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• B-Tree Revision

  - by stan

  Hi, If we are looking for line intersections (horizontal and vertical lines only) and we have n lines with half of them vertical and no intersections then Sorting the list of line end points on y value will take N log N using mergesort Each insert delete and search of our data structue (assuming its a b-tree) will be < log n so the total search time will be N log N What am i missing here, if the time to sort using mergesort takes a time of N log N and insert and delete takes a time of < log n are we dropping the constant factor to give an overal time of N log N. If not then how comes < log n goes missing in total ONotation run time? Thanks

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• CODE1 at SPOJ - cannot solve it

  - by VaioIsBorn

  I am trying to solve the problem Secret Code on SPOJ, and it's obviously a math problem. The full problem For those who are lazy to go and read, it's like this: a0, a1, a2, ..., an - sequence of N numbers B - a Complex Number (has both real and imaginary components) X = a0 + a1*B + a2*(B^2) + a3*(B^3) + ... + an*(B^n) So if you are given B and X, you should find a0, a1, ..an. I don't know how or where to start, because not even N is known, just X and B. The problem is not as easy as expressing a number in a base B, because B is a complex number. How can it be solved?

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• Is there a website to look up common, already written functions?

  - by pinnacler

  I'm sitting here writing a function that I'm positive has been written before, somewhere on earth. It's just too common to have not been attempted, and I'm wondering why I can't just go to a website and search for a function that I can then copy and paste into my project in 2 seconds, instead of wasting my day reinventing the wheel. Sure there are certain libraries you can use, but where do you find these libraries and when they are absent, is there a site like I'm describing? Possibly a wiki of some type that contains free code that anybody can edit and improve? Edit: I can code things fine, I just don't know HOW to do them. So for example, right now, I'm trying to localize a robot/car/point in space. I KNOW there is a way to do it, just based off of range and distance. Triangulation and Trilateration. How to code that is a different story. A site that could have psuedo code, step by step how to do that would be ridiculously helpful. It would also ensure the optimal solution since everybody can edit it. I'm also writing in Matlab, which I hate because it's quirky, adding to my desire for creating a website like I describe.

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• Accenture interview question - Find the only unpaired element in the array

  - by karank

  You have been given an array of size 2n+1 that have n pair of integers(can be +ve, -ve or 0) and one unpaired element. How would you find the unpaired element. Pair means duplicate. So (3,3) is a pair and (3,-3) is not a pair.

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• Drawing N-width lines?

  - by user146780

  Given a series of points, how could I calculate the vector for that line 5 pixels away? Ex: Given: \ \ \ How could I find the vector for \ \ \ \ \ \ The ones on the right. But bear in mind that it may not always be a nice straight line. I'm trying to figure out how programs like Flash can make thick outlines. Thanks

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• How should i set the while loop counter?? when is it supposed to be 1 and when is it supposed to be

  - by Dina

  How should i set the while loop counter?? when is it supposed to be 1 and when is it supposed to be 0? and in general how should i start with a while loop problem? Thnx.

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• MATLAB: Reading floating point numbers and strings from a file

  - by xsound

  I am using the following functions for writing and reading 4098 floating point numbers in MATLAB: Writing: fid = fopen(completepath, 'w'); fprintf(fid, '%1.30f\r\n', y) Reading: data = textread(completepath, '%f', 4098); where y contains 4098 numbers. I now want to write and read 3 strings at the end of this data. How do I read two different datatypes? Please help me. Thanks in advance.

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• Return a number between 0 and 4

  - by munchine

  How do I return a number between 0 and 4, depending the input number? For example if I pass it number 23 it will return 3. The number set should look like 0 5 10 15 20 .. 1 6 11 16 21 .. 2 7 12 17 22 .. 3 8 13 18 23 .. 4 9 14 19 24 What's the math for this?

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• Detecting Singularities in a Graph

  - by nasufara

  I am creating a graphing calculator in Java as a project for my programming class. There are two main components to this calculator: the graph itself, which draws the line(s), and the equation evaluator, which takes in an equation as a String and... well, evaluates it. To create the line, I create a Path2D.Double instance, and loop through the points on the line. To do this, I calculate as many points as the graph is wide (e.g. if the graph itself is 500px wide, I calculate 500 points), and then scale it to the window of the graph. Now, this works perfectly for most any line. However, it does not when dealing with singularities. If, when calculating points, the graph encounters a domain error (such as 1/0), the graph closes the shape in the Path2D.Double instance and starts a new line, so that the line looks mathematically correct. Example: However, because of the way it scales, sometimes it is rendered correctly, sometimes it isn't. When it isn't, the actual asymptotic line is shown, because within those 500 points, it skipped over x = 2.0 in the equation 1 / (x-2), and only did x = 1.98 and x = 2.04, which are perfectly valid in that equation. Example: In that case, I increased the window on the left and right one unit each. My question is: Is there a way to deal with singularities using this method of scaling so that the resulting line looks mathematically correct? I myself have thought of implementing a binary search-esque method, where, if it finds that it calculates one point, and then the next point is wildly far away from the last point, it searches in between those points for a domain error. I had trouble figuring out how to make it work in practice, however. Thank you for any help you may give!

