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• Clojure - tail recursive sieve of Eratosthenes

  - by Konrad Garus

  I have this implementation of the sieve of Eratosthenes in Clojure: (defn sieve [n] (loop [last-tried 2 sift (range 2 (inc n))] (if (or (nil? last-tried) (> last-tried n)) sift (let [filtered (filter #(or (= % last-tried) (< 0 (rem % last-tried))) sift)] (let [next-to-try (first (filter #(> % last-tried) filtered))] (recur next-to-try filtered)))))) For larger n (like 20000) it ends with stack overflow. Why doesn't tail call elimination work here? How to fix it?

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• Url shortening algorithm

  - by Bozho

  Now, this is not strictly about URL shortening, but my purpose is such anyway, so let's view it like that. Of course the steps to URL shortening are: Take the full URL Generate a unique short string to be the key for the URL Store the URL and the key in a database (a key-value store would be a perfect match here) Now, about the 2nd point. Here's what I've come up with: ByteArrayOutputStream baos = new ByteArrayOutputStream(); DataOutputStream dos = new DataOutputStream(baos); UUID uuid = UUID.randomUUID(); dos.writeLong(uuid.getMostSignificantBits()); String encoded = new String(Base64.encodeBase64(baos.toByteArray()), "ISO-8859-1"); String shortUrl = StringUtils.left(6); // returns the leftmost 6 characters // check if exists in database, repeat until it does not I wonder if this is good enough. Is it?

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• Array sorting efficiency... Beginner need advice

  - by SoleSoft

  I'll start by saying I am very much a beginner programmer, this is essentially my first real project outside of using learning material. I've been making a 'Simon Says' style game (the game where you repeat the pattern generated by the computer) using C# and XNA, the actual game is complete and working fine but while creating it, I wanted to also create a 'top 10' scoreboard. The scoreboard would record player name, level (how many 'rounds' they've completed) and combo (how many buttons presses they got correct), the scoreboard would then be sorted by combo score. This led me to XML, the first time using it, and I eventually got to the point of having an XML file that recorded the top 10 scores. The XML file is managed within a scoreboard class, which is also responsible for adding new scores and sorting scores. Which gets me to the point... I'd like some feedback on the way I've gone about sorting the score list and how I could have done it better, I have no other way to gain feedback =(. I know .NET features Array.Sort() but I wasn't too sure of how to use it as it's not just a single array that needs to be sorted. When a new score needs to be entered into the scoreboard, the player name and level also have to be added. These are stored within an 'array of arrays' (10 = for 'top 10' scores) scoreboardComboData = new int[10]; // Combo scoreboardTextData = new string[2][]; scoreboardTextData[0] = new string[10]; // Name scoreboardTextData[1] = new string[10]; // Level as string The scoreboard class works as follows: - Checks to see if 'scoreboard.xml' exists, if not it creates it - Initialises above arrays and adds any player data from scoreboard.xml, from previous run - when AddScore(name, level, combo) is called the sort begins - Another method can also be called that populates the XML file with above array data The sort checks to see if the new score (combo) is less than or equal to any recorded scores within the scoreboardComboData array (if it's greater than a score, it moves onto the next element). If so, it moves all scores below the score it is less than or equal to down one element, essentially removing the last score and then places the new score within the element below the score it is less than or equal to. If the score is greater than all recorded scores, it moves all scores down one and inserts the new score within the first element. If it's the only score, it simply adds it to the first element. When a new score is added, the Name and Level data is also added to their relevant arrays, in the same way. What a tongue twister. Below is the AddScore method, I've added comments in the hope that it makes things clearer O_o. You can get the actual source file HERE. Below the method is an example of the quickest way to add a score to follow through with a debugger. public static void AddScore(string name, string level, int combo) { // If the scoreboard has not yet been filled, this adds another 'active' // array element each time a new score is added. The actual array size is // defined within PopulateScoreBoard() (set to 10 - for 'top 10' if (totalScores < scoreboardComboData.Length) totalScores++; // Does the scoreboard even need sorting? if (totalScores > 1) { for (int i = totalScores - 1; i > - 1; i--) { // Check to see if score (combo) is greater than score stored in // array if (combo > scoreboardComboData[i] && i != 0) { // If so continue to next element continue; } // Check to see if score (combo) is less or equal to element 'i' // score && that the element is not the last in the // array, if so the score does not need to be added to the scoreboard else if (combo <= scoreboardComboData[i] && i != scoreboardComboData.Length - 1) { // If the score is lower than element 'i' and greater than the last // element within the array, it needs to be added to the scoreboard. This is achieved // by moving each element under element 'i' down an element. The new score is then inserted // into the array under element 'i' for (int j = totalScores - 1; j > i; j--) { // Name and level data are moved down in their relevant arrays scoreboardTextData[0][j] = scoreboardTextData[0][j - 1]; scoreboardTextData[1][j] = scoreboardTextData[1][j - 1]; // Score (combo) data is moved down in relevant array scoreboardComboData[j] = scoreboardComboData[j - 1]; } // The new Name, level and score (combo) data is inserted into the relevant array under element 'i' scoreboardTextData[0][i + 1] = name; scoreboardTextData[1][i + 1] = level; scoreboardComboData[i + 1] = combo; break; } // If the method gets the this point, it means that the score is greater than all scores within // the array and therefore cannot be added in the above way. As it is not less than any score within // the array. else if (i == 0) { // All Names, levels and scores are moved down within their relevant arrays for (int j = totalScores - 1; j != 0; j--) { scoreboardTextData[0][j] = scoreboardTextData[0][j - 1]; scoreboardTextData[1][j] = scoreboardTextData[1][j - 1]; scoreboardComboData[j] = scoreboardComboData[j - 1]; } // The new number 1 top name, level and score, are added into the first element // within each of their relevant arrays. scoreboardTextData[0][0] = name; scoreboardTextData[1][0] = level; scoreboardComboData[0] = combo; break; } // If the methods get to this point, the combo score is not high enough // to be on the top10 score list and therefore needs to break break; } } // As totalScores < 1, the current score is the first to be added. Therefore no checks need to be made // and the Name, Level and combo data can be entered directly into the first element of their relevant // array. else { scoreboardTextData[0][0] = name; scoreboardTextData[1][0] = level; scoreboardComboData[0] = combo; } } } Example for adding score: private static void Initialize() { scoreboardDoc = new XmlDocument(); if (!File.Exists("Scoreboard.xml")) GenerateXML("Scoreboard.xml"); PopulateScoreBoard("Scoreboard.xml"); // ADD TEST SCORES HERE! AddScore("EXAMPLE", "10", 100); AddScore("EXAMPLE2", "24", 999); PopulateXML("Scoreboard.xml"); } In it's current state the source file is just used for testing, initialize is called within main and PopulateScoreBoard handles the majority of other initialising, so nothing else is needed, except to add a test score. I thank you for your time!

