I know that once all the cubes that are connected are destroyed, the unconnected blocks collapse. How do you find out the unconnected blocks?  edit 1: How would you determine the collapsible object if it spans multiple chunks?
I'm looking for a good algorithms for the following problem: Given a 3D grid of voxels (which may be either empty or filled), if I pick two non-adjacent voxels, I want to know if they are connected to each other by other voxels.  For example (to illustrate the situation in 2D), where # is a filled square:    1 2 3 a # # # b # # c # # #   If I pick a3 and c3, I want to determine as quickly as possible if they they are connected; if there is a path between a3 and c3 through filled pixels. (The real situation is in a 3D voxel grid, of course.)  I've looked at floodfill algorithms and path finding algorithms, but I'm not sure which to choose. Both do unneccesary work: Flood fill tries to fill all voxels, but this is not needed. Path-finding algorithms are usually concerned with finding the shortest path, which is also not necessary. I only need to know if there is a path.  What algorithm should I be using?  Edit: based on the comments, I think should add the following: the content of the voxels are not known in advance, and also, the algorithm is needed to detect if removal (emptying) of a voxel would cause the group of voxels to break into two or more smaller groups.
I'm trying to make a map using the Javascript API.  I want to use my own basemap, but I can't find the most simple code to do this.  I always see something like this:    function init() {     map = new esri.Map("mapDiv", {       basemap: "satellite",       center: [-97.395, 37.537],       zoom: 11     });   But I don't want to use the ArcGIS online basemaps.  What is the code to make a map service I am hosting my basemap? A famous exercise which one encounters while doing Complex Analysis (Residue theory) is to prove that the given integral: $$\int\limits_0^\infty \frac{\sin x} x \,\mathrm  dx = \frac \pi 2$$ Well, can anyone prove this without using Residue theory?  I actually thought of using the series representation of $\sin x$: $$\int\limits_0^\infty \frac{\sin x} x \, dx = \lim\limits_{n \to \infty} \int\limits_0^n \frac{1}{t} \left( t - \frac{t^3}{3!} + \frac{t^5}{5!} + \cdots \right) \,\mathrm  dt$$ but I don't see how $\pi$ comes here, since we need the answer to be equal to $\dfrac{\pi}{2}$. If banks offer a fixed rate lower than the variable rate, is that an indication interest rates may head down? This is one of the major banks in Australia:   At present time, the variable rate is 7.80% but the fixed rate is 6.99% for one year.  And it seems most banks in Australia, if you fix the rate (at the moment), you will get a lower rate.  Is this an indication that in the eyes of the banks, that they believe the interest rates are going to down? I just ask because it seems most people in the media think the rates are going up and they've risen about 6 times in a row now.  Could it be that the banks are secretly preparing for rates to drop? SQL query to convert columns into rows How do Minecraft biomes work? I've never seen any information about the distribution of biomes in a generated world.   First, are all types of biomes, guaranteed to exist in a world? Will I always find snow somewhere, and desert somewhere? I've got one world that doesn't seem to have cactus (so I guess the sand is beaches, no actual desert).  Second, is there any kind of pattern or relation to biomes? Is snow to the North, and desert South, for example?  Third, how about density of biomes? If all types do exist, would I find them all within distance X of my spawnpoint, or have to travel for weeks to find a given type? What's up with Vic? In the TV series Glitch, we see several people returning from the dead.  We see Vic, a police officer,      getting in a car accident and seemingly .   Afterwards, he behaves very strange. He searches for the doctor and the risen, whom he seems to know a lot about, sometimes even more than they know themselves.      He rekills Maria by breaking her neck.   And he threatens the other risen.  Most of the risen, especially those that have been dead longer, have some difficulty remembering their past lives. Vic on the other hand, seems to remember fine but to have a complete change of character instead.   Why is he after the other risen? How does he know so much about them? Why did he have such a change of character?     