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• How can I create set of small bounding boxes given a large area?

  - by David Arsenault

  Given a large bounding box (say 1 km square), I want to divide this area into a set of smaller bounding boxes to form a grid pattern. I know there are some Earth geometry issues to contend with where. Can anyone help? I'm doing with with Ruby and I'm working with the excellent GeoKit library. Thank you!

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• Deletion procedure for a Binary Search Tree

  - by Metz

  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. 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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• Reverse factorial

  - by dada

  Well, we all know that if N is given it's easy to calculate N!. But what about reversing? N! is given and you are about to find N - Is that possible ? I'm curious.

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• Test if single linked list is circular by traversing it only once

  - by user1589754

  I am a fresher and I was asked this question in a recent interview I gave. The question was --- By traversing each element of linked list just once find if the single linked list is circular at any point. To this I answered that we will store reference of each node while traversing the list in another linked list and for every node in the list being tested we will find if the reference exists in the list I am storing the references. The interviewer said that he needs a more optimized way to solve this problem. Can anyone please tell me what would be a more optimized method to solve this problem.

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• Random access gzip stream

  - by jkff

  I'd like to be able to do random access into a gzipped file. I can afford to do some preprocessing on it (say, build some kind of index), provided that the result of the preprocessing is much smaller than the file itself. Any advice? My thoughts were: Hack on an existing gzip implementation and serialize its decompressor state every, say, 1 megabyte of compressed data. Then to do random access, deserialize the decompressor state and read from the megabyte boundary. This seems hard, especially since I'm working with Java and I couldn't find a pure-java gzip implementation :( Re-compress the file in chunks of 1Mb and do same as above. This has the disadvantage of doubling the required disk space. Write a simple parser of the gzip format that doesn't do any decompressing and only detects and indexes block boundaries (if there even are any blocks: I haven't yet read the gzip format description)

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• KD-Trees and missing values (vector comparison)

  - by labratmatt

  I have a system that stores vectors and allows a user to find the n most similar vectors to the user's query vector. That is, a user submits a vector (I call it a query vector) and my system spits out "here are the n most similar vectors." I generate the similar vectors using a KD-Tree and everything works well, but I want to do more. I want to present a list of the n most similar vectors even if the user doesn't submit a complete vector (a vector with missing values). That is, if a user submits a vector with three dimensions, I still want to find the n nearest vectors (stored vectors are of 11 dimensions) I have stored. I have a couple of obvious solutions, but I'm not sure either one seem very good: Create multiple KD-Trees each built using the most popular subset of dimensions a user will search for. That is, if a user submits a query vector of thee dimensions, x, y, z, I match that query to my already built KD-Tree which only contains vectors of three dimensions, x, y, z. Ignore KD-Trees when a user submits a query vector with missing values and compare the query vector to the vectors (stored in a table in a DB) one by one using something like a dot product. This has to be a common problem, any suggestions? Thanks for the help.

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• C++ string array binary search

  - by Jose Vega

  string Haystack[] = { "Alabama", "Alaska", "American Samoa", "Arizona", "Arkansas", "California", "Colorado", "Connecticut", "Delaware", "District of Columbia", "Florida", "Georgia", "Guam", "Hawaii", "Idaho", "Illinois", "Indiana", "Iowa", "Kansas", "Kentucky", "Louisiana", "Maine", "Maryland", "Massachusetts", "Michigan", "Minnesota", "Mississippi", "Missouri", "Montana", "Nebraska", "Nevada", "New Hampshire", "New Jersey", "New Mexico", "New York", "North Carolina", "North Dakota", "Northern Mariana Islands", "Ohio", "Oklahoma", "Oregon", "Pennsylvania", "Puerto Rico", "Rhode Island", "South Carolina", "South Dakota", "Tennessee", "Texas", "US Virgin Islands", "Utah", "Vermont", "Virginia", "Washington", "West Virginia", "Wisconsin", "Wyoming"}; string Needle = "Virginia"; if(std::binary_search(Haystack, Haystack+56, Needle)) cout<<"Found"; If I also wanted to find the location of the needle in the string array, is there an "easy" way to find out?

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• Pruning: When to Stop?

  - by cam

  When does pruning stop being efficient in a depth-first search? I've been working on an efficient method to solve the N-Queens problem and I'm looking at pruning for the first time. I've implemented it for the first two rows, but when does it stop being efficient? How far should I prune to?

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• Find a missing 32bit integer among a unsorted array containing at most 4 billion ints

  - by pierr

  Hi, This is the problem described in Programming pearls. I can not understand binary search method descrbied by the author. Can any one helps to elaborate? Thanks. EDIT: I can understand binary search in general. I just can not understand how to apply binary search in this special case. How to decide the missing number is in or not in some range so that we can choose another. English is not my native language, that is one reason I can not understand the author well. So, use plain english please:) EDIT: Thank you all for your great answer and comments ! The most important lesson I leant from solving this question is Binary search applies not only on sorted array!

