Shapes

A drawing app keeps rectangles, squares and triangles in one list. Write the shape types so that code holding that list can ask any shape for its name and its perimeter (the length all the way around it) without knowing which kind of shape it is. That is polymorphism: one call, shape.perimeter(), and each kind of shape runs its own version.

Every shape class inherits from the class Shape, the common type. Shape has two methods:

• name() returns the kind of shape as text: "Shape" for a plain Shape.
• perimeter() returns the length around the shape: 0 for a plain Shape.

Each shape class overrides both:

• Rectangle(width, height): its name is "Rectangle", its perimeter 2 × (width + height).
• Square(side): its name is "Square", its perimeter 4 × side.
• Triangle(a, b, c): its name is "Triangle", its perimeter a + b + c.

In Scala each shape class extends Shape and writes its versions of the methods with override def. Each shape class gets its sizes as val parameters of its constructor.

Then write two methods of the class Solution, as in the course's other lessons. Both get the shapes as Array[Shape]:

• totalPerimeter(shapes) returns the sum of the perimeters of all the shapes.
• largestShape(shapes) returns the name of the shape with the largest perimeter. If several shapes share the largest perimeter, the one that comes first wins.

Both functions must work through the common type's methods only: never check which kind a shape is. Then a new kind of shape, added later, works with them unchanged.

The starter code already has every class header, constructor included, and every method header: write the method bodies. For each test, the harness reads the shapes, builds them in the order given, calls totalPerimeter and largestShape, and prints the two results on one line, separated by a space.

Example 1:

Input:
    Rectangle(3, 4)
    Square(5)
    Triangle(3, 4, 5)
Output: 46 Square
Explanation: The perimeters are 2 × (3 + 4) = 14, 4 × 5 = 20 and 3 + 4 + 5 = 12. Their total is 46, and the square's 20 is the largest.

Example 2:

Input:
    Rectangle(2, 4)
    Square(3)
    Triangle(4, 4, 4)
Output: 36 Rectangle
Explanation: All three perimeters are 12: 2 × (2 + 4), 4 × 3 and 4 + 4 + 4. On a tie the shape that comes first in the list wins, so the answer is the rectangle.

Example 3:

Input:
    Square(1)
    Rectangle(1, 1)
    Triangle(2, 2, 3)
Output: 15 Triangle
Explanation: The perimeters are 4, 4 and 7, so the last shape, the triangle, is the largest. A 1 by 1 rectangle has the same sides as a square, but it is still a Rectangle: each object answers name() for its own class.

Constraints:

• Every test has between 1 and 100 shapes: the list is never empty.
• Every size (width, height, side, and each side of a triangle) is an integer from 1 to 10⁴.
• A triangle's three sides always make a real triangle: each side is shorter than the other two together.