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• Implementing a horizontal compass on the iPhone - algorithm?

  - by Andrew Johnson

  A horizontal compass looks something like this if you are facing due East (90 degrees). 85----90---95 If you were facing due 355 degrees northwest, it would look like this: 350----355---0 As you turn the compass, the number should cycle from 0 - 360 - 0 So, my question is, how would you implement a view like this on the iPhone? I had a couple of ideas: Make one long image with all numbers and tick marks, and shift it left/right when the compass heading changes Create pieces of the view as tiles and append them when the compass heading changes. Create a line of tick marks that shifts with the compass heading, and just write numbers on it as needed. How would you attack this problem? Im mainly looking for algorithmic advice, but if you ave code or pseudo-code to demonstrate, that would be helpful too.

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• given two bits in a set of four, fine position of two other bits

  - by aaa

  hello I am working on a simple combinatorics part, and found that I need to recover position of two bits given position of other two bits in 4-bits srring. for example, (0,1) maps to (2,3), (0,2) to (1,3), etc. for a total of six combinations. My solution is to test bits using four nested ternary operators: ab is a four bit string, with two bits set. c = ((((ab & 1) ? (((ab & 2) ? ... ))) : 0) abc = ab | c recover the last bit in the same fashion from abc. can you think of a better way/more clever way? thanks

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• Encoding / Error Correction Challenge

  - by emi1faber

  Is it mathematically feasible to encode and initial 4 byte message into 8 bytes and if one of the 8 bytes is completely dropped and another is wrong to reconstruct the initial 4 byte message? There would be no way to retransmit nor would the location of the dropped byte be known. If one uses Reed Solomon error correction with 4 "parity" bytes tacked on to the end of the 4 "data" bytes, such as DDDDPPPP, and you end up with DDDEPPP (where E is an error) and a parity byte has been dropped, I don't believe there's a way to reconstruct the initial message (although correct me if I am wrong)... What about multiplying (or performing another mathematical operation) the initial 4 byte message by a constant, then utilizing properties of an inverse mathematical operation to determine what byte was dropped. Or, impose some constraints on the structure of the message so every other byte needs to be odd and the others need to be even. Alternatively, instead of bytes, it could also be 4 decimal digits encoded in some fashion into 8 decimal digits where errors could be detected & corrected under the same circumstances mentioned above - no retransmission and the location of the dropped byte is not known. I'm looking for any crazy ideas anyone might have... Any ideas out there?

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• Heuristic to identify if a series of 4 bytes chunks of data are integers or floats

  - by flint

  What's the best heuristic I can use to identify whether a chunk of X 4-bytes are integers or floats? A human can do this easily, but I wanted to do it programmatically. I realize that since every combination of bits will result in a valid integer and (almost?) all of them will also result in a valid float, there is no way to know for sure. But I still would like to identify the most likely candidate (which will virtually always be correct; or at least, a human can do it). For example, let's take a series of 4-bytes raw data and print them as integers first and then as floats: 1 1.4013e-45 10 1.4013e-44 44 6.16571e-44 5000 7.00649e-42 1024 1.43493e-42 0 0 0 0 -5 -nan 11 1.54143e-44 Obviously they will be integers. Now, another example: 1065353216 1 1084227584 5 1085276160 5.5 1068149391 1.33333 1083179008 4.5 1120403456 100 0 0 -1110651699 -0.1 1195593728 50000 These will obviously be floats. PS: I'm using C++ but you can answer in any language, pseudo code or just in english.

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• Effects of changing a node in a binary tree

  - by eSKay

  Suppose I want to change the orange node in the following tree. So, the only other change I'll need to make is in the left pointer of the green node. The blue node will remain the same. Am I wrong somewhere? Because according to this article (that explains zippers), even the blue node needs to be changed. Similarly, in this picture (recolored) from the same article, why do we change the orange nodes at all (when we change x)?

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• MD5 algorithm in Objective C

  - by Biranchi

  How to calculate the MD5 in objective C ?

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• PostgreSQL: Auto-partition a table

  - by Adam Matan

  Hi, I have a huge database which holds pairs of numbers (A,B), each ranging from 0 to 10,000 and stored as floats. e.g., (1, 9984.4), (2143.44, 124.243), (0.55, 0), ... Since the PostgreSQL table which stores these pairs grew quite large, I have decided to partition it into inheriting sub-tables. I intend to create 100 such tables, each storing a range of 1000x1000. The problem is that these numbers tend to come in large chunks of nearby numbers. It means that in the future, some tables will be nearly empty and some will hold a very large portion of the database. Unfortunately, the distribution of future pairs is yet unknown. I am looking for a way to automatically repartition my table. That means that if a certain subtable holds more than a specific number of pairs, it will be automatically partitioned into four sub-sub tables, and so on. My questions are: Is recursive partitioning and inheritance possible in PostgreSQL 8.3? Will indexes and query plans understand it? What's the best way to split a subtable once it grew too large? I should point out that this isn't a live database, so a downtime of few hours every week is totally acceptable. Thanks in advance, Adam

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• Convert latitude and longitude into northings and eastings

  - by Rippo

  Hi I have the following UK postcode dy8 3xt and know that the latitude and longitude is:- 54.452772 -2.156082 I also know that the Eastings, Northings for the postcode is:- 389490 283880 However I am struggling to find the equation that converts lat/long to northings and Eastings, I would prefer to have the equation in both in jScript and c# (I am being greedy)! Can anyone help? EDIT Thanks for your help so far guys, I am starting to learn something here esp. the terminology... Some more info, if you click on this link you can see the results I am looking for. The postcode I entered projects to lat/lng using WG S84 and the grid ref projects to OSGB. So my question is how is this done? WHAT I LEARNT Thanks to all that answered, I finally got led to here which I can confirm works great

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• How do bezier handles work?

