or some other shape.