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• SQL SERVER When are Statistics Updated What triggers Statistics to Update

  If you are an SQL Server Consultant/Trainer involved with Performance Tuning and Query Optimization, I am sure you have faced the following questions many times.When is statistics updated? What is the interval of Statistics update? What is the algorithm behind update statistics? These are the puzzling questions and more.I searched the Internet as well many [...]...Did you know that DotNetSlackers also publishes .net articles written by top known .net Authors? We already have over 80 articles in several categories including Silverlight. Take a look: here.

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• Detect line line collision in an Untangled game

  - by Vish

  Pardon me if this is a repeat question,but I've been searching google for vain since the past few days, I'm a flash actionscript game developer who is a bit backward with mathematics, though I find physics both interesting and cool. Similiar game : Untangled flash game I have made an untangled game almost to full completion of logic. But, when two lines intersect , I need those intersected or 'tangled' lines to show a different color; red. It would be really kind of you people if you could suggest an algorithm with / without math for detecting line segment collisions. I'm basically a person who likes to think 'visually' than 'arithmetically' :) P.S I'm trying to make a function as private function isIntersecting(A:Point, B:Point, C:Point, D:Point):Boolean Thanks in advance. Vishnu Ajit

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• VG.net 8.5 Released

  - by Frank Hileman

  We have released version 8.5 of the VG.net vector graphics system. This release supports Visual Studio 2013. Companies who purchased a VG.net license after October 1, 2013, are eligible for a free upgrade. We will be sending you an email. There is one cosmetic problem which wasted our time, as we could not find a work around. It occurs when your display is set to a high DPI. You can see the problem in the image of the toolbox below, which uses a DPI of 125%, on Windows 7: The ToolboxItem class accepts only Bitmaps with a size of 16x16. We tried many sizes and many bitmap formats. As you can see, this tiny Bitmap is then scaled by the toolbox, and the scaling algorithm adds artifacts. This is an "improvement" Microsoft recently added to Visual Studio 2013.

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• How does Google maintain its codes?

  - by John Maxim

  Pagerank algorithm is not revealed to any of their associates programmers, but only accessible by Larry Page or maybe Sergey Brin. I wonder how do they go about managing their coding? There are times when you need to build something up and you may need more hands to help with coding, but you may also want to keep some secrets to yourself, I'm not saying I have secrets, but I wonder how do they manage their coding. I'm sure there are some ways to do it decently and professionally. The reason why friendster failed was because one of the factors they lost control over their coding part. I think this is an interesting question. But not easy to answer, maybe only a marginal knew.