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• How to combine elements of a list

  - by Addie

  I'm working in c#. I have a sorted List of structures. The structure has a DateTime object which stores month and year and an integer which stores a value. The list is sorted by date. I need to traverse the list and combine it so that I only have one instance of the structure per date. For example: My initial list would look like this: { (Apr10, 3), (Apr10, 2), (Apr10, -3), (May10, 1), (May10, 1), (May10, -3), (Jun10, 3) } The resulting list should look like this: { (Apr10, 2), (May10, -1), (Jun10, 3) } I'm looking for a simple / efficient solution. The struct is: class CurrentTrade { public DateTime date; public int dwBuy; } The list is: private List<CurrentTrade> FillList

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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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• 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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• 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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• Finding unreachable sections of a 2D map

  - by dada

  I don't want you to solve this problem for me, i just want to ask for some ideas. This is the input below, and it represents a map. The 'x' represents land, and the dots - water. So with the 'x' you can represent 'islands' on the map. xxx.x...xxxxx xxxx....x...x ........x.x.x ..xxxxx.x...x ..x...x.xxx.x ..x.x.x...x.. ..x...x...xxx ...xxxxxx.... x............ As you can see, there are some islands which are closed, i.e. if some boat is inside its territory, it won't be able to get out, for ex: ..xxxxx. ..x...x. ..x.x.x. ..x...x. ..xxxxx. And there are some open islands which is possible to get out of them, ex: .xxxxx .x...x .x.x.x .xxx.x The problem is this: For a given NxM map like those above, calculate howm any of the islands are open, and how many are closed. I repeat: I don't want you to solve it, just need some sugestions, ideas for solving. thanks

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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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• Refining data stored in SQLite - how to join several contacts?

