Assignment $-5$: Heap

Write a program which manages heap, where the elements of heap are geometries.

It is arranged with the area of geometry. The program supports the following

functions:

inserting a geometry:

action: insert a geometry and arrange the heap by the area of geometry

input format: I t $\{$geometry$\}$

t: type of geometry among c for circle, r for rectangle, s for square

$\{$geometry$\}$ field depends on the type of geometry $($as given t $)$

c x y r $//($ x$,$y$)$ for center, r for radius

rx$1$y$1$x$2$y$2////($x$1,$y$1)$ for left bottom comer and $($ x$2,$y$2)$ for right top corner

sxy$!////($x$,$y$)$ for left bottom corner and $1$ for side length

output: none

get the largest area

action: remove the geometry from the heap and print its area

input format: get

output format: area of the removed geometry $($two floating point values$)$ and

$0\mathrm{.}00$ if no geometry is in the heap.

Example

We assume pi$=3\mathrm{.}14$

Neither STL nor any libraries are allowed. This program should be implemented

from scratch not by using any butl$-$in libraries or functions

NO USE OF CHAT GPT IS ALLOWED!!!