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• VBA compare and sort strings with quirky characters

  - by Smandoli

  I am comparing text values from two DAO recordsets in MS Access. I sort on the text field, then go through both recordsets comparing the values from each. The sets are substantially different and while they're mostly alpha-numeric, spaces and symbols like hyphens and periods are very common. My program depends on predictable sorting and fool-proof comparing. But unfortunately, the sort will rank two values differently than the comparison function. StrComp is the obvious first choice: varResult = StrComp(Val_1, Val_2) RFA-300 14.9044 RFA300 14-2044 But for the two pairs above, StrComp returns a different value than one would expect based on the sort. Including vbTextCompare or vbBinaryCompare affects StrComp's result, but not so as to solve the problem. Note the values must always be compared as strings. Of course I make sure that "14-2044" and "14.9044" aren't evaluated as -2030 and ~15. That's not the cause of my problem. I learned API-based functions are more reliable for quirky texts, so I tried these: varResult = CompareString(LOCALE_SYSTEM_DEFAULT, _ SORT_STRINGSORT, strVal_2, -1, strVal_1, -1) varResult = CompareString(LOCALE_SYSTEM_DEFAULT, _ NORM_IGNOREWIDTH, strVal_2, -1, strVal_1, -1) The first one returns the opposite of StrComp. The second one returns the same as StrComp. But neither yields a result that is consistent with the sort order. (NORM_IGNOREWIDTH is probably not relevant, but I needed a place-holder substitute and it looked as good as any.) UPDATE: This is a complete rewrite of the original post, deleting all the info about why I really need this -- just take my word for it and enjoy the brevity.

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• open source smooth particle hydrodynamics

  - by user325181

  Anyone know of any open source libraries for particle based large scale smooth particle hydrodynamics. I am looking for a easier way of simulating large scale planetary body impacts with rotation. I was also wondering if you had any ideas on how to visualize the output from said simulation. I have tried using IBM graphviz, but it is very difficult to work with. Any pointers would be appreciated. Thanks!

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• Minimum cost strongly connected digraph

  - by Kazoom

  I have a digraph which is strongly connected (i.e. there is a path from i to j and j to i for each pair of nodes (i, j) in the graph G). I wish to find a strongly connected graph out of this graph such that the sum of all edges is the least. To put it differently, I need to get rid of edges in such a way that after removing them, the graph will still be strongly connected and of least cost for the sum of edges. I think it's an NP hard problem. I'm looking for an optimal solution, not approximation, for a small set of data like 20 nodes. Edit A more general description: Given a grap G(V,E) find a graph G'(V,E') such that if there exists a path from v1 to v2 in G than there also exists a path between v1 and v2 in G' and sum of each ei in E' is the least possible. so its similar to finding a minimum equivalent graph, only here we want to minimize the sum of edge weights rather than sum of edges. Edit: My approach so far: I thought of solving it using TSP with multiple visits, but it is not correct. My goal here is to cover each city but using a minimum cost path. So, it's more like the cover set problem, I guess, but I'm not exactly sure. I'm required to cover each and every city using paths whose total cost is minimum, so visiting already visited paths multiple times does not add to the cost.

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• Best way to Fingerprint and Verify html structure.

  - by Lukas Šalkauskas

  Hello there, I just want to know what is your opinion about how to fingerprint/verify html/links structure. The problem I want to solve is: fingerprint for example 10 different sites, html pages. And after some time I want to have possibility to verify them, so is, if site has been changed, links changed, verification fails, othervise verification success. My base Idea is to analyze link structure by splitting it in some way, doing some kind of tree, and from that tree generate some kind of code. But I'm still in brainstorm stage, where I need to discuss this with someone, and know other ideas. So any ideas, algos, and suggestions would be usefull.

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• calculating parameters for defining subsections of quadratic bezier curves

  - by jedierikb

  I have a quadratic bezier curve described as (startX, startY) to (anchorX, anchorY) and using a control point(controlX, controlY). I have two questions: (1) I want to determine y points on that curve based on an x point. (2) Then, given two intermediary points on that bezier curve, I want to know the 6 parameters needed to create that mini-bezier curve.

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• Reduce number of points in line

  - by culebrón

  I'm searching for algorithms to reduce the LOD of polylines, lines (looped or not) of nodes. In simple words, I want to take hi-resolution coastline data and be able to reduce its LOD hundred- or thousandfold to render it in small-scale. I found polygon reduction algorithms (but they require triangles) and Laplacian smoothing, but that doesn't seem exactly what I need.

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• php -Merging an Array

  - by Vidhu Shresth Bhatnagar

  I have two array which i want to merge in a specific way in php. So i need your help in helping me with it as i tried and failed. So say i have two arrays: $array1= array( "foo" => 3, "bar" => 2, "random1" => 4, ); $array2= array( "random2" => 3, "random3" => 4, "foo" => 6, ); Now when during merging i would like the common key's values to be added. So like foo exists in array1 and in array2 so when merging array1 with array 2 i should get "foo" => "9" I better illustration would be the final array which looks like this: $array1= array( "foo" => 9, "bar" => 2, "random1" => 4, "random2" => 3, "random3" => 4, ); So again i would like the values of the common keys to be added together and non common keys to be added to array or a new array I hope i was clear enough Thanks, Vidhu

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