  - by Krab

  Problem background Imagine this problem. You have a water molecule which is in contact with other molecules (if the contact is a hydrogen bond, there can be 4 other molecules around my water). Like in the following picture (A, B, C, D are some other atoms and dots mean the contact). A B . . O / \ H H . . C D I have the information about all the dots and I need to eliminate the water in the center and create records describing contacts of A-C, A-D, A-B, B-C, B-D, and C-D. Database structure Currently, I have the following structure in the database: Table atoms: "id" integer PRIMARY KEY, "amino" char(3) NOT NULL, (HOH for water or other value) other columns identifying the atom Table contacts: "acceptor_id" integer NOT NULL, (the atom near to my hydrogen, here C or D) "donor_id" integer NOT NULL, (here A or B) "directness" char(1) NOT NULL, (this should be D for direct and W for water-mediated) other columns about the contact, such as the distance Current solution (insufficient) Now, I'm going through all the contacts which have donor.amino = "HOH". In this sample case, this would select contacts from C and D. For each of these selected contacts, I look up contacts having the same acceptor_id as is the donor_id in the currently selected contact. From this information, I create the new contact. At the end, I delete all contacts to or from HOH. This way, I am obviously unable to create C-D and A-B contacts (the other 4 are OK). If I try a similar approach - trying to find two contacts having the same donor_id, I end up with duplicate contacts (C-D and D-C). Is there a simple way to retrieve all six contacts without duplicates? I'm dreaming about some one page long SQL query which retrievs just these six wanted rows. :-) It is preferable to conserve information about who is donor where possible, but not strictly necessary. Big thanks to all of you who read this question to this point.

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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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• How to find nth element from the end of a singly linked list?

  - by Codenotguru

  The following function is trying to find the nth to last element of a singly linked list. For example: If the elements are 8->10->5->7->2->1->5->4->10->10 then the result is 7th to last node is 7. Can anybody help me on how this code is working or is there a better and simpler approach? LinkedListNode nthToLast(LinkedListNode head, int n) { if (head == null || n < 1) { return null; } LinkedListNode p1 = head; LinkedListNode p2 = head; for (int j = 0; j < n - 1; ++j) { // skip n-1 steps ahead if (p2 == null) { return null; // not found since list size < n } p2 = p2.next; } while (p2.next != null) { p1 = p1.next; p2 = p2.next; } return p1; }

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• curious ill conditioned numerical problem

  - by aaa

  hello. somebody today showed me this curious ill conditioned problem (apparently pretty famous), which looks relatively simple ƒ = (333.75 - a^2)b^6 + a^2 (11a^2 b^2 - 121b^4 - 2) + 5.5b^8 + a/(2^b) where a = 77617 and b = 33096 can you determine correct answer?

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• Refresh decorator

  - by Morgoth

  I'm trying to write a decorator that 'refreshes' after being called, but where the refreshing only occurs once after the last function exits. Here is an example: @auto_refresh def a(): print "In a" @auto_refresh def b(): print "In b" a() If a() is called, I want the refresh function to be run after exiting a(). If b() is called, I want the refresh function to be run after exiting b(), but not after a() when called by b(). Here is an example of a class that does this: class auto_refresh(object): def __init__(self, f): print "Initializing decorator" self.f = f def __call__(self, *args, **kwargs): print "Before function" if 'refresh' in kwargs: refresh = kwargs.pop('refresh') else: refresh = False self.f(*args, **kwargs) print "After function" if refresh: print "Refreshing" With this decorator, if I run b() print '---' b(refresh=True) print '---' b(refresh=False) I get the following output: Initializing decorator Initializing decorator Before function In b Before function In a After function After function --- Before function In b Before function In a After function After function Refreshing --- Before function In b Before function In a After function After function So when written this way, not specifying the refresh argument means that refresh is defaulted to False. Can anyone think of a way to change this so that refresh is True when not specified? Changing the refresh = False to refresh = True in the decorator does not work: Initializing decorator Initializing decorator Before function In b Before function In a After function Refreshing After function Refreshing --- Before function In b Before function In a After function Refreshing After function Refreshing --- Before function In b Before function In a After function Refreshing After function because refresh then gets called multiple times in the first and second case, and once in the last case (when it should be once in the first and second case, and not in the last case).

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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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• 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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• Grouping rectangles (getting the bounding boxes of rects)

  - by hyn

  What is a good, fast way to get the "final" bounding boxes of a set of random (up to about 40, not many) rectangles? By final I mean that all bounding boxes don't intersect with any other. Brute force way: in a double for loop, for each rect, test for intersection against every other rect. The intersecting rects become a new rect (replaced), indicating the bounding box. Start over and repeat until no intersection is detected. Because the rects are random every time, and the rect count is relatively small, collision detection using spatial hashing seems like overkill. Is there a way to do this more effectively?