Yes, these are several questions, but they are closely related, so I opted to ask them in one question. Do I need a UK visa? How and where to apply? One of whom destroys the Earth, perhaps accidentally, while fighting another... the plot also involves a human colony ship or planet that loses contact with the Earth; I think a small boy is also involved with the plot, although it's been 20-30 years since I read this story.  Any help would be appreciated!  It's driving my brother and me a bit batty.  Here's the batty brother's take: the main being has created others who are now at war, exploding stars. To escape, the main being accelerates the star of the human colony as a decoy. However, most of the story centers on some guy who winds up living forever, as they keep sticking him in cryogenic sleep and reawakening him. If memory serves me right, they abandon the colony planet for a while and move to asteroids as the star is weakening because it is using it's energy to accelerate. When it decelerates, it is the only star left in the universe. The one "being" was almost reduced to living off the energy of a black hole when it appears, and he sees it and sets off to go there, with a cryptic ending that the humans very well might fight him off. invalid conversion from 'int' to 'char *' Changed response to Recommendation questions now that there's a site for them? Understanding the proof of infinitely many primes $\equiv 3\pmod{\!4}$ Theorem: There are infinitely many primes congruent to $3 \mod 4$. Proof: Assume that $p_1 = 3, . . . , p_n$ are primes of the form $p_j ≡ 3 \mod 4$. We will construct a new one by looking at $N = 4p_1 · · · p_n − 1$ (putting $N = 4p_1 · · · p_n+3$ would also work).  There is more to this proof but the rest of it I understand, what I don't get is where it says &quot;$N = 4p_1 · · · p_n − 1$ (putting $N = 4p_1 · · · p_n+3$ would also work)&quot;. I do not understand why we are writing $4p_1 · · · p_n − 1$. Is there a more clear way to prove this theorem? Thanks to the internet, graphic design and programming are becoming increasingly overlapping fields.   As a programmer, I constantly find myself needing basic knowledge of Graphic Design, but have trouble locating thorough yet concise graphic design learning resources, and instead usually find bits and pieces of knowledge applicable to the task at hand.  Can you guys offer some tips or recommend some good books, tutorials, blogs, and websites which provide a beginner level overview of web design that have been, in your experience, effective and high quality learning materials. I'm not looking for tips on how to use image editing tools, but assuming a basic grasp of those, which resources and advice will best help a new designer create professional looking designs? Is the following proof correct, or are certain steps illegal?  Suppose $f:G_1\to G_2$ is a surjective group isomorphism, $N_1\lhd G_1, N_2\lhd G_2$ normal subgroups, with $N_1=f^{-1}(N_2)$. Prove that $(G_1/N_1)\cong (G_2/N_2)$.  Proof:  As $f$ is surjective, we an use the first isomorphism theorem to get $G_1/\ker(f)\cong G_2$, which implies that $$(G_1/\ker f)/(N_1/\ker f)\cong G_2/(N_1/\ker f)$$  Using the first isomorphism theorem we also know that $$N_1/\ker (f)\cong f(N_1)=f(f^{-1}(N_2))=N_2$$  Combining this we can see that $(G_1/\ker f)/(N_1/\ker f)\cong G_2/(N_1/\ker f)\cong G_2/N_2$.  Using the third isomorphism theorem we have that: $$ (G_1/\ker f)/(N_1/\ker f)\cong G_1/N_1$$  And from the last two lines we have $G_1/N_1\cong G_2/N_2$ $\tag*{$\Box$}$ After startup for 5 minutes my system is very slow. The Task Manager shows that the disk usage is at 100%. (Later this number is around 2-4 %, but sometimes for 1-2 minutes go up again at 100%.)  I searched a lot on Google. For example I read , and also other pages. I opened two topic on Microsoft answer.  and one in Hungarian.  But I didn't found the solution yet. So I would like to ask Community's help. :)  Here the steps I already done:   I disabled everything at startups (including services) and the issue is the same.  I disabled Prefetch and Superfetch, the Baground Intellingent Transmission, Windows Search and Windows Defender but the issue is still persists. I made a health check on HDD, I made defrag and file system error check, but there are no errors. Also I tried to reinstall the HDD's driver. I made a full hardware check up, with no errors. The Windows and all the drivers are up-to-date. I tried a clean start. The issue is the same. I deleted Dropbox and all antivirus. I turned of the MSI mode.      I using also Linux, where this error is not occurs. Good to know, that Windows had 4 partitions, but I deleted 2 of them for the Linux. I don't know what partitions was these but both was only 10 - 20 MB.  