Is a Point Inside a Rectangle?

Computers typically use a coordinate system when displaying graphics. The fundamental unit of a

computer screen is typically the pixel, a tiny square on the screen that can$$t be subdivided.

Generally, the pixel at coordinates $(0,0)$ is at the top left corner of the screen. The x$-$coordinates of

pixels increase as we move toward the right side of the screen, while the y$-$coordinates increase as

we move toward the bottom of the screen.

In this kind of coordinate system, a point $($i$.$e$.,$ a single pixel$)$ on screen can be represented as two

integers, the x$-$ and y$-$coordinates of the point. For example, we could create a C$++$ structure to

represent a point like this:

struct point

$\{$

int x $=0,//$ x$-$coordinate of point

int y $=0$; $//$ y$-$coordinate of point

$\}$;

A rectangle on the screen can easily be represented using four integers: the x$-$ and y$-$coordinates

of the upper left vertex of the rectangle, the width of the rectangle, and the height of the rectangle.

For example, a C$++$ structure to represent a rectangle on screen might look like this:

struct rectangle

$\{$

point origin; $//$ point representing upper left vertex of rectangle

int width $=0$; $//$ width of rectangle

int height $=0$; $//$ height of rectangle

$\}$;

height

width

$($x$,$ y$)$

$($x$,$ y$)$

Write a function to determine whether a given point lies inside a specified rectangle. The point is

inside the rectangle if it lies within the boundaries of the rectangle or on one of its four edges.

bool is$\_$inside$($const point& p$,$ const rectangle& r$)$;

The definitions for the point and rectangle structures are available in a header file named

shapes.h$.$

Files We Give You: A makefile $,$ the header file shapes.h$,$ and a sample main program

$($inside$.$cpp$)$ to test your solution. The executable file created by a successful build will be

named inside.

File You Must Submit: Place your solution code in a file named solution.cpp$.$ You will need to

#include "shapes.h$"$ at the top of the file in order to access the point and rectangle structures.

This will be the only file that you submit.

Examples

Input: p $=[$x: $25,$ y: $35],$

r $=[$origin: $[$x: $20,$ y: $30],$ width: $20,$ height: $15]$

Returns: true

Input: p $=[$ x: $12,$ y: $35],$

r $=[$ origin: $[$x: $20,$ y: $30],$ width: $20,$ height: $15]$

Returns: false

Input: p $=[$x: $40,$ y: $17],$

r $=[$origin: $[$x: $40,$ y: $15],$ width: $5,$ height: $8]$

Returns: true

Input: p $=[$x : $60,$ y: $23],$

r $=[$origin: $[$x: $40,$ y: $15],$ width: $5,$ height: $8]$

Returns: false