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  • Algorithm for finding symmetries of a tree

    - by Paxinum
    I have n sectors, enumerated 0 to n-1 counterclockwise. The boundaries between these sectors are infinite branches (n of them). The sectors live in the complex plane, and for n even, sector 0 and n/2 are bisected by the real axis, and the sectors are evenly spaced. These branches meet at certain points, called junctions. Each junction is adjacent to a subset of the sectors (at least 3 of them). Specifying the junctions, (in pre-fix order, lets say, starting from junction adjacent to sector 0 and 1), and the distance between the junctions, uniquely describes the tree. Now, given such a representation, how can I see if it is symmetric wrt the real axis? For example, n=6, the tree (0,1,5)(1,2,4,5)(2,3,4) have three junctions on the real line, so it is symmetric wrt the real axis. If the distances between (015) and (1245) is equal to distance from (1245) to (234), this is also symmetric wrt the imaginary axis. The tree (0,1,5)(1,2,5)(2,4,5)(2,3,4) have 4 junctions, and this is never symmetric wrt either imaginary or real axis, but it has 180 degrees rotation symmetry if the distance between the first two and the last two junctions in the representation are equal. Edit: This is actually for my research. I have posted the question at mathoverflow as well, but my days in competition programming tells me that this is more like an IOI task. Code in mathematica would be excellent, but java, python, or any other language readable by a human suffices. Here are some examples (pretend the double edges are single and we have a tree) http://www2.math.su.se/~per/files.php?file=contr_ex_1.pdf http://www2.math.su.se/~per/files.php?file=contr_ex_2.pdf http://www2.math.su.se/~per/files.php?file=contr_ex_5.pdf Example 1 is described as (0,1,4)(1,2,4)(2,3,4)(0,4,5) with distances (2,1,3). Example 2 is described as (0,1,4)(1,2,4)(2,3,4)(0,4,5) with distances (2,1,1). Example 5 is described as (0,1,4,5)(1,2,3,4) with distances (2). So, given the description/representation, I want to find some algorithm to decide if it is symmetric wrt real, imaginary, and rotation 180 degrees. The last example have 180 degree symmetry. (These symmetries corresponds to special kinds of potential in the Schroedinger equation, which has nice properties in quantum mechanics.)

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  • Efficient Array Storage for Binary Tree

    - by Sundararajan S
    We have to write the nodes of a binary tree to a file. What is the most space efficient way of writing a binary tree . We can store it in array format with parent in position 'i' and its childs in 2i,2i+1. But this will waste lot of space in case of sparse binary trees.

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  • question about tree

    - by davit-datuashvili
    i have question for example i want to implement binary tree with array i want understand what will indexes for left child and rigth child ?my array is 0 based i want implement searching in tree using array can anybody help me?

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  • What tool to use to draw file tree diagram

    - by Michael
    Given a file tree - a directory with directories in it etc, what software would you recommend to create a diagram of the file-tree as a graphic file that I can embed in a word processor document I prefer vector (SVG, EPS, EMF...) files. The tool must run on Windows, but preferably cross-platform. The tool may be commercial but preferably free.

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  • Looking for a good Python Tree data structure

    - by morpheous
    I am looking for a good Tree data structure class. I have come across this package, but since I am relatively new to Python (not programming), I dont know if there are any better ones out there. I'd like to hear from the Pythonistas on here - do you have a favorite tree script that you regularly use and would recommend?

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  • Mutating the expression tree of a predicate to target another type

