Well, I was trying to come up with some sort of algorithm for this which took into account the largest potential area the cars could take up, as well as the least amount of area the cars could take up, and came up with this. The problem is, I can only work it out if the width of the cars are known, as I don't really know how this can be solved without knowing this.
PHP Code:
function onCreated(){
temp.n = 100;
temp.car_length = 2;
temp.car_width = 2; // Because I can't do it with an unknown value
/* Using Pythagoras' theorm, I found the hypotenuse of the triangle inside
the car, which also gave me the radius of the circle around the car,
which represents the total amount of area it could potentially take up, as
they are parking randomly.
*/
temp.car_potential_area = ((car_length / 2)^2 + (car_width / 2)^2)^0.5;
/* I then used the radius of the circle found above so that I could
calculate the length of the radius between the center of the inner
circle and the center of the car's "circle"
*/
temp.car_middle = (n / pi / 2) + car_potential_area;
/* And then, using the radius from above, calculated how many cars
could fit along the circumference of this line, like beads on a string
if you imagine the circles around the cars.
*/
temp.parking_places = 2 * pi * car_middle;
/* From this, I divided the total parking space by the diameter of the
circle of potential area they could take up, to get a decimal value
for the number of cars.
*/
temp.cars = parking_places / (car_potential_size * 2);
// Echoes a value for the minimum number of cars (38 cars)
echo(int(temp.cars)); // Integer because you can't have a fraction of a car
/* A value for the maximum number of cars, parking side by side around the
circle
*/
temp.max_cars = parking_places / car_length;
// Echoes a value for the maximum number of cars if they were lined up side by side (54 cars)
echo(int(temp.max_cars));
}
So my answer is that there could be any number between 38 and 54 cars in the parking lot.
This is the best I could come up with, tell me if I'm along the right lines.
