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• reconstructing a tree from its preorder and postorder lists.

  - by NomeN

  Consider the situation where you have two lists of nodes of which all you know is that one is a representation of a preorder traversal of some tree and the other a representation of a postorder traversal of the same tree. I believe it is possible to reconstruct the tree exactly from these two lists, and I think I have an algorithm to do it, but have not proven it. As this will be a part of a masters project I need to be absolutely certain that it is possible and correct (Mathematically proven). However it will not be the focus of the project, so I was wondering if there is a source out there (i.e. paper or book) I could quote for the proof. (Maybe in TAOCP? anybody know the section possibly?) In short, I need a proven algorithm in a quotable resource that reconstructs a tree from its pre and post order traversals. Note: The tree in question will probably not be binary, or balanced, or anything that would make it too easy. Note2: Using only the preorder or the postorder list would be even better, but I do not think it is possible. Note3: A node can have any amount of children. Note4: I only care about the order of siblings. Left or right does not matter when there is only one child.

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• What is the most efficient/elegant way to parse a flat table into a tree?

  - by Tomalak

  Assume you have a flat table that stores an ordered tree hierarchy: Id Name ParentId Order 1 'Node 1' 0 10 2 'Node 1.1' 1 10 3 'Node 2' 0 20 4 'Node 1.1.1' 2 10 5 'Node 2.1' 3 10 6 'Node 1.2' 1 20 What minimalistic approach would you use to output that to HTML (or text, for that matter) as a correctly ordered, correctly intended tree? Assume further you only have basic data structures (arrays and hashmaps), no fancy objects with parent/children references, no ORM, no framework, just your two hands. The table is represented as a result set, which can be accessed randomly. Pseudo code or plain English is okay, this is purely a conceptional question. Bonus question: Is there a fundamentally better way to store a tree structure like this in a RDBMS? EDITS AND ADDITIONS To answer one commenter's (Mark Bessey's) question: A root node is not necessary, because it is never going to be displayed anyway. ParentId = 0 is the convention to express "these are top level". The Order column defines how nodes with the same parent are going to be sorted. The "result set" I spoke of can be pictured as an array of hashmaps (to stay in that terminology). For my example was meant to be already there. Some answers go the extra mile and construct it first, but thats okay. The tree can be arbitrarily deep. Each node can have N children. I did not exactly have a "millions of entries" tree in mind, though. Don't mistake my choice of node naming ('Node 1.1.1') for something to rely on. The nodes could equally well be called 'Frank' or 'Bob', no naming structure is implied, this was merely to make it readable. I have posted my own solution so you guys can pull it to pieces.

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• What data is actually stored in a B-tree database in CouchDB?

  - by Andrey Vlasovskikh

  I'm wondering what is actually stored in a CouchDB database B-tree? The CouchDB: The Definitive Guide tells that a database B-tree is used for append-only operations and that a database is stored in a single B-tree (besides per-view B-trees). So I guess the data items that are appended to the database file are revisions of documents, not the whole documents: +---------|### ... | | +------|###|------+ ... ---+ | | | | +------+ +------+ +------+ +------+ | doc1 | | doc2 | | doc1 | ... | doc1 | | rev1 | | rev1 | | rev2 | | rev7 | +------+ +------+ +------+ +------+ Is it true? If it is true, then how the current revision of a document is determined based on such a B-tree? Doesn't it mean, that CouchDB needs a separate "view" database for indexing current revisions of documents to preserve O(log n) access? Wouldn't it lead to race conditions while building such an index? (as far as I know, CouchDB uses no write locks).

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• Paged binary trees vs. AVL trees and B-trees

  - by Phenom

  How are paged binary trees different from AVL trees and B-trees?

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• Help me understand Inorder Traversal without using recursion

  - by vito

  I am able to understand preorder traversal without using recursion, but I'm having a hard time with inorder traversal. I just don't seem to get it, perhaps, because I haven't understood the inner working of recursion. This is what I've tried so far: def traverseInorder(node): lifo = Lifo() lifo.push(node) while True: if node is None: break if node.left is not None: lifo.push(node.left) node = node.left continue prev = node while True: if node is None: break print node.value prev = node node = lifo.pop() node = prev if node.right is not None: lifo.push(node.right) node = node.right else: break The inner while-loop just doesn't feel right. Also, some of the elements are getting printed twice; may be I can solve this by checking if that node has been printed before, but that requires another variable, which, again, doesn't feel right. Where am I going wrong? I haven't tried postorder traversal, but I guess it's similar and I will face the same conceptual blockage there, too. Thanks for your time! P.S.: Definitions of Lifo and Node: class Node: def __init__(self, value, left=None, right=None): self.value = value self.left = left self.right = right class Lifo: def __init__(self): self.lifo = () def push(self, data): self.lifo = (data, self.lifo) def pop(self): if len(self.lifo) == 0: return None ret, self.lifo = self.lifo return ret

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• Algorithm for evaluating nested logical expression