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• Slow boot on Ubuntu 12.04

  - by Hailwood

  My Ubuntu is booting really slow (Windows is booting faster...). I am using Ubuntu a Dell Inspiron 1545 Pentium(R) Dual-Core CPU T4300 @ 2.10GHz, 4GB Ram, 500GB HDD running Ubuntu 12.04 with gnome-shell 3.4.1. After running dmesg the culprit seems to be this section, in particular the last three lines: [26.557659] ADDRCONF(NETDEV_UP): eth0: link is not ready [26.565414] ADDRCONF(NETDEV_UP): eth0: link is not ready [27.355355] Console: switching to colour frame buffer device 170x48 [27.362346] fb0: radeondrmfb frame buffer device [27.362347] drm: registered panic notifier [27.362357] [drm] Initialized radeon 2.12.0 20080528 for 0000:01:00.0 on minor 0 [27.617435] init: udev-fallback-graphics main process (1049) terminated with status 1 [30.064481] init: plymouth-stop pre-start process (1500) terminated with status 1 [51.708241] CE: hpet increased min_delta_ns to 20113 nsec [59.448029] eth2: no IPv6 routers present But I have no idea how to start debugging this. sudo lshw -C video $ sudo lshw -C video *-display description: VGA compatible controller product: RV710 [Mobility Radeon HD 4300 Series] vendor: Hynix Semiconductor (Hyundai Electronics) physical id: 0 bus info: pci@0000:01:00.0 version: 00 width: 32 bits clock: 33MHz capabilities: pm pciexpress msi vga_controller bus_master cap_list rom configuration: driver=fglrx_pci latency=0 resources: irq:48 memory:e0000000-efffffff ioport:de00(size=256) memory:f6df0000-f6dfffff memory:f6d00000-f6d1ffff After loading the propriety driver my new dmesg log is below (starting from the first major time gap): [2.983741] EXT4-fs (sda6): mounted filesystem with ordered data mode. Opts: (null) [25.094327] ADDRCONF(NETDEV_UP): eth0: link is not ready [25.119737] udevd[520]: starting version 175 [25.167086] lp: driver loaded but no devices found [25.215341] fglrx: module license 'Proprietary. (C) 2002 - ATI Technologies, Starnberg, GERMANY' taints kernel. [25.215345] Disabling lock debugging due to kernel taint [25.231924] wmi: Mapper loaded [25.318414] lib80211: common routines for IEEE802.11 drivers [25.318418] lib80211_crypt: registered algorithm 'NULL' [25.331631] [fglrx] Maximum main memory to use for locked dma buffers: 3789 MBytes. [25.332095] [fglrx] vendor: 1002 device: 9552 count: 1 [25.334206] [fglrx] ioport: bar 1, base 0xde00, size: 0x100 [25.334229] pci 0000:01:00.0: PCI INT A -> GSI 16 (level, low) -> IRQ 16 [25.334235] pci 0000:01:00.0: setting latency timer to 64 [25.337109] [fglrx] Kernel PAT support is enabled [25.337140] [fglrx] module loaded - fglrx 8.96.4 [Mar 12 2012] with 1 minors [25.342803] Adding 4189180k swap on /dev/sda7. Priority:-1 extents:1 across:4189180k [25.364031] type=1400 audit(1338241723.027:2): apparmor="STATUS" operation="profile_load" name="/sbin/dhclient" pid=606 comm="apparmor_parser" [25.364491] type=1400 audit(1338241723.031:3): apparmor="STATUS" operation="profile_load" name="/usr/lib/NetworkManager/nm-dhcp-client.action" pid=606 comm="apparmor_parser" [25.364760] type=1400 audit(1338241723.031:4): apparmor="STATUS" operation="profile_load" name="/usr/lib/connman/scripts/dhclient-script" pid=606 comm="apparmor_parser" [25.394328] wl 0000:0c:00.0: PCI INT A -> GSI 17 (level, low) -> IRQ 17 [25.394343] wl 0000:0c:00.0: setting latency timer to 64 [25.415531] acpi device:36: registered as cooling_device2 [25.416688] input: Video Bus as /devices/LNXSYSTM:00/device:00/PNP0A03:00/device:34/LNXVIDEO:00/input/input6 [25.416795] ACPI: Video Device [VID] (multi-head: yes rom: no post: no) [25.416865] [Firmware Bug]: Duplicate ACPI video bus devices for the same VGA controller, please try module parameter "video.allow_duplicates=1"if the current driver doesn't work. [25.425133] lib80211_crypt: registered algorithm 'TKIP' [25.448058] snd_hda_intel 0000:00:1b.0: PCI INT A -> GSI 21 (level, low) -> IRQ 21 [25.448321] snd_hda_intel 0000:00:1b.0: irq 47 for MSI/MSI-X [25.448353] snd_hda_intel 0000:00:1b.0: setting latency timer to 64 [25.738867] eth1: Broadcom BCM4315 802.11 Hybrid Wireless Controller 5.100.82.38 [25.761213] input: HDA Intel Mic as /devices/pci0000:00/0000:00:1b.0/sound/card0/input7 [25.761406] input: HDA Intel Headphone as /devices/pci0000:00/0000:00:1b.0/sound/card0/input8 [25.783432] dcdbas dcdbas: Dell