How to calculate time and space complexity for these algorithms? I referred many sites but its confusing me. please any one explain me.   1.   for(i=0;i&lt;n;i++)  {     for(j=i;j&lt;n;j++)//this for loop is based on previous 'i'     {        foo();     }  }   2.  while(m&lt;n) {     for(i=0;i&lt;n;i++)     {          foo();     } }   If possible explain me with some more example. Thanks.
Most people with a degree in CS will certainly know what . It helps us to measure how well an algorithm scales.   But I'm curious, how do you calculate or approximate the complexity of your algorithms?
I need a little hint in a proof on convergence of a sequence. The problem I have is: Suppose $(x_n)$ is a monotone decreasing sequence of real numbers such that $\sum x_n$ converges, prove that:  $$\lim_{n \to \infty} nx_n=0$$  My idea is: proving this fact aims to prove that given $\epsilon &gt;0$ there's some natural $n_0 \in \mathbb{N}$ such that if $n &gt;n_0$ we have $|nx_n|&lt;\epsilon$.  Now, I know that $\sum x_n$ converges, so that given $\epsilon'&gt;0$ there's some $k_0 \in \mathbb{N}$ such that if $k &gt; k_0$ we have:  $$\left|\sum_{i=1}^{k}x_i - S\right|&lt;\epsilon'$$  Where $S = \sum x_n$. Now, since $(x_n)$ is monotone decreasing we know that we must have $x_1 &gt; \cdots &gt; x_k$ so that the sum of all $x_i$ should be less or equal to $k x_k$. So I know that I have:  $$\left|\sum_{i=1}^{k}x_i - S\right|\leq\left|\sum_{i=1}^{k}x_i\right|+|S|\leq|kx_k|+|S|$$  I feel that the proof will come from this, however I'm stuck at this point. Can someone give just a little hint on how to proceed from here?  Thanks very much in advance for your help. stop Ipod from asking for old Apple ID password Which annotation should I use: @IdClass or @EmbeddedId The JPA (Java Persistence API) specification has 2 different ways to specify entity composite keys: @IdClass and @EmbeddedId.   I'm using both annotations on my mapped entities, but it turns out to be a big mess to people who aren't very familiar with JPA.   I want to adopt only one way to specify composite keys. Which one is really the best? Why? Deferring admission to a computer science graduate program There does not exist an entire function which satisfies $f({1\over n})={1\over 2^n}$, what I tried is if possible then define $g(z)=f(z)-{1\over 2^{1\over z}}$ Then $g({1\over n})=0$ and so $g(z)$ is entire and its $0$ set has limit point in it and so $f(z)={1\over 2^{1\over z}}$ which is not analytic at $0$? Please help!  Edit: OOps! the way I defined $g(z)$ that is not entire! could any one give me hint? Windows Subsystem for Linux (WSL): what can't I do with the Ubuntu application for Microsoft Windows? How can you dynamically create variables via a while loop? This post has been locked; locked posts can't be voted on Union of a finite set and a countably infinite set is countably infinite This is a  about File Permission and Why 777 is "destructive".   I'm not asking how to fix this problem, as there are a ton of references of that already on Server Fault (reinstall OS). Why does it do anything destructive at all?  If you've ever ran this command you pretty much immediately destroy your operating system. I'm not clear why removing restrictions has any impact on existing processes. For example, if I don't have read access to something and after a quick mistype in the terminal suddenly I now have access well... why does that cause Linux to break? I need this desperately but can't find it. Am I doing something wrong? How do I turn off some formats in GeoServer's WMS? Equivalent Resistance? How do you find the equivalent resistance here? (I realized it's a Wheatstone bridge, but it's unbalanced, so that doesn't help.) I tried using Kirchhoff's laws, but there is no cell given. I have a 250G disk on my Mac with around 100G in use. But the system reports only around 20G of free space. I'm using macOS 10.13.2. I have the problem at least since the upgrade to High Sierra, but probably also before.  "About This Mac" --> "Storage" reports that "System" is using around 180G. But if I check the complete disk, it looks like that:  $ sudo du -cxhd 1 /   0B    /.HFS+ Private Directory Data 1.0K    /home 4.3G    /usr 4.2G    /.Spotlight-V100 1.0K    /net  34G    /nix   0B    /.PKInstallSandboxManager   0B    /.PKInstallSandboxManager-SystemSoftware 2.6M    /bin   0B    /Network 1.1M    /sbin 3.8G    /Library   0B    /.Trashes 6.5G    /System 476K    /.fseventsd du: /private/var/db/ConfigurationProfiles/Store: Operation not permitted du: /private/var/folders/z7/[...]