  - by TravelingSalesman

  I have a logical expression that I would like to evaluate. The expression can be nested and consists of T (True) or F (False) and parenthesis. The parenthesis "(" means "logical OR". Two terms TF beside each others (or any other two combinations beside each others), should be ANDED (Logical AND). For example, the expression: ((TFT)T) = true I need an algorithm for solving this problem. I thought of converting the expression first to disjunctive or conjunctive normal form and then I can easily evaluate the expression. However, I couldn't find an algorithm that normalizes the expression. Any suggestions? Thank you. The problem statement can be found here: https://icpcarchive.ecs.baylor.edu/index.php?option=com_onlinejudge&Itemid=2&category=378&page=show_problem&problem=2967

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• [BST] Deletion procedure

  - by Metz

  Hi all. Consider the deletion procedure on a BST, when the node to delete has two children. Let's say i always replace it with the node holding the minimum key in its right subtree. The question is: is this procedure commutative? That is, deleting x and then y has the same result than deleting first y and then x? I think the answer is no, but i can't find a counterexample, nor figure out any valid reasoning. Thank you. EDIT: Maybe i've got to be clearer. Consider the transplant(node x, node y) procedure: it replace x with y (and its subtree). So, if i want to delete a node (say x) which has two children i replace it with the node holding the minimum key in its right subtree: y = minimum(x.right) transplant(y, y.right) // extracts the minimum (it doesn't have left child) y.right = x.right y.left = x.left transplant(x,y) The question was how to prove the procedure above is not commutative.

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• New Sample Demonstrating the Traversing of Tree Bindings

  - by Duncan Mills

  A technique that I seem to use a fair amount, particularly in the construction of dynamic UIs is the use of a ADF Tree Binding to encode a multi-level master-detail relationship which is then expressed in the UI in some kind of looping form – usually a series of nested af:iterators, rather than the conventional tree or treetable. This technique exploits two features of the treebinding. First the fact that an treebinding can return both a collectionModel as well as a treeModel, this collectionModel can be used directly by an iterator. Secondly that the “rows” returned by the collectionModel themselves contain an attribute called .children. This attribute in turn gives access to a collection of all the children of that node which can also be iterated over. Putting this together you can represent the data encoded into a tree binding in all sorts of ways. As an example I’ve put together a very simple sample based on the HT schema and uploaded it to the ADF Sample project. It produces this UI: The important code is shown here for a Region -> Country -> Location Hierachy: <af:iterator id="i1" value="#{bindings.AllRegions.collectionModel}" var="rgn"> <af:showDetailHeader text="#{rgn.RegionName}" disclosed="true" id="sdh1"> <af:iterator id="i2" value="#{rgn.children}" var="cnty">     <af:showDetailHeader text="#{cnty.CountryName}" disclosed="true" id="sdh2">       <af:iterator id="i3" value="#{cnty.children}" var="loc">         <af:panelList id="pl1">         <af:outputText value="#{loc.City}" id="ot3"/>           </af:panelList>         </af:iterator>       </af:showDetailHeader>     </af:iterator>   </af:showDetailHeader> </af:iterator>  You can download the entire sample from here:

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• Failed to load viewstate.The control tree into which viewstate is being loaded...etc

  - by alaa9jo

  Two days ago,a colleague of mine tried to publish an asp.net website (which is built in VS2008 using framework 3.5) to our server,he configured everything in IIS (he made sure that the selected asp.net version is 2.0) and launched the website..at first it was working great but when he tried to click on a specific treeview...BOOM..: "Failed to load viewstate. The control tree into which viewstate is being loaded must match the control tree that was used to save viewstate during the previous request. For example, when adding controls dynamically, the controls added during a post-back must match the type and position of the controls added during the initial request." In that page there were these control: a TreeView and a Placeholder,when the user selects any node then it's controls will be created dynamically into that placeholder..for the first time it's working fine but when (s)he select another node then that issue appears. He called me to help him with this issue,for me this is the first time I see such an issue,scratch my head then I decided to eliminate the possibilities of this issue one by one,at the development machine it's working perfectly,he published the website at the local IIS and again..it's working perfectly,I took a copy of the website and published it into my laptop but no issues at all,so this is means that it's not an issue in the code. So there is something missing/wrong in our server [it has Windows Server 2003],we went to the server and checked on the web-config and the configurations on IIS...nothing wrong so far,so I decided to check if the framework 3.5 is installed or not and the answer: it wasn't installed Of course he assumed that it was installed and there was nothing to tell if it wasn't from the "ASP.Net version" in IIS because frameworks 3.0 and 3.5 will not be listed there [2.0 will be listed there instead],the only way to check if it was installed or not is to search for the framework in this path:[WINDOWS Folder]\Microsoft.NET\Framework or check if it was installed in Add or remove programs. The obvious solution for his case: We installed Framework 3.5 SP1 into our server,did a restart to the machine and it worked ! If anyone faced the same issue and solved it using the same solution or with a different one please post it here to share experience.

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• How exactly is an Abstract Syntax Tree created?