    - by Jon
    Intro In the application I 'm currently working on, there are two kinds of each business object: the "ActiveRecord" type, and the "DataContract" type. So for example, we have: namespace ActiveRecord { class Widget { public int Id { get; set; } } } namespace DataContracts { class Widget { public int Id { get; set; } } } The database access layer takes care of "translating" between hierarchies: you can tell it to update a DataContracts.Widget, and it will magically create an ActiveRecord.Widget with the same property values and save that. The problem I have surfaced when attempting to refactor this database access layer. The Problem I want to add methods like the following to the database access layer: // Widget is DataContract.Widget interface DbAccessLayer { IEnumerable<Widget> GetMany(Expression<Func<Widget, bool>> predicate); } The above is a simple general-use "get" method with custom predicate. The only point of interest is that I 'm not passing in an anonymous function but rather an expression tree. This is done because inside DbAccessLayer we have to query ActiveRecord.Widget efficiently (LINQ to SQL) and not have the database return all ActiveRecord.Widget instances and then filter the enumerable collection. We need to pass in an expression tree, so we ask for one as the parameter for GetMany. The snag: the parameter we have needs to be magically transformed from an Expression<Func<DataContract.Widget, bool>> to an Expression<Func<ActiveRecord.Widget, bool>>. This is where I haven't managed to pull it off... Attempted Solution What we 'd like to do inside GetMany is: IEnumerable<DataContract.Widget> GetMany( Expression<Func<DataContract.Widget, bool>> predicate) { var lambda = Expression.Lambda<Func<ActiveRecord.Widget, bool>>( predicate.Body, predicate.Parameters); // use lambda to query ActiveRecord.Widget and return some value } This won't work because in a typical scenario, for example if: predicate == w => w.Id == 0; ...the expression tree contains a MemberAccessExpression instance which has a MemberInfo property (named Member) that point to members of DataContract.Widget. There are also ParameterExpression instances both in the expression tree and in its parameter expression collection (predicate.Parameters); After searching a bit, I found System.Linq.Expressions.ExpressionVisitor (its source can be found here in the context of a how-to, very helpful) which is a convenient way to modify an expression tree. Armed with this, I implemented a visitor. This simple visitor only takes care of changing the types in member access and parameter expressions. It may not be complete, but it's fine for the expression w => w.Id == 0. internal class Visitor : ExpressionVisitor { private readonly Func<Type, Type> dataContractToActiveRecordTypeConverter; public Visitor(Func<Type, Type> dataContractToActiveRecordTypeConverter) { this.dataContractToActiveRecordTypeConverter = dataContractToActiveRecordTypeConverter; } protected override Expression VisitMember(MemberExpression node) { var dataContractType = node.Member.ReflectedType; var activeRecordType = this.dataContractToActiveRecordTypeConverter(dataContractType); var converted = Expression.MakeMemberAccess( base.Visit(node.Expression), activeRecordType.GetProperty(node.Member.Name)); return converted; } protected override Expression VisitParameter(ParameterExpression node) { var dataContractType = node.Type; var activeRecordType = this.dataContractToActiveRecordTypeConverter(dataContractType); return Expression.Parameter(activeRecordType, node.Name); } } With this visitor, GetMany becomes: IEnumerable<DataContract.Widget> GetMany( Expression<Func<DataContract.Widget, bool>> predicate) { var visitor = new Visitor(...); var lambda = Expression.Lambda<Func<ActiveRecord.Widget, bool>>( visitor.Visit(predicate.Body), predicate.Parameters.Select(p => visitor.Visit(p)); var widgets = ActiveRecord.Widget.Repository().Where(lambda); // This is just for reference, see below Expression<Func<ActiveRecord.Widget, bool>> referenceLambda = w => w.Id == 0; // Here we 'd convert the widgets to instances of DataContract.Widget and // return them -- this has nothing to do with the question though. } Results The good news is that lambda is constructed just fine. The bad news is that it isn't working; it's blowing up on me when I try to use it (the exception messages are really not helpful at all). I have examined the lambda my code produces and a hardcoded lambda with the same expression; they look exactly the same. I spent hours in the debugger trying to find some difference, but I can't. When predicate is w => w.Id == 0, lambda looks exactly like referenceLambda. But the latter works with e.g. IQueryable<T>.Where, while the former does not (I have tried this in the immediate window of the debugger). I should also mention that when predicate is w => true, it all works just fine. Therefore I am assuming that I 'm not doing enough work in Visitor, but I can't find any more leads to follow on. Can someone point me in the right direction? Thanks in advance for your help!

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  • Is there a programming language with not a tree but tags idea behind OOP?

    - by kolupaev
    I'm thinking about tree structures, and I feel that I don't like them. It's like when you have a shop, then you try to put all products to tree-like catalog, and then you need to place one product to multiple categories, now you have multiple routing, bla-bla. I don't feel like everything in the world could be put to a tree. Instead, I like idea of tags. I would like to store everything with tags. With tags I could do much more. I can even simulate trees if I want. I want to have tag-based filesystem! But hey - modern OOP paradigm with inheritance is based on tree. I want to see how it is when you don't have such basement. Closest thing I found is mixins in some languages. Do you know what else is also about this ideas?

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  • Why create a Huffman tree per character instead of a Node?