I using a Dell Inspiron 15R SE 7520 with Windows 10 Home.  Personally I think it can be the Intel Rapid Store Technology "driver", because the problem started around when I installed it. (However I'm not sure.) And my hardware not supported yet by Intel, so I have no the newest driver. However I deleted Intel's software and driver and the issue is the same.    Thank you in advance for your assistance! This is a general, community wiki  question and answer pair intended to address any questions   concerning the reasons a site or specific site contents do not appear   in search engine results.      If your question was closed as a duplicate of this question and you   feel that the information provided here does not provide a sufficient   answer, please open a discussion on .   My site (or specific pages on my site) is not appearing in search engine results.  Why isn't my content indexed and what can I do about it? I am aware that there are plenty of threads on intensifiers(very, rather, pretty, quite, fairly, etc.), both on this site and on the web, because of their ambiguity in terms of meaning. What I have learned is that their meaning can change depending on which country you are from, which context they are used, or your intonation. So instead of comparing all intensifiers, I decided to make my question more specific. I chose to focus on the word pretty because of its "common" usage.  So as we can see, the word pretty has two meanings and unfortunately they are "pretty" opposite. My question is can you tell me, just by taking into account  the example sentences below, in which sentences "pretty" means "fairly,", and in which it means "very?"  Does "Tom looks pretty tired" always mean "Tom looks a little/fairly tired" ? Flat quads (or, why is my mesh so funky?) I think my question relates to a fundamental of 3D modeling that I haven't picked up on yet. It's very simple:  Let's say I have a flat quad. A plane on the XY plane inserted into am empty blender file is a great example. Now let's say I start moving each of the 4 vertices around on in any direction, especially the Z axis.   At this point, there would still be one face, but its extremely unlikely that the face would be planar (I just learned this word). So blender does its best to make sense of what this should look like.  The problem I'm having is that it seems like my quads are always like this, but they never look the way I want. There are edges and seams that look like they are dangling in space, and what tends to happen is that my mesh looks great when viewed from most angles, but if you look at it from just the right angle, you notice the dangling edges or sometimes even some kind of impossible geometry. And so I might try to nudge the problematic vertices around, but this often seems to either make it worse, or just hide the bad geometry until you see it from a different angle.  For me, this always seems to happen whenever I'm trying to move vertices to add roundness to something that is originally square.   There is another question on here about how to actually flatten the quads. That's great, and I might use some of the techniques mentioned there. My question is:   Why does this happen? (Can someone explain this better?) What are some tips and tricks to avoid this situation? What are some tips and tricks to mitigate this situation?   EDIT Here is an illustration:  The overall mesh as viewed from a distance looks decent (for my skill level)    But if you get closer and look from a certain angle...    Super close up:    The "edge" that is pointed to by the arrow is not actually an edge, but some kind of artifact created when blender tries to show the quad. The way the vertices are positioned, it shouldn't actually be possible to see the sliver of the face that I marked in red, since this face is supposed to be around the corner from the edges. The edges should form the silhouette on the right side of my figure.     Here is the side view. Maybe it is the angled topology that skews the face in a funny way?  But I'm not looking for help with this one particular issue, but rather a better understanding of why this happens, and ideas to prevent this in future models. Is there a rule forbidding the use of “is” at the end of a sentence? Is there any justification for using “is” at the end of an English sentence, or is there a rule that forbids this? What are the differences between "to talk" and "to speak"? I know that : $\mathbf{Q}(\sqrt{2}) = \mathbf{Q}+ \sqrt{2} \mathbf{Q}$ , but then what is $\mathbf{Q}(\sqrt{2},\sqrt{3})$?