  - by Howcan

  I think I understand the goal of an AST, and I've build a couple of tree structures before, but never an AST. I'm mostly confused because the nodes are text and not number, so I can't think of a nice way to input a token/string as I'm parsing some code. For example, when I looked at diagrams of AST's, the variable and its value were leaf nodes to an equal sign. This makes perfect sense to me, but how would I go about implementing this? I guess I can do it case by case, so that when I stumble upon an "=" I use that as a node, and add the value parsed before the "=" as the leaf. It just seems wrong, because I'd probably have to make cases for tons and tons of things, depending on the syntax. And then I came upon another problem, how is the tree traversed? Do I go all the way down the height, and go back up a node when I hit the bottom, and do the same for it's neighbor? I've seen tons of diagrams on ASTs, but I couldn't find a fairly simple example of one in code, which would probably help.

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• Is there a program that will show a tree of the differences in two file trees?

  - by Huckle

  In windows I manually back up from time to time by formatting my external drive and copying the contents of my data partition over. Inevitably there is a difference in the number and size of the files copied because of system files, etc. Is there a program that would diff two directories recursively and compile the differences into a nice GUI tree that I could peruse (preferably filter) to ensure that everything I want made it over to the drive? It should only show files that are not in both directories. (Also, please ignore the inadequacy of my backup solution)

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• d3 tree - parents having same children

  - by Larry Anderson

  I've been transitioning my code from JIT to D3, and working with the tree layout. I've replicated http://mbostock.github.com/d3/talk/20111018/tree.html with my tree data, but I wanted to do a little more. In my case I will need to create child nodes that merge back to form a parent at a lower level, which I realize is more of a directed graph structure, but would like the tree to accomodate (i.e. notice that common id's between child nodes should merge). So basically a tree that divides like normal on the way from parents to children, but then also has the ability to bring those children nodes together to be parents (sort of an incestual relationship or something :)). Asks something similar - How to layout a non-tree hierarchy with D3 It sounds like I might be able to use hierarchical edge bundling in conjunction with the tree hierarchy layout, but I haven't seen that done. I might be a little off with that though.

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• DrScheme versus mzscheme: treatment of definitions

  - by speciousfool

  One long term project I have is working through all the exercises of SICP. I noticed something a bit odd with the most recent exercise. I am testing a Huffman encoding tree. When I execute the following code in DrScheme I get the expected result: (a d a b b c a) However, if I execute this same code in mzscheme by calling (load "2.67.scm") or by running mzscheme -f 2.67.scm, it reports: symbols: expected symbols as arguments, given: (leaf D 1) My question is: why? Is it because mzscheme and drscheme use different rules for loading program definitions? The program code is below. ;; Define an encoding tree and a sample message ;; Use the decode procedure to decode the message, and give the result. (define (make-leaf symbol weight) (list 'leaf symbol weight)) (define (leaf? object) (eq? (car object) 'leaf)) (define (symbol-leaf x) (cadr x)) (define (weight-leaf x) (caddr x)) (define (make-code-tree left right) (list left right (append (symbols left) (symbols right)) (+ (weight left) (weight right)))) (define (left-branch tree) (car tree)) (define (right-branch tree) (cadr tree)) (define (symbols tree) (if (leaf? tree) (list (symbol-leaf tree)) (caddr tree))) (define (weight tree) (if (leaf? tree) (weight-leaf tree) (cadddr tree))) (define (decode bits tree) (define (decode-1 bits current-branch) (if (null? bits) '() (let ((next-branch (choose-branch (car bits) current-branch))) (if (leaf? next-branch) (cons (symbol-leaf next-branch) (decode-1 (cdr bits) tree)) (decode-1 (cdr bits) next-branch))))) (decode-1 bits tree)) (define (choose-branch bit branch) (cond ((= bit 0) (left-branch branch)) ((= bit 1) (right-branch branch)) (else (error "bad bit -- CHOOSE-BRANCH" bit)))) (define (test s-exp) (display s-exp) (newline)) (define sample-tree (make-code-tree (make-leaf 'A 4) (make-code-tree (make-leaf 'B 2) (make-code-tree (make-leaf 'D 1) (make-leaf 'C 1))))) (define sample-message '(0 1 1 0 0 1 0 1 0 1 1 1 0)) (test (decode sample-message sample-tree))

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• Freeware (preferably open-source) tool for creating multi-file spanning archives as a self merging SFX

  - by Lockszmith

  I have a large file I want to transfer using either Internet storage hosting, DVD-Rs or USB storage, which sometimes is limited to FAT file-systems (for example: mobile phones) What I'm basically looking for is a tool that create multiple files/volumes (less than 2GB each - FAT's file size limit) which are packed with a self-extracting executable. Currently the only tool I found doing this is WinRAR, but that's shareware, and not free. Is there any Free, preferably Open-Source tool that does that? Thank in advance

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• Minimum spanning tree [closed]

  - by Arion

  Iam having difficulty in implementing a minimum spanning tree. So please can someone please post a link to it's source code.