Systems Management Base Driver (version 5.6.0-3.2) [25.908318] EXT4-fs (sda6): re-mounted. Opts: errors=remount-ro [25.928155] input: Dell WMI hotkeys as /devices/virtual/input/input9 [25.960561] udevd[543]: renamed network interface eth1 to eth2 [26.285688] init: failsafe main process (835) killed by TERM signal [26.396426] input: PS/2 Mouse as /devices/platform/i8042/serio2/input/input10 [26.423108] input: AlpsPS/2 ALPS GlidePoint as /devices/platform/i8042/serio2/input/input11 [26.511297] Bluetooth: Core ver 2.16 [26.511383] NET: Registered protocol family 31 [26.511385] Bluetooth: HCI device and connection manager initialized [26.511388] Bluetooth: HCI socket layer initialized [26.511391] Bluetooth: L2CAP socket layer initialized [26.512079] Bluetooth: SCO socket layer initialized [26.530164] Bluetooth: BNEP (Ethernet Emulation) ver 1.3 [26.530168] Bluetooth: BNEP filters: protocol multicast [26.553893] type=1400 audit(1338241724.219:5): apparmor="STATUS" operation="profile_replace" name="/sbin/dhclient" pid=928 comm="apparmor_parser" [26.554860] Bluetooth: RFCOMM TTY layer initialized [26.554866] Bluetooth: RFCOMM socket layer initialized [26.554868] Bluetooth: RFCOMM ver 1.11 [26.557910] type=1400 audit(1338241724.223:6): apparmor="STATUS" operation="profile_load" name="/usr/lib/lightdm/lightdm/lightdm-guest-session-wrapper" pid=927 comm="apparmor_parser" [26.559166] type=1400 audit(1338241724.223:7): apparmor="STATUS" operation="profile_replace" name="/usr/lib/NetworkManager/nm-dhcp-client.action" pid=928 comm="apparmor_parser" [26.559574] type=1400 audit(1338241724.223:8): apparmor="STATUS" operation="profile_replace" name="/usr/lib/connman/scripts/dhclient-script" pid=928 comm="apparmor_parser" [26.575519] type=1400 audit(1338241724.239:9): apparmor="STATUS" operation="profile_load" name="/usr/lib/telepathy/mission-control-5" pid=931 comm="apparmor_parser" [26.581100] type=1400 audit(1338241724.247:10): apparmor="STATUS" operation="profile_load" name="/usr/lib/telepathy/telepathy-*" pid=931 comm="apparmor_parser" [26.582794] type=1400 audit(1338241724.247:11): apparmor="STATUS" operation="profile_load" name="/usr/bin/evince" pid=929 comm="apparmor_parser" [26.605672] ppdev: user-space parallel port driver [27.592475] sky2 0000:09:00.0: eth0: enabling interface [27.604329] ADDRCONF(NETDEV_UP): eth0: link is not ready [27.606962] ADDRCONF(NETDEV_UP): eth0: link is not ready [27.852509] vesafb: mode is 1024x768x32, linelength=4096, pages=0 [27.852513] vesafb: scrolling: redraw [27.852515] vesafb: Truecolor: size=0:8:8:8, shift=0:16:8:0 [27.852523] mtrr: type mismatch for e0000000,400000 old: write-back new: write-combining [27.852527] mtrr: type mismatch for e0000000,200000 old: write-back new: write-combining [27.852531] mtrr: type mismatch for e0000000,100000 old: write-back new: write-combining [27.852534] mtrr: type mismatch for e0000000,80000 old: write-back new: write-combining [27.852538] mtrr: type mismatch for e0000000,40000 old: write-back new: write-combining [27.852541] mtrr: type mismatch for e0000000,20000 old: write-back new: write-combining [27.852544] mtrr: type mismatch for e0000000,10000 old: write-back new: write-combining [27.852548] mtrr: type mismatch for e0000000,8000 old: write-back new: write-combining [27.852551] mtrr: type mismatch for e0000000,4000 old: write-back new: write-combining [27.852554] mtrr: type mismatch for e0000000,2000 old: write-back new: write-combining [27.852558] mtrr: type mismatch for e0000000,1000 old: write-back new: write-combining [27.853154] vesafb: framebuffer at 0xe0000000, mapped to 0xffffc90005580000, using 3072k, total 3072k [27.853405] Console: switching to colour frame buffer device 128x48 [27.853426] fb0: VESA VGA frame buffer device [28.539800] fglrx_pci 0000:01:00.0: irq 48 for MSI/MSI-X [28.540552] [fglrx] Firegl kernel thread PID: 1168 [28.540679] [fglrx] Firegl kernel thread PID: 1169 [28.540789] [fglrx] Firegl kernel thread PID: 1170 [28.540932] [fglrx] IRQ 48 Enabled [29.845620] [fglrx] Gart USWC size:1236 M. [29.845624] [fglrx] Gart cacheable size:489 M. [29.845629] [fglrx] Reserved FB block: Shared offset:0, size:1000000 [29.845632] [fglrx] Reserved FB block: Unshared offset:fc21000, size:3df000 [29.845635] [fglrx] Reserved FB block: Unshared offset:1fffb000, size:5000 [59.700023] eth2: no IPv6 routers present