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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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• 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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• 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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• 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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• red black tree balancing?

  - by Anirudh Kaki

  i am working to generate tango tree, where i need to check whether every sub tree in tango is balanced or not. if its not balanced i need to make it balance? I trying so hard to make entire RB-tree balance but i not getting any proper logic so can any one help me out?? here i am adding code to check how to find my tree is balanced are not but when its not balanced how can i make it balance. static boolean verifyProperty5(rbnode n) { int left = 0, right = 0; if (n != null) { bh++; left = blackHeight(n.left, 0); right = blackHeight(n.right, 0); } if (left == right) { System.out.println("black height is :: " + bh); return true; } else { System.out.println("in balance"); return false; } } public static int blackHeight(rbnode root, int len) { bh = 0; blackHeight(root, path1, len); return bh; } private static void blackHeight(rbnode root, int path1[], int len) { if (root == null) return; if (root.color == "black"){ root.black_count = root.parent.black_count+1; } else{ root.black_count = root.parent.black_count; } if ((root.left == null) && (root.right == null)) { bh = root.black_count; } blackHeight(root.left, path1, len); blackHeight(root.right, path1, len); }

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• All words in a trie data-structure

  - by John Smith

  I'm trying to put all words in a trie in a string, a word is detonated by the eow field being true for a certain character in the trie data structure, hence a trie can could have letters than lead up to no word, for ex "abc" is in the trie but "c"'s eow field is false so "abc" is not a word Here is my Data structure struct Trie { bool eow; //when a Trie field isWord = true, hence there is a word char letter; Trie *letters[27]; }; and here is my attemped print-all function, basically trying to return all words in one string seperated by spaces for words string printAll( string word, Trie& data) { if (data.eow == 1) return word + " "; for (int i = 0; i < 26; i++) { if (data.letters[i] != NULL) printAll( word + data.letters[i]->letter, *(data.letters[i])); } return ""; } Its not outputting what i want, any suggestions?

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• Problem implementing sorting algorithm in C with an array of structs

  - by dilog

  Well here is my little problem, first my code: struct alumn { char name[100]; char lastname[100]; int par; int nota; }; typedef struct alumn alumn; int bubble(alumn **arr, int length) { int i,j; alumn *temp; for (i=0; i<=length-2; i++) { for (j=i+1; j<=length-1;j++) { if ((*arr)[i].nota > (*arr)[j].nota) { temp = arr[i]; arr[i] = arr[j]; arr[j] = temp; } } } } int main(int argc, char **argv) { alumn *alumns; ... here goes some other code ... bubble(&alumns,totalAlumns); return 0; } My problem is that this algorith is not sorting anything. I'm having a hard time doing the swap, i tried everything but nothing works :( . Any help??? struct alumn { char name[100]; char lastname[100]; int par; int nota; }; typedef struct alumn alumn; int bubble(alumn **arr, int length) { int i,j; alumn *temp; for (i=0; i<=length-2; i++) { for (j=i+1; j<=length-1;j++) { if ((*arr)[i].nota > (*arr)[j].nota) { temp = arr[i]; arr[i] = arr[j]; arr[j] = temp; } } } } int main(int argc, char **argv) { alumn *alumns; ... here goes some other code ... bubble(&alumns,totalAlumns); return 0; } My problem is that this algorith is not sorting anything. I'm having a hard time doing the swap, i tried everything but nothing works :( . Any help???

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• Zoom image to pixel level

  - by zaf

  For an art project, one of the things I'll be doing is zooming in on an image to a particular pixel. I've been rubbing my chin and would love some advice on how to proceed. Here are the input parameters: Screen: sw - screen width sh - screen height Image: iw - image width ih - image height Pixel: px - x position of pixel in image py - y position of pixel in image Zoom: zf - zoom factor (0.0 to 1.0) Background colour: bc - background colour to use when screen and image aspect ratios are different Outputs: The zoomed image (no anti-aliasing) The screen position/dimensions of the pixel we are zooming to. When zf is 0 the image must fit the screen with correct aspect ratio. When zf is 1 the selected pixel fits the screen with correct aspect ratio. One idea I had was to use something like povray and move the camera towards a big image texture or some library (e.g. pygame) to do the zooming. Anyone think of something more clever with simple pseudo code? To keep it more simple you can make the image and screen have the same aspect ratio. I can live with that. I'll update with more info as its required.

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