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• Snort monitoring of spanning interface

  - by aHunter

  I have configured a Cisco 3500 switch with a port SPAN and have my snort node (fedora 13) plugged into it. I am running snort as a daemon and have configured a rule to log all tcp traffic but I am only seeing traffic with a destination of the snort node. I know that the SPAN port is working and wanted to know if there is a specific option that I needed to start snort with in order for it to pickup all the traffic? Or is there something that I have missed here? Many thanks.

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• Second min cost spanning tree.

  - by Evil

  Hello. I'm writing an algorithm for finding the second min cost spanning tree. my idea was as follows: 1) Use kruskals to find lowest MST. 2) Delete the lowest cost edge of the MST. 3) Run kruskals again on the entire graph. 4) return the new MST. My question is this: Will this work? Is there a better way perhaps to do this?

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• Teaming/Spanning Switch Ports

  - by KTech

  I like to team NICs on my servers. Since most workstations are giga-bit anymore I want to provide my servers a bit more bandwidth. I've read various things that say I am/am not supposed to bond the ports on the switch. I see benefit in doing it as I'm not sure how the switch ARP table handles the same MAC address on multiple ports. Suggestions on the "ideal" way to do it? If it matters, I have mix (various locations) of Dell and HP, web managed, Layer 2 switches. Servers are mostly Dell with Broadcom NICs.

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• VMware vSwitches and spanning tree

  - by dunxd

  I have two redundant core switches I want to connect to a new vSwitch I am setting up on a VMware ESX host. The switch will have two physical NICs each of which will connect to one of the core switches. The core switches are connected. If this was a physical switch, I would worry about connecting it to both core switches, because this would create a network loop. Do I need to worry about this for a VMware virtual switch? VMware's documentation says it is not possible to connect two vSwitches in a loop, therefore STP is not required. However, I am worried about connecting two physical switches together via a vSwitch.

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• How to completely remove ldap and remove the directory tree

  - by rugbert

  so I followed this guide: https://help.ubuntu.com/11.04/serverguide/C/openldap-server.html to install and configure ldap but then I discoverd both phpLDAPadmin and Luma and have decided to rebuild my tree from scratch using one of those tools. However Im not sure how to completely remove LDAP now. I can remove it using apt-get, but if I attempt to reinstall it and login using phpLDAPadmin it seems that it's still looking for older authentication and gives me a credential error

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• RecursiveIterator: used to explode tree structure, or only flatten?

  - by Stephen J. Fuhry

  There are tons of examples of using the RecursiveIterator to flatten a tree structure.. but what about using it to explode a tree structure? Is there an elegant way to use this, or some other SPL library to recursively build a tree (read: turn a flat array into array of arbitrary depth) given a table like this: SELECT id, parent_id, name FROM my_tree EDIT: You know how you can do this with Directories? $it = new RecursiveDirectoryIterator("/var/www/images"); foreach(new RecursiveIteratorIterator($it) as $file) { echo $file . PHP_EOL; } .. What if you could do something like this: $it = new RecursiveParentChildIterator($result_array); foreach(new RecursiveIteratorIterator($it) as $group) { echo $group->name . PHP_EOL; echo implode(PHP_EOL, $group->getChildren()) . PHP_EOL . PHP_EOL; } :END EDIT

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• Python loop | "do-while" over a tree

  - by johannix

  Is there a more Pythonic way to put this loop together?: while True: children = tree.getChildren() if not children: break tree = children[0] UPDATE: I think this syntax is probably what I'm going to go with: while tree.getChildren(): tree = tree.getChildren()[0]

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• traverse a binary decison tree using python?

  - by kaushik

  how to traverse a binary decision tree using python language. given a tree,i want know how can we travesre from root to required leaf the feature of the required leaf are given in an dictionary form assume and have to traverse from root to leaf answering the questions at each node with the details given in feature list.. the decision tree node has format ((question)(left tree)(right tree)) while traversing it should answer question at each node and an choose left or right and traverse till leaf?

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• compass-rails 1.03 - TypeError: can't convert nil into String