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• How do one improve him/her problem-solving ability ?

  - by gcc

  How can one improve him/her problem-solving ability? Every one says same thing "a real programmer knows how to handle real problem", but they forget how they learn this ability, or where (I know in school, no one gives us any ability, of course in my opinion). If you have any idea except above ones, feel free when you give your advice solve more problems do more exercises, write code, search google then write more ... For me, my question is like "Use complex/known library instead of using your own." In other words,t I want your presonal experience, book recommendation, web page on problem solving. Moreover, look your problem-solving method and give us your personal ability as if it is an algorithm

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• Drawing territories border in 2d map

  - by Gabriel A. Zorrilla

  I'm programming a little web strategy game. In the country map I pretend to display each country with a national color. The issue is how to render the borders in a simple and efficient way. Right now I'm planning to set a field to each tile called "border" with values from 0 to 8. The algorithm would check for EVERY tile is its adjacent has a different "owner". If the tile is inside the territory, the border value would be 0, because would not have adjacent any tile with different owner, if not, would vary between 1 (north) clockwise to 9 (north-west) and then draw the border. I find this simple but too processor-intensive. Are there any other "pro" choices to render territories borders?

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• Raycasting tutorial / vector math question

  - by mattboy

  I'm checking out this nice raycasting tutorial at http://lodev.org/cgtutor/raycasting.html and have a probably very simple math question. In the DDA algorithm I'm having trouble understanding the calcuation of the deltaDistX and deltaDistY variables, which are the distances that the ray has to travel from 1 x-side to the next x-side, or from 1 y-side to the next y-side, in the square grid that makes up the world map (see below screenshot). In the tutorial they are calculated as follows, but without much explanation: //length of ray from one x or y-side to next x or y-side double deltaDistX = sqrt(1 + (rayDirY * rayDirY) / (rayDirX * rayDirX)); double deltaDistY = sqrt(1 + (rayDirX * rayDirX) / (rayDirY * rayDirY)); rayDirY and rayDirX are the direction of a ray that has been cast. How do you get these formulas? It looks like pythagorean theorem is part of it, but somehow there's division involved here. Can anyone clue me in as to what mathematical knowledge I'm missing here, or "prove" the formula by showing how it's derived?

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• Convert DVD to MKV (et al) without transcoding/recompression

  - by Oli

  Like a lot of people, I have a lot of DVDs. But we also have a stupid amount of disk space and a media centre (Boxee) so the DVDs are getting less and less use. It would be nice to convert our DVDs into something more relevant to our needs. I've dabbled with DVD ripping before but whereas I'd usually transcode down to a smaller picture size with a better video compression algorithm, this takes a silly amount of time. I don't have a couple of hours available for each disk. (Sidebar: is there dedicated, Linux-friendly hardware to improve h264 encoding performance?) So I was wondering if there's anything that take the DVD filesystem, De-CSS it, and then stitch together any the VOBs that make up the main part of the film and package that up in a wrapping format like MKV. A bonus would be if it could grab the subtitles and stick them in too but that's not a requirement as Boxee can grab the subtitles online if it needs to.

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• Predicting advantages of database denormalization

  - by Janus Troelsen

  I was always taught to strive for the highest Normal Form of database normalization, and we were taught Bernstein's Synthesis algorithm to achieve 3NF. This is all very well and it feels nice to normalize your database, knowing that fields can be modified while retaining consistency. However, performance may suffer. That's why I am wondering whether there is any way to predict the speedup/slowdown when denormalizing. That way, you can build your list of FD's featuring 3NF and then denormalize as little as possible. I imagine that denormalizing too much would waste space and time, because e.g. giant blobs are duplicated or it because harder to maintain consistency because you have to update multiple fields using a transaction. Summary: Given a 3NF FD set, and a set of queries, how do I predict the speedup/slowdown of denormalization? Link to papers appreciated too.

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• Is running "milli"-benchmarks a good idea?

  - by Konstantin Weitz

  I just came across the Caliper project and it looks very nice. Reading the introduction to microbenchmarks, one gets the feeling that the developers would not suggest to use the framework if the benchmark takes longer than a second or so. I looked at the code and it looks like a RuntimeOutOfRangeException is actually thrown if a scenario takes longer than 10s to execute. Could you explain to me what the problems are with running larger benchmarks? My motivation for using Caliper was to compare two join-algorithm implementations. Those will definitely run for quite some time and will do some disk IO, yet running the entire database would make it hard to do the comparison, because the configuration of the algorithms and the visualization of the results would be a pain.

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• How to detect two moving shapes overlapped?

  - by user1389813

  Given a list of circles with its coordinates (x and y) that are moving every second in different direction (South-East, South-West, North-East and North-West), and the circle will change direction if it hits the wall sort of like bouncing, so how do we detect if any of them collide or overlap with each other ? I am not sure if we can use some data structures like a Binary Search Tree because since all the coordinates vary every seconds, so the tree will have to re-build accordingly. Or can we use Vertical Sweep Line Algorithm each time ? Any ideas on how to do this in a efficient way ?

