Why you need to decrease the "unit" in the loop?

while( result.length() % unit != 0 ) unit /= 3;

I suggest replacing "regex_search" with "sregex_iterator":

	regex reg("1+|0+");
	int unit = INT_MAX;
	for (std::sregex_iterator it(text.begin(), text.end(), reg), end; it != end; ++it)
	{
		const auto length = (*it)[0].length();
		if (length < unit)
			unit = length;
	}

Converting to int makes the * 2 + 1 operations done in integer arithmetics, which probably ends up saving a few cpu cycles.

Also prevents warnings about losing precision when implicitly converting from double to int.

This solution does not actually pass the tests...
As mentioned, it should take into account the case where the ball bounces at the exact height of the window.
It would have been nice if it worked like this.

And I think that (int)floor() is redundant.

In this test, you should have the char 255 at some point in the input.
Then 255+1 = 0, and it breaks the loop.

Tricky :D