  - by Romiko

  I am running: ruby 1.9.3p392 (2013-02-22) [i386-mingw32] compass-rails 1.0.3 I used the Windows RailsInstaller to install Ruby on Rails Gemfile group :assets do gem 'sass-rails', '~> 3.2.3' gem 'coffee-rails', '~> 3.2.1' gem 'compass-rails','~> 1.0.2' # See https://github.com/sstephenson/execjs#readme for more supported runtimes # gem 'therubyracer', :platforms => :ruby gem 'uglifier', '>= 1.0.3' end I am currently experiencing issues importing sprites. My sprites are in: assets/images/source in my _shared.scss file I have: //Sprites @import "./source/*.png"; $source-sprite-dimensions: true; In my application.scss I have: /* * This is a manifest file that'll be compiled into application.css, which will include all the files * listed below. * * Any CSS and SCSS file within this directory, lib/assets/stylesheets, vendor/assets/stylesheets, * or vendor/assets/stylesheets of plugins, if any, can be referenced here using a relative path. * * You're free to add application-wide styles to this file and they'll appear at the top of the * compiled file, but it's generally better to create a new file per style scope. * *= require_self */ @import "_shared.scss"; @import "baseline.scss"; @import "global.scss"; @import "normalize.scss"; @import "print.scss"; @import "desktop.scss"; @import "tablet.scss"; @import "home.css.scss"; I am also using rails server and not compass watcher. However when I browse to the page at localhost:3000/assets/application.css, I get the following error: body:before { font-weight: bold; content: "\000a TypeError: can't convert nil into String\000a (in c:\002f RangerRomOnRails\002f RangerRom\002f app\002f assets\002f stylesheets\002f desktop.scss)"; } body:after { content: "\000a C:\002f RailsInstaller\002f Ruby1.9.3\002f lib\002f ruby\002f gems\002f 1.9.1\002f gems\002f compass-0.12.2\002f lib\002f compass\002f sass_extensions\002f functions\002f image_size.rb:17:in `extname'"; } Here is the full stack trace: compass (0 .12.2) lib/compass/sass_extensions/functions/image_size.rb:17:in `extname' compass (0.12.2) lib/compass/sass_extensions/functions/image_size.rb:17:in `initialize' compass (0.12.2) lib/compass/sass_extensions/functions/image_size.rb:50:in `new' compass (0.12.2) lib/compass/sass_extensions/functions/image_size.rb:50:in `image_dimensions' compass (0.12.2) lib/compass/sass_extensions/functions/image_size.rb:4:in `image_width' sass (3.2.9) lib/sass/script/funcall.rb:112:in `_perform' sass (3.2.9) lib/sass/script/node.rb:40:in `perform' sass (3.2.9) lib/sass/tree/visitors/perform.rb:298:in `visit_prop' sass (3.2.9) lib/sass/tree/visitors/base.rb:37:in `visit' sass (3.2.9) lib/sass/tree/visitors/perform.rb:100:in `visit' sass (3.2.9) lib/sass/tree/visitors/base.rb:53:in `block in visit_children' sass (3.2.9) lib/sass/tree/visitors/base.rb:53:in `map' sass (3.2.9) lib/sass/tree/visitors/base.rb:53:in `visit_children' sass (3.2.9) lib/sass/tree/visitors/perform.rb:109:in `block in visit_children' sass (3.2.9) lib/sass/tree/visitors/perform.rb:121:in `with_environment' sass (3.2.9) lib/sass/tree/visitors/perform.rb:108:in `visit_children' sass (3.2.9) lib/sass/tree/visitors/base.rb:37:in `block in visit' sass (3.2.9) lib/sass/tree/visitors/perform.rb:320:in `visit_rule' sass (3.2.9) lib/sass/tree/visitors/base.rb:37:in `visit' sass (3.2.9) lib/sass/tree/visitors/perform.rb:100:in `visit' sass (3.2.9) lib/sass/tree/visitors/base.rb:53:in `block in visit_children' sass (3.2.9) lib/sass/tree/visitors/base.rb:53:in `map' sass (3.2.9) lib/sass/tree/visitors/base.rb:53:in `visit_children' sass (3.2.9) lib/sass/tree/visitors/perform.rb:109:in `block in visit_children' sass (3.2.9) lib/sass/tree/visitors/perform.rb:121:in `with_environment' sass (3.2.9) lib/sass/tree/visitors/perform.rb:108:in `visit_children' sass (3.2.9) lib/sass/tree/visitors/base.rb:37:in `block in visit' sass (3.2.9) lib/sass/tree/visitors/perform.rb:320:in `visit_rule' sass (3.2.9) lib/sass/tree/visitors/base.rb:37:in `visit' sass (3.2.9) lib/sass/tree/visitors/perform.rb:100:in `visit' sass (3.2.9) lib/sass/tree/visitors/base.rb:53:in `block in visit_children' sass (3.2.9) lib/sass/tree/visitors/base.rb:53:in `map' sass (3.2.9) lib/sass/tree/visitors/base.rb:53:in `visit_children' sass (3.2.9) lib/sass/tree/visitors/perform.rb:109:in `block in visit_children' sass (3.2.9) lib/sass/tree/visitors/perform.rb:121:in `with_environment' sass (3.2.9) lib/sass/tree/visitors/perform.rb:108:in `visit_children' sass (3.2.9) lib/sass/tree/visitors/base.rb:37:in `block in visit' sass (3.2.9) lib/sass/tree/visitors/perform.rb:362:in `visit_media' sass (3.2.9) lib/sass/tree/visitors/base.rb:37:in `visit' sass (3.2.9) lib/sass/tree/visitors/perform.rb:100:in `visit' sass (3.2.9) lib/sass/tree/visitors/base.rb:53:in `block in visit_children' sass (3.2.9) lib/sass/tree/visitors/base.rb:53:in `map' sass (3.2.9) lib/sass/tree/visitors/base.rb:53:in `visit_children' sass (3.2.9) lib/sass/tree/visitors/perform.rb:109:in `block in visit_children' sass (3.2.9) lib/sass/tree/visitors/perform.rb:121:in `with_environment' sass (3.2.9) lib/sass/tree/visitors/perform.rb:108:in `visit_children' sass (3.2.9) lib/sass/tree/visitors/base.rb:37:in `block in visit' sass (3.2.9) lib/sass/tree/visitors/perform.rb:128:in `visit_root' sass (3.2.9) lib/sass/tree/visitors/base.rb:37:in `visit' sass (3.2.9) lib/sass/tree/visitors/perform.rb:100:in `visit' sass (3.2.9) lib/sass/tree/visitors/perform.rb:7:in `visit' sass (3.2.9) lib/sass/tree/root_node.rb:20:in `render' sass (3.2.9) lib/sass/engine.rb:315:in `_render' sass (3.2.9) lib/sass/engine.rb:262:in `render' sass-rails (3.2.6) lib/sass/rails/template_handlers.rb:106:in `evaluate' tilt (1.4.1) lib/tilt/template.rb:103:in `render' sprockets (2.2.2) lib/sprockets/context.rb:193:in `block in evaluate' sprockets (2.2.2) lib/sprockets/context.rb:190:in `each' sprockets (2.2.2) lib/sprockets/context.rb:190:in `evaluate' sprockets (2.2.2) lib/sprockets/processed_asset.rb:12:in `initialize' sprockets (2.2.2) lib/sprockets/base.rb:249:in `new' sprockets (2.2.2) lib/sprockets/base.rb:249:in `block in build_asset' sprockets (2.2.2) lib/sprockets/base.rb:270:in `circular_call_protection' sprockets (2.2.2) lib/sprockets/base.rb:248:in `build_asset' sprockets (2.2.2) lib/sprockets/index.rb:93:in `block in build_asset' sprockets (2.2.2) lib/sprockets/caching.rb:19:in `cache_asset' sprockets (2.2.2) lib/sprockets/index.rb:92:in `build_asset' sprockets (2.2.2) lib/sprockets/base.rb:169:in `find_asset' sprockets (2.2.2) lib/sprockets/index.rb:60:in `find_asset' sprockets (2.2.2) lib/sprockets/processed_asset.rb:111:in `block in resolve_dependencies' sprockets (2.2.2) lib/sprockets/processed_asset.rb:105:in `each' sprockets (2.2.2) lib/sprockets/processed_asset.rb:105:in `resolve_dependencies' sprockets (2.2.2) lib/sprockets/processed_asset.rb:97:in `build_required_assets' sprockets (2.2.2) lib/sprockets/processed_asset.rb:16:in `initialize' sprockets (2.2.2) lib/sprockets/base.rb:249:in `new' sprockets (2.2.2) lib/sprockets/base.rb:249:in `block in build_asset' sprockets (2.2.2) lib/sprockets/base.rb:270:in `circular_call_protection' sprockets (2.2.2) lib/sprockets/base.rb:248:in `build_asset' sprockets (2.2.2) lib/sprockets/index.rb:93:in `block in build_asset' sprockets (2.2.2) lib/sprockets/caching.rb:19:in `cache_asset' sprockets (2.2.2) lib/sprockets/index.rb:92:in `build_asset' sprockets (2.2.2) lib/sprockets/base.rb:169:in `find_asset' sprockets (2.2.2) lib/sprockets/index.rb:60:in `find_asset' sprockets (2.2.2) lib/sprockets/bundled_asset.rb:38:in `init_with' sprockets (2.2.2) lib/sprockets/asset.rb:24:in `from_hash' sprockets (2.2.2) lib/sprockets/caching.rb:15:in `cache_asset' sprockets (2.2.2) lib/sprockets/index.rb:92:in `build_asset' sprockets (2.2.2) lib/sprockets/base.rb:169:in `find_asset' sprockets (2.2.2) lib/sprockets/index.rb:60:in `find_asset' sprockets (2.2.2) lib/sprockets/environment.rb:78:in `find_asset' sprockets (2.2.2) lib/sprockets/base.rb:177:in `[]' actionpack (3.2.13) lib/sprockets/helpers/rails_helper.rb:126:in `asset_for' actionpack (3.2.13) lib/sprockets/helpers/rails_helper.rb:44:in `block in stylesheet_link_tag' actionpack (3.2.13) lib/sprockets/helpers/rails_helper.rb:43:in `collect' actionpack (3.2.13) lib/sprockets/helpers/rails_helper.rb:43:in `stylesheet_link_tag' app/views/layouts/application.html.erb:16:in `_app_views_layouts_application_html_erb___824639613_33845076' actionpack (3.2.13) lib/action_view/template.rb:145:in `block in render' activesupport (3.2.13) lib/active_support/notifications.rb:125:in `instrument' actionpack (3.2.13) lib/action_view/template.rb:143:in `render' actionpack (3.2.13) lib/action_view/renderer/template_renderer.rb:59:in `render_with_layout' actionpack (3.2.13) lib/action_view/renderer/template_renderer.rb:45:in `render_template' actionpack (3.2.13) lib/action_view/renderer/template_renderer.rb:18:in `render' actionpack (3.2.13) lib/action_view/renderer/renderer.rb:36:in `render_template' actionpack (3.2.13) lib/action_view/renderer/renderer.rb:17:in `render' actionpack (3.2.13) lib/abstract_controller/rendering.rb:110:in `_render_template' actionpack (3.2.13) lib/action_controller/metal/streaming.rb:225:in `_render_template' actionpack (3.2.13) lib/abstract_controller/rendering.rb:103:in `render_to_body' actionpack (3.2.13) lib/action_controller/metal/renderers.rb:28:in `render_to_body' actionpack (3.2.13) lib/action_controller/metal/compatibility.rb:50:in `render_to_body' actionpack (3.2.13) lib/abstract_controller/rendering.rb:88:in `render' actionpack (3.2.13) lib/action_controller/metal/rendering.rb:16:in `render' actionpack (3.2.13) lib/action_controller/metal/instrumentation.rb:40:in `block (2 levels) in render' activesupport (3.2.13) lib/active_support/core_ext/benchmark.rb:5:in `block in ms' C:/RailsInstaller/Ruby1.9.3/lib/ruby/1.9.1/benchmark.rb:295:in `realtime' activesupport (3.2.13) lib/active_support/core_ext/benchmark.rb:5:in `ms' actionpack (3.2.13) lib/action_controller/metal/instrumentation.rb:40:in `block in render' actionpack (3.2.13) lib/action_controller/metal/instrumentation.rb:83:in `cleanup_view_runtime' activerecord (3.2.13) lib/active_record/railties/controller_runtime.rb:24:in `cleanup_view_runtime' actionpack (3.2.13) lib/action_controller/metal/instrumentation.rb:39:in `render' actionpack (3.2.13) lib/action_controller/metal/implicit_render.rb:10:in `default_render' actionpack (3.2.13) lib/action_controller/metal/implicit_render.rb:5:in `send_action' actionpack (3.2.13) lib/abstract_controller/base.rb:167:in `process_action' actionpack (3.2.13) lib/action_controller/metal/rendering.rb:10:in `process_action' actionpack (3.2.13) lib/abstract_controller/callbacks.rb:18:in `block in process_action' activesupport (3.2.13) lib/active_support/callbacks.rb:414:in `_run__956028316__process_action__416811168__callbacks' activesupport (3.2.13) lib/active_support/callbacks.rb:405:in `__run_callback' activesupport (3.2.13) lib/active_support/callbacks.rb:385:in `_run_process_action_callbacks' activesupport (3.2.13) lib/active_support/callbacks.rb:81:in `run_callbacks' actionpack (3.2.13) lib/abstract_controller/callbacks.rb:17:in `process_action' actionpack (3.2.13) lib/action_controller/metal/rescue.rb:29:in `process_action' actionpack (3.2.13) lib/action_controller/metal/instrumentation.rb:30:in `block in process_action' activesupport (3.2.13) lib/active_support/notifications.rb:123:in `block in instrument' activesupport (3.2.13) lib/active_support/notifications/instrumenter.rb:20:in `instrument' activesupport (3.2.13) lib/active_support/notifications.rb:123:in `instrument' actionpack (3.2.13) lib/action_controller/metal/instrumentation.rb:29:in `process_action' actionpack (3.2.13) lib/action_controller/metal/params_wrapper.rb:207:in `process_action' activerecord (3.2.13) lib/active_record/railties/controller_runtime.rb:18:in `process_action' actionpack (3.2.13) lib/abstract_controller/base.rb:121:in `process' actionpack (3.2.13) lib/abstract_controller/rendering.rb:45:in `process' actionpack (3.2.13) lib/action_controller/metal.rb:203:in `dispatch' actionpack (3.2.13) lib/action_controller/metal/rack_delegation.rb:14:in `dispatch' actionpack (3.2.13) lib/action_controller/metal.rb:246:in `block in action' actionpack (3.2.13) lib/action_dispatch/routing/route_set.rb:73:in `call' actionpack (3.2.13) lib/action_dispatch/routing/route_set.rb:73:in `dispatch' actionpack (3.2.13) lib/action_dispatch/routing/route_set.rb:36:in `call' journey (1.0.4) lib/journey/router.rb:68:in `block in call' journey (1.0.4) lib/journey/router.rb:56:in `each' journey (1.0.4) lib/journey/router.rb:56:in `call' actionpack (3.2.13) lib/action_dispatch/routing/route_set.rb:612:in `call' actionpack (3.2.13) lib/action_dispatch/middleware/best_standards_support.rb:17:in `call' rack (1.4.5) lib/rack/etag.rb:23:in `call' rack (1.4.5) lib/rack/conditionalget.rb:25:in `call' actionpack (3.2.13) lib/action_dispatch/middleware/head.rb:14:in `call' actionpack (3.2.13) lib/action_dispatch/middleware/params_parser.rb:21:in `call' actionpack (3.2.13) lib/action_dispatch/middleware/flash.rb:242:in `call' rack (1.4.5) lib/rack/session/abstract/id.rb:210:in `context' rack (1.4.5) lib/rack/session/abstract/id.rb:205:in `call' actionpack (3.2.13) lib/action_dispatch/middleware/cookies.rb:341:in `call' activerecord (3.2.13) lib/active_record/query_cache.rb:64:in `call' activerecord (3.2.13) lib/active_record/connection_adapters/abstract/connection_pool.rb:479:in `call' actionpack (3.2.13) lib/action_dispatch/middleware/callbacks.rb:28:in `block in call' activesupport (3.2.13) lib/active_support/callbacks.rb:405:in `_run__360878605__call__248365880__callbacks' activesupport (3.2.13) lib/active_support/callbacks.rb:405:in `__run_callback' activesupport (3.2.13) lib/active_support/callbacks.rb:385:in `_run_call_callbacks' activesupport (3.2.13) lib/active_support/callbacks.rb:81:in `run_callbacks' actionpack (3.2.13) lib/action_dispatch/middleware/callbacks.rb:27:in `call' actionpack (3.2.13) lib/action_dispatch/middleware/reloader.rb:65:in `call' actionpack (3.2.13) lib/action_dispatch/middleware/remote_ip.rb:31:in `call' actionpack (3.2.13) lib/action_dispatch/middleware/debug_exceptions.rb:16:in `call' actionpack (3.2.13) lib/action_dispatch/middleware/show_exceptions.rb:56:in `call' railties (3.2.13) lib/rails/rack/logger.rb:32:in `call_app' railties (3.2.13) lib/rails/rack/logger.rb:16:in `block in call' activesupport (3.2.13) lib/active_support/tagged_logging.rb:22:in `tagged' railties (3.2.13) lib/rails/rack/logger.rb:16:in `call' actionpack (3.2.13) lib/action_dispatch/middleware/request_id.rb:22:in `call' rack (1.4.5) lib/rack/methodoverride.rb:21:in `call' rack (1.4.5) lib/rack/runtime.rb:17:in `call' activesupport (3.2.13) lib/active_support/cache/strategy/local_cache.rb:72:in `call' rack (1.4.5) lib/rack/lock.rb:15:in `call' actionpack (3.2.13) lib/action_dispatch/middleware/static.rb:63:in `call' railties (3.2.13) lib/rails/engine.rb:479:in `call' railties (3.2.13) lib/rails/application.rb:223:in `call' rack (1.4.5) lib/rack/content_length.rb:14:in `call' railties (3.2.13) lib/rails/rack/log_tailer.rb:17:in `call' rack (1.4.5) lib/rack/handler/webrick.rb:59:in `service' C:/RailsInstaller/Ruby1.9.3/lib/ruby/1.9.1/webrick/httpserver.rb:138:in `service' C:/RailsInstaller/Ruby1.9.3/lib/ruby/1.9.1/webrick/httpserver.rb:94:in `run' C:/RailsInstaller/Ruby1.9.3/lib/ruby/1.9.1/webrick/server.rb:191:in `block in start_thread'