  - by user146780

  On Wikipedia I found information about bezier curves and made a function to generate the inbetween points for a bezier polygon. I noticed that Expression Design uses bezier handles. This allows a circle to be made with 4 points each with a bezier handle. I'm just not sure mathematically how this works in relation with the formula for bezier point at time T. How do these handle vectors work to modify the shape? Basically what's there relation to the bezier formula? Thanks

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• Matplotlib canvas drawing

  - by Morgoth

  Let's say I define a few functions to do certain matplotlib actions, such as def dostuff(ax): ax.scatter([0.],[0.]) Now if I launch ipython, I can load these functions and start a new figure: In [1]: import matplotlib.pyplot as mpl In [2]: fig = mpl.figure() In [3]: ax = fig.add_subplot(1,1,1) In [4]: run functions # run the file with the above defined function If I now call dostuff, then the figure does not refresh: In [6]: dostuff(ax) I have to then explicitly run: In [7]: fig.canvas.draw() To get the canvas to draw. Now I can modify dostuff to be def dostuff(ax): ax.scatter([0.],[0.]) ax.get_figure().canvas.draw() This re-draws the canvas automatically. But now, say that I have the following code: def dostuff1(ax): ax.scatter([0.],[0.]) ax.get_figure().canvas.draw() def dostuff2(ax): ax.scatter([1.],[1.]) ax.get_figure().canvas.draw() def doboth(ax): dostuff1(ax) dostuff2(ax) ax.get_figure().canvas.draw() I can call each of these functions, and the canvas will be redrawn, but in the case of doboth(), it will get redrawn multiple times. My question is: how could I code this, such that the canvas.draw() only gets called once? In the above example it won't change much, but in more complex cases with tens of functions that can be called individually or grouped, the repeated drawing is much more obvious, and it would be nice to be able to avoid it. I thought of using decorators, but it doesn't look as though it would be simple. Any ideas?

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• Tiered Design With Analytical Widgets - Is This Code Smell?

  - by Repo Man

  The idea I'm playing with right now is having a multi-leveled "tier" system of analytical objects which perform a certain computation on a common object and then create a new set of analytical objects depending on their outcome. The newly created analytical objects will then get their own turn to run and optionally create more analytical objects, and so on and so on. The point being that the child analytical objects will always execute after the objects that created them, which is relatively important. The whole apparatus will be called by a single thread so I'm not concerned with thread safety at the moment. As long as a certain base condition is met, I don't see this being an unstable design but I'm still a little bit queasy about it. Is this some serious code smell or should I go ahead and implement it this way? Is there a better way? Here is a sample implementation: namespace WidgetTier { public class Widget { private string _name; public string Name { get { return _name; } } private TierManager _tm; private static readonly Random random = new Random(); static Widget() { } public Widget(string name, TierManager tm) { _name = name; _tm = tm; } public void DoMyThing() { if (random.Next(1000) > 1) { _tm.Add(); } } } //NOT thread-safe! public class TierManager { private Dictionary<int, List<Widget>> _tiers; private int _tierCount = 0; private int _currentTier = -1; private int _childCount = 0; public TierManager() { _tiers = new Dictionary<int, List<Widget>>(); } public void Add() { if (_currentTier + 1 >= _tierCount) { _tierCount++; _tiers.Add(_currentTier + 1, new List<Widget>()); } _tiers[_currentTier + 1].Add(new Widget(string.Format("({0})", _childCount), this)); _childCount++; } //Dangerous? public void Sweep() { _currentTier = 0; while (_currentTier < _tierCount) //_tierCount will start at 1 but keep increasing because child objects will keep adding more tiers. { foreach (Widget w in _tiers[_currentTier]) { w.DoMyThing(); } _currentTier++; } } public void PrintAll() { for (int t = 0; t < _tierCount; t++) { Console.Write("Tier #{0}: ", t); foreach (Widget w in _tiers[t]) { Console.Write(w.Name + " "); } Console.WriteLine(); } } } class Program { static void Main(string[] args) { TierManager tm = new TierManager(); for (int c = 0; c < 10; c++) { tm.Add(); //create base widgets; } tm.Sweep(); tm.PrintAll(); Console.ReadLine(); } } }

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• CodeGolf: Brothers

  - by John McClane

  Hi guys, I just finished participating in the 2009 ACM ICPC Programming Conest in the Latinamerican Finals. These questions were for Brazil, Bolivia, Chile, etc. My team and I could only finish two questions out of the eleven (not bad I think for the first try). Here's one we could finish. I'm curious to seeing any variations to the code. The question in full: ps: These questions can also be found on the official ICPC website available to everyone. In the land of ACM ruled a greeat king who became obsessed with order. The kingdom had a rectangular form, and the king divided the territory into a grid of small rectangular counties. Before dying the king distributed the counties among his sons. The king was unaware of the rivalries between his sons: The first heir hated the second but not the rest, the second hated the third but not the rest, and so on...Finally, the last heir hated the first heir, but not the other heirs. As soon as the king died, the strange rivaly among the King's sons sparked off a generalized war in the kingdom. Attacks only took place between pairs of adjacent counties (adjacent counties are those that share one vertical or horizontal border). A county X attacked an adjacent county Y whenever X hated Y. The attacked county was always conquered. All attacks where carried out simultanously and a set of simultanous attacks was called a battle. After a certain number of battles, the surviving sons made a truce and never battled again. For example if the king had three sons, named 0, 1 and 2, the figure below shows what happens in the first battle for a given initial land distribution: INPUT The input contains several test cases. The first line of a test case contains