    - by Omega
    For a school assignment we're supposed to make a Java implementation of a compressor/decompresser using Huffman's algorithm. I've been reading a bit about it, specially this C++ tutorial: http://www.cprogramming.com/tutorial/computersciencetheory/huffman.html In my program, I've been thinking about having Nodes that have the following properties: Total Frequency Character (if a leaf) Right child (if any) Left child (if any) Parent (if any) So when building the Huffman tree, it is just a matter of linking a node to others, etc. However, I'm a bit confused with the following quote (emphasis mine): First, every letter starts off as part of its own tree and the trees are ordered by the frequency of the letters in the original string. Then the two least-frequently used letters are combined into a single tree, and the frequency of that tree is set to be the combined frequency of the two trees that it links together. My question: why should I create a tree per letter, instead of just a node per letter and then do the linking later? I have not begun coding, I'm just studying the algorithm first, so I guess I'm missing an important detail. What is it?

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  • Why don't we store the syntax tree instead of the source code?

    - by Calmarius
    We have a lot of programming languages. Every language is parsed and syntax checked before translated into code so an abstract syntax tree is built. We have this abstract syntax tree, why don't we store this syntax tree instead of the source code (or next to the source code)? By using an AST instead of the source code. Every programmer in a team can serialize this tree to any language, they want (with the appropriate context free grammar) and parse back to AST when they finished. So this would eliminate the debate about the coding style questions (where to put the { and }, where to put whitespace, indentation, etc.) What are the pros and cons of this approach?

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  • Java+DOM: How do I convert a DOM tree without namespaces to a namespace-aware DOM tree?

    - by java.is.for.desktop
    Hello, everyone! I receive a Document (DOM tree) from a certain API (not in JDK). Sadly, this Document is not namespace-aware. As far as I know DOM, once generated, namespace-awareness can't be "added" afterwards. When converting this Document using a Transformer to a string, the XML is correct. Elements have xmlns:... attributes and name prefixes. But from the DOM point of view, there are no namespaces and no prefixes. I need to be able to convert this Document into a new Document which is namespace-aware. Yes, I could do this by just converting it to a string and back to DOM with namespaces enabled. But: nodes of the original tree have user-objects set. Converting to string and back would make a mapping of these user-objects to the new Document very complicated, if not impossible. So I really need a way to convert non-namespace DOM to namespace DOM. Are there any more-or-less straightforward solutions for this? Worst case (what I'm hoping to avoid) would be to manually iterate through old Document tree and create new namespace-aware Node for each old Node. Doing so, one had to manually "parse" namespace prefixes, watch out for xmlns-attributes, and maintain a mapping between prefixes and namespace-URIs. Lots of things to go wrong.

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  • ACL actions tag cause 'roles resource tree' draw incorrectly in admin/system/permissions/roles

    - by latvian
    Hi, We created new action similar to 'hold', 'ship' and others in the 'sales_order/view' admin section that can be triggered by clicking at the button. Afterward, we added our new action to the ACL with the following code in config.xml: <acl> <resources> <admin> <children> <sales> <children> <order> <children> <actions translate="title"> <title>Actions</title> <children> <shipNew translate="title"><title>Ship Ups</title></shipNew> </children> </actions> </children> <sort_order>10</sort_order> </order> </children> </sales> </children> </admin> </resources> </acl> ACL functionality works, however, in the 'Resources Tree'(System/Permissions/Roles/Role Resources) our new action does never show up as selected(checked) even thou it is allowed for particular Role. I can see that from table 'admin_rule' with resource id for our new action that it is allowed, so it needs to be selected, but it is not. When trying to solve this issue i looked into the template(permissions/rolesedit.phtml) and I found that the 'resource tree' is draw with Javascript...thats where i got stock due to my limited knowledge in Javascript. Why the resource tree does not display our new ACL entry correctly, that is the check box is never checked? Thank You for helping margots

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  • converting a Tree to newick format. java

    - by Esmond
    I'm having problems converting a binary rooted tree to newick format. The full explanation for such a format can be found: http://code.google.com/p/mrsrf/wiki/NewickTree An example of a newick format would be as follows: for a tree T such as http://www.cs.mcgill.ca/~cs251/OldCourses/1997/topic8/images/completetreetwo.gif the newick representation would be: (((8,9),(10,11)),((12,13),(14,15))) the internal node will become the commas while the leaves will be retained. such trees have internal nodes which will always have 2 children. I have a problem using recursion to come out with this newick format. The output contains far too many nodes and braces. Any comments to resolve this problem is appreciated or even an iterative algorithm would be welcomed import java.util.Stack; public class Tree { .... public String inOrderNewick(Node root, String output) throws ItemNotFoundException { if (root.hasChild()) { output += "("; output += inOrderNewick(root.child1, output); output += ","; output += inOrderNewick(root.child2, output); output += ")"; return output; } else { output += root.getSeq(); return output; } } }