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• Friendly URLs: is there a max length for search engines?

  - by Olivier Pons

  People from stackoverflow have been working closely with google team to help them make the panda algorithm more efficient, so I guess they've learned a lot from the google team. Thus they may have done very clever friendly URLs to maximize the page rank. I've seen from time to time very long URLs (can't find where) in stackoverflow, but after a certain "amount" of character there were only numbers, kind of "ok passed this length, SEOs will ignore this so let's put only numbers". I've done a huge work on my framework to make very friendly URLs, and my website can come up with URLs like: http://www.mysite.fr/recherche/region/provence-alpes-cote-d-azur/departement/bouches-du-rhone/categorie-de-metiers/paramedical/ It's very long and I'm wondering if the previous URL won't be mixed with, say, this one: http://www.mysite.fr/recherche/region/provence-alpes-cote-d-azur/departement/bouches-du-rhone/categorie-de-metiers/art/

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• How will Quantum computing affect us?

  - by CiscoIPPhone

  I am interested in quantum computing, but have not studied it in depth. Things like Shor's algorithm intrigue me. My question is: If quantum computing took off in a big way (i.e. functional quantum home computers were available) how would it affect us programmers and software developers? Would we have to learn how to make use of superposition and entanglement - would it change how we write algorithms? Would more mathematical programmers be required/would we need new skills? Would it change nothing at all from our perspective (i.e. would it be abstracted)? Your opinion is welcome.

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• Should pathfinder in A* hold closedSet and openedSet or each object should hold its sets?

  - by Patryk

  I am about to implement A* pathfinding algorithm and I wonder how should I implement this - from the point of view of architecture. I have the pathfinder as a class - I think I will instantiate only one object of this class (or maybe make it a Singleton - this is not so important). The hardest part for me is whether the closedSet and openedSet should be attached to objects that can find the path for them or should be stored in pathfinder class ? I am opened to any hints and critique whatsoever. What is the best practice considering pathfinding in terms of design ?

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• Convert DVD to MKV (et al) without transcoding/recompression

  - by Oli

  Like a lot of people, I have a lot of DVDs. But we also have a stupid amount of disk space and a media centre (Boxee) so the DVDs are getting less and less use. It would be nice to convert our DVDs into something more relevant to our needs. I've dabbled with DVD ripping before but whereas I'd usually transcode down to a smaller picture size with a better video compression algorithm, this takes a silly amount of time. I don't have a couple of hours available for each disk. (Sidebar: is there dedicated, Linux-friendly hardware to improve h264 encoding performance?) So I was wondering if there's anything that take the DVD filesystem, De-CSS it, and then stitch together any the VOBs that make up the main part of the film and package that up in a wrapping format like MKV. A bonus would be if it could grab the subtitles and stick them in too but that's not a requirement as Boxee can grab the subtitles online if it needs to.

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• How to achieve a Gaussian Blur effect for shadows in LWJGL/Slick2D?

  - by user46883

  I am currently trying to implement shadows into my game, and after a lot of searching in the interwebs I came to the conclusion that drawing hard edged shadows to a low resolution pass combined with a Gaussian blur effect would fit best and make a good compromise between performance and looks - even though theyre not 100% physically accurate. Now my problem is, that I dont really know how to implement the Gaussian blur part. Its not difficult to draw shadows to a low resolutions buffer image and then stretch it which makes it more smooth, but I need to add the Gaussian blur effect. I have searched a lot on that and found some approachs for GLSL, some even here, but none of them really helped it. My game is written in Java using Slick2D/LWJGL and I would appreciate any help or approaches for an algorithm or maybe even an existing library to achieve that effect. Thanks for any help in advance.

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• How can I generate a 2d navigation mesh in a dynamic environment at runtime?

  - by Stephen

  So I've grasped how to use A* for path-finding, and I am able to use it on a grid. However, my game world is huge and I have many enemies moving toward the player, which is a moving target, so a grid system is too slow for path-finding. I need to simplify my node graph by using a navigational mesh. I grasp the concept of "how" a mesh works (finding a path through nodes on the vertices and/or the centers of the edges of polygons). My game uses dynamic obstacles that are procedurally generated at run-time. I can't quite wrap my head around how to take a plane that has multiple obstacles in it and programatically divide the walkable area up into polygons for the navigation mesh, like the following image. Where do I start? How do I know when a segment of walk-able area is already defined, or worse, when I realize I need to subdivide a previously defined walk-able area as the algorithm "walks" through the map? I'm using javascript in nodejs, if it matters.