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• How to display a hierarchical skill tree in php

  - by user3587554

  If I have skill data set up in a tree format (where earlier skills are prerequisites for later ones), how would I display it as a tree, using php? The parent would be on top and have 3 children. Each of these children can then have one more child so its parent would be directly above it. I'm having trouble figuring out how to add the root element in the middle of the top div, and the child of the children below each child of the root. I'm not looking for code, but an explanation of how to do it. My data in array form is this: Data: Array ( [1] => Array ( [id] => 1 [title] => Jutsu [description] => Skill that makes you awesomer at using ninjutsu [tiers] => 1 [prereq] => [image] => images/skills/jutsu.png [children] => Array ( [2] => Array ( [id] => 2 [title] => fireball [description] => Increase your damage with fire jutsu and weapons [tiers] => 5 [prereq] => 1 [image] => images/skills/fireball.png [children] => Array ( [5] => Array ( [id] => 5 [title] => pin point [description] => Increases jutsu accuracy [tiers] => 5 [prereq] => 2 [image] => images/skills/pinpoint.png ) ) ) [3] => Array ( [id] => 3 [title] => synergy [description] => Reduce the amount of chakra needed to use ninjutsu [tiers] => 1 [prereq] => 1 [image] => images/skills/synergy.png ) [4] => Array ( [id] => 4 [title] => ebb & flow [description] => Increase the damage of water jutsu, water weapons, and reduce the damage of jutsu and weapons that use water element [tiers] => 5 [prereq] => 1 [image] => images/skills/ebbandflow.png [children] => Array ( [6] => Array ( [id] => 6 [title] => IQ [description] => Decrease the time it takes to learn a jutsu [tiers] => 5 [prereq] => 4 [image] => images/skills/iq.png ) ) ) ) ) ) An example would be this demo image minus the hover stuff.

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