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  • Realizing program with decision tree logics

    - by Vytas999
    The system realizes a game “Think animal”. Main use case is: 1. System offers user to think about any animal and the system will try to guess it 2. The system starts asking questions from the start of decision tree. Ex., “Question: It has fur?”, and provides possible answers – yes or no. 3. If the user answers Yes, the system proceeds to these steps: a. System tries to guess animal that has that feature, ex. “My guess: Is it bear?” and provides with possible answers – yes or no. b. If the user answer is Yes, the system offers to think off another animal 4. If the user answers is No, the system moves to No node in decision tree and moves to 2 step (and starts from asking from new node). 5. If system runs out of nodes (i.e., empty yes or no node was reached): a. the system announces that it has given up, and ask user to enter: i. What animal he had in mind ii. What is his characteristic feature b. User enters requested data c. The system creates a new node and links it to yes or no of last active node. Where i can get some information and some examples, when implementing decision tree logics in MS SQL Server and C#..? Any information will be usefull. Thanks

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  • Parse a CSV file using python (to make a decision tree later)

    - by Margaret
    First off, full disclosure: This is going towards a uni assignment, so I don't want to receive code. :). I'm more looking for approaches; I'm very new to python, having read a book but not yet written any code. The entire task is to import the contents of a CSV file, create a decision tree from the contents of the CSV file (using the ID3 algorithm), and then parse a second CSV file to run against the tree. There's a big (understandable) preference to have it capable of dealing with different CSV files (I asked if we were allowed to hard code the column names, mostly to eliminate it as a possibility, and the answer was no). The CSV files are in a fairly standard format; the header row is marked with a # then the column names are displayed, and every row after that is a simple series of values. Example: # Column1, Column2, Column3, Column4 Value01, Value02, Value03, Value04 Value11, Value12, Value13, Value14 At the moment, I'm trying to work out the first part: parsing the CSV. To make the decisions for the decision tree, a dictionary structure seems like it's going to be the most logical; so I was thinking of doing something along these lines: Read in each line, character by character If the character is not a comma or a space Append character to temporary string If the character is a comma Append the temporary string to a list Empty string Once a line has been read Create a dictionary using the header row as the key (somehow!) Append that dictionary to a list However, if I do things that way, I'm not sure how to make a mapping between the keys and the values. I'm also wondering whether there is some way to perform an action on every dictionary in a list, since I'll need to be doing things to the effect of "Everyone return their values for columns Column1 and Column4, so I can count up who has what!" - I assume that there is some mechanism, but I don't think I know how to do it. Is a dictionary the best way to do it? Would I be better off doing things using some other data structure? If so, what?

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  • Makefile; mirroring a growing tree through a process

    - by Martineau
    I would like to periodically mirror a growing tree, say, from $in to $out, doing a process in between (saving the only file header). As; #!/bin/bash in=./segd out=./db for f in `find $in -name "*.segd"`;do # Deduct output (dir + name) d=`dirname $f|perl -pe 's!'$in'!'$out'!'` n=`basename $f|perl -pe 's!$!_hdr!'` if [ ! -e $d/$n ]; then [ ! -d $d ] && mkdir -p $d; printf "From %s now build %s\n" $f "$d/$n" # Do something, whathever. For example e.g; dd if=$f bs=32 count=1 conv=swab 2>/dev/null|od -x > $d/$n fi done That is about fair. However; to be more robust, for a better synchronization (say if a source file did change or whatever), I would like to use a Makefile, as in; HDR := $(patsubst ./segd/%.segd,./db/%.segd_hdr,$(wildcard ./segd/*.segd)) all: ${HDR} db/%.segd_hdr: ./segd/%.segd echo "Doing" dd if=$< bs=32 count=1 conv=swab 2>/dev/null|od -x > $@ My problem; I cannot code this Makefile to "dive" more deeply within the source ./segd tree. How can we do it and is there a way ? Many thanks for your kind recommendations. PS: The idea will be to later rsync the (smaller) destination tree over a sat connection.