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• Is finding graph minors without single node pinch points possible?

  - by Alturis

  Is it possible to robustly find all the graph minors within an arbitrary node graph where the pinch points are generally not single nodes? I have read some other posts on here about how to break up your graph into a Hamiltonian cycle and then from that find the graph minors but it seems to be such an algorithm would require that each "room" had "doorways" consisting of single nodes. To explain a bit more a visual aid is necessary. Lets say the nodes below are an example of the typical node graph. What I am looking for is a way to automatically find the different colored regions of the graph (or graph minors)

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• Efficient way to sort large set of numbers

  - by 7Aces

  I have to sort a set of 100000 integers as a part of a programming Q. The time limit is pretty restrictive, so I have to use the most time-efficient approach possible. My current code - #include<cstdio> #include<algorithm> using namespace std; int main() { int n,d[100000],i; for(i=0;i<n;++i) { scanf("%d",&d[i]); } sort(d,d+n); .... } Would this approach be more efiicient? int main() { int n,d[100000],i; for(i=0;i<n;++i) { scanf("%d",&d[i]); sort(d,d+i+1); } .... } What is the most efficient way to sort a large dataset? Note - Not homework...

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• How should I replan A*?

  - by Gregory Weir

  I've got a pathfinding boss enemy that seeks the player using the A* algorithm. It's a pretty complex environment, and I'm doing it in Flash, so the search can get a bit slow when it's searching over long distances. If the player was stationary, I could just search once, but at the moment I'm searching every frame. This takes long enough that my framerate is suffering. What's the usual solution to this? Is there a way to "replan" A* without redoing the entire search? Should I just search a little less often (every half-second or second) and accept that there will be a little inaccuracy in the path?

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• Unity Dash/Lens - Auto-completion based on recent search strings

  - by Anant

  Sometimes, I find myself typing the same (or quite similar) search strings inside a Unity Lens. So, I thought whether it's possible for the Lens to remember previous searches, and provide a drop-down menu of possible suggestions (based on the past) when I start typing my new query. With Lenses for sites like Wikipedia and DuckDuckGo, the search strings are getting longer, and this feature would lend a helping hand in filling out queries faster. This could be something applicable to all Lenses, with later versions allowing individual Lenses to run their own auto-completion algorithm.

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• Reverse horizontal and vertical for a HTML table

  - by porton

  There is a two-dimensional array describing a HTML table. Each element of the array consists of: the cell content rowspan colspan Every row of this two dimensional array corresponds to <td> cells of a <tr> of the table which my software should generate. I need to "reverse" the array (interchange vertical and horizontal direction). Insofar I considered algorithm based on this idea: make a rectangular matrix of the size of the table and store in every element of this matrix the corresponding index of the element of the above mentioned array. (Note that two elements of the matrix may be identical due rowspan/colspan.) Then I could use this matrix to calculate rowspan/colspan for the inverted table. But this idea seems bad for me. Any other algorithms? Note that I program in PHP.

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• A* Jump Point Search - how does pruning really work?

  - by DeadMG

  I've come across Jump Point Search, and it seems pretty sweet to me. However, I'm unsure as to how their pruning rules actually work. More specifically, in Figure 1, it states that we can immediately prune all grey neighbours as these can be reached optimally from the parent of x without ever going through node x However, this seems somewhat at odds. In the second image, node 5 could be reached by first going through node 7 and skipping x entirely through a symmetrical path- that is, 6 -> x -> 5 seems to be symmetrical to 6 -> 7 -> 5. This would be the same as how node 3 can be reached without going through x in the first image. As such, I don't understand how these two images are not entirely equivalent, and not just rotated versions of each other. Secondly, I'd like to understand how this algorithm could be generalized to a three-dimensional search volume.

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• How does one improve one's problem-solving ability?

  - by gcc

  How can one improve one's problem-solving ability? Everyone says same thing: "a real programmer knows how to handle real problem." But they forget how they learn this ability, or where (I know in school, no one gives us any ability, of course in my opinion). If you have any idea except above ones, feel free when you give your advice solve more problems do more exercises, write code, search google then write more ... For me, my question is like "use complex/known library instead of using your own." In other words, I want your personal experience, book recommendation, webpage on problem solving. Moreover, look your problem-solving method and give us your personal ability as if it is an algorithm

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