/0/SafariFamily: Operation not permitted du: /private/var/folders/z7/[...]/0/com.apple.LaunchServices.dv: Operation not permitted du: /private/var/folders/z7/[...]/0/com.apple.nsurlsessiond: Operation not permitted du: /private/var/folders/z7/[...]/0/com.apple.routined: Operation not permitted du: /private/var/folders/zz/[...]/0/com.apple.nsurlsessiond: Operation not permitted 8.0G    /private 8.6M    /.DocumentRevisions-V100   0B    /.vol  32G    /Users  11G    /Applications 207M    /opt 5.0K    /dev 4.0K    /Volumes   0B    /cores 104G    / 104G    total   df also says that only 20G are available:  $ df -h / Filesystem     Size   Used  Avail Capacity iused               ifree %iused  Mounted on /dev/disk1s1  234Gi  211Gi   20Gi    92% 4019132 9223372036850756675    0%   /   Any tool I was using (Finder, Disk Inventory X, etc.) shows more or less the same numbers like df and du.  Output of mount:  $ mount /dev/disk1s1 on / (apfs, local, journaled) devfs on /dev (devfs, local, nobrowse) /dev/disk1s4 on /private/var/vm (apfs, local, noexec, journaled, noatime, nobrowse) map -hosts on /net (autofs, nosuid, automounted, nobrowse) map auto_home on /home (autofs, automounted, nobrowse)   I read and tested many, many things like:         ... but with no success. So what could consume more than 100G of disk space without showing up in any tool?  Update  Running „First Aid“ in recovery mode:   What does this error message mean?  error: btn:1: invalid key order (1) oid 440198 / oxid 114577 fsroot tree is invalid.   Update 2018-01-25  Another report of the same error:  (but no answers, yet)  I'm pretty sure this file system error is the root cause for the missing disk space. But I have no idea how to fix that. I was hoping that 10.13.3 would maybe solve it, but it didn't change anything. I guess I need to reinstall... $X$ is Hausdorff if and only if the diagonal of $X\times X$ is closed Let $X$ be a topological space. The diagonal of $X \times X$ is the subset $$D = \{(x,x)\in X\times X\mid x \in X\}.$$   Show that $X$ is Hausdorff if and only if $D$ is closed in $X \times X$.   First, I tried to show that $X \times X \setminus D$ is open using the fact that $X \times X$ is Hausdorff (because $X$ is Hausdorff), but I couldn't find an open set that contains a point outside $D$ and is disjoint to it... A simple algebra that is not semisimple I am new to the netplan on Ubuntu 18.04, just discovered it exists today. I have an interface that I am trying to add to create a floating IP on google cloud. It is based on this example:   I tested the example, and it works, but now I try to do the same on ubuntu, and I don't know how to convert this:  cat &lt;&lt; EOF &gt;&gt; /etc/network/interfaces auto eth0:0 iface eth0:0 inet static     address 10.190.1.1     netmask 255.255.255.255 EOF   to netplan.  The output for ls /etc/netplan is '50-cloud-init.yaml'. and the output for cat /etc/netplan/*.yaml is:  network:     version: 2     ethernets:         ens4:             dhcp4: true             match:                 macaddress: 42:01:0a:8e:00:3e             set-name: ens4   my ifconfig:  # ifconfig  ens4 ens4: flags=4163&lt;UP,BROADCAST,RUNNING,MULTICAST&gt;  mtu 1460     inet 10.142.0.62  netmask 255.255.255.255  broadcast 0.0.0.0     inet6 fe80::4001:aff:fe8e:3e  prefixlen 64  scopeid 0x20&lt;link&gt;     ether 42:01:0a:8e:00:3e  txqueuelen 1000  (Ethernet)     RX packets 9430  bytes 1635180 (1.6 MB)     RX errors 0  dropped 0  overruns 0  frame 0     TX packets 13383  bytes 1513428 (1.5 MB)     TX errors 0  dropped 0 overruns 0  carrier 0  collisions 0   What is the equivalent of what he said to put in the file, for netplan? Parse HTML in Android What are good strategies for booster drafts? I know that doing a booster draft can be somewhat complicated, because to really be good you need to know a lot about the set you're drafting (or be really good at evaluating cards quickly) and to pay attention to signal cards.    Besides going into the whole complicated strategies of knowing the set and paying attention to signal cards, what are some relatively simple/basic guidelines for drafting? I know that new arXiv papers usually appear in Google Scholar within a few days or weeks. My question is: if someone submits a replacement of his/her arXiv paper, does the new version of the paper also appear in Google Scholar?