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  • Bidirectional real-time sync of large file tree between two distant linux servers

    - by dlo
    By large file tree I mean about 200k files, and growing all the time. A relatively small number of files are being changed in any given hour though. By bidirectional I mean that changes may occur on either server and need to be pushed to the other, so rsync doesn't seem appropriate. By distant I mean that the servers are both in data centers, but geographically remote from each other. Currently there are only 2 servers, but that may expand over time. By real-time, it's ok for there to be a little latency between syncing, but running a cron every 1-2 minutes doesn't seem right, since a very small fraction of files may change in any given hour, let alone minute. EDIT: This is running on VPS's so I might be limited on the kinds of kernel-level stuff I can do. Also, the VPS's are not resource-rich, so I'd shy away from solutions that require lots of ram (like Gluster?). What's the best / most "accepted" approach to get this done? This seems like it would be a common need, but I haven't been able to find a generally accepted approach yet, which was surprising. (I'm seeking the safety of the masses. :) I've come across lsyncd to trigger a sync at the filesystem change level. That seems clever though not super common, and I'm a bit confused by the various lsyncd approaches. There's just using lsyncd with rsync, but it seems this could be fragile for bidirectionality since rsync doesn't have a notion of memory (eg- to know whether a deleted file on A should be deleted on B or whether it's a new file on B that should be copied to A). lipsync appears to be just a lsyncd+rsync implementation, right? Then there's using lsyncd with csync2, like this: http://www.axivo.com/community/threads/lightning-fast-synchronization-with-csync2-and-lsyncd.121/ ... I'm leaning towards this approach, but csync2 is a little quirky, though I did do a successful test of it. I'm mostly concerned that I haven't been able to find a lot of community confirmation of this method. People on here seem to like Unison a lot, but it seems that it is no longer under active development and it's not clear that it has an automatic trigger like lsyncd. I've seen Gluster mentioned, but maybe overkill for what I need? UPDATE: fyi- I ended up going with the original solution I mentioned: lsyncd+csync2. It seems to work quite well, and I like the architectural approach of having the servers be very loosely joined, so that each server can operate indefinitely on its own regardless of the link quality between them.

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  • Explode all folders

    - by sam
    Ive got a folder with about a hundred sub folders and again each ones of those has between 10 and 20 sub folders, so all in all a pretty large folder tree. Is there a simple way i can explode or export all of the files in the tree to a new folder which will just be one folder contain the files (no folders, no trees). Im running OSX 10.8, although ive also got Parallels so if there is a windows solution i could just run that as its not something i need to do everyday.

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  • Constructing a Binary Tree from its traversals

    - by user991710
    I'm trying to construct a binary tree (unbalanced), given its traversals. I'm currently doing preorder + inorder but when I figure this out postorder will be no issue at all. I realize there are some question on the topic already but none of them seemed to answer my question. I've got a recursive method that takes the Preorder and the Inorder of a binary tree to reconstruct it, but is for some reason failing to link the root node with the subsequent children. Note: I don't want a solution. I've been trying to figure this out for a few hours now and even jotted down the recursion on paper and everything seems fine... so I must be missing something subtle. Here's the code: public static <T> BinaryNode<T> prePlusIn( T[] pre, T[] in) { if(pre.length != in.length) throw new IllegalArgumentException(); BinaryNode<T> base = new BinaryNode(); base.element = pre[0]; // * Get root from the preorder traversal. int indexOfRoot = 0; if(pre.length == 0 && in.length == 0) return null; if(pre.length == 1 && in.length == 1 && pre[0].equals(in[0])) return base; // * If both arrays are of size 1, element is a leaf. for(int i = 0; i < in.length -1; i++){ if(in[i].equals(base.element)){ // * Get the index of the root indexOfRoot = i; // in the inorder traversal. break; } // * If we cannot, the tree cannot be constructed as the traversals differ. else throw new IllegalArgumentException(); } // * Now, we recursively set the left and right subtrees of // the above "base" root node to whatever the new preorder // and inorder traversals end up constructing. T[] preleft = Arrays.copyOfRange(pre, 1, indexOfRoot + 1); T[] preright = Arrays.copyOfRange(pre, indexOfRoot + 1, pre.length); T[] inleft = Arrays.copyOfRange(in, 0, indexOfRoot); T[] inright = Arrays.copyOfRange(in, indexOfRoot + 1, in.length); base.left = prePlusIn( preleft, inleft); // * Construct left subtree. base.right = prePlusIn( preright, inright); // * Construc right subtree. return base; // * Return fully constructed tree } Basically, I construct additional arrays that house the pre- and inorder traversals of the left and right subtree (this seems terribly inefficient but I could not think of a better way with no helpers methods). Any ideas would be quite appreciated. Side note: While debugging it seems that the root note never receives the connections to the additional nodes (they remain null). From what I can see though, that should not happen... EDIT: To clarify, the method is throwing the IllegalArgumentException @ line 21 (else branch of the for loop, which should only be thrown if the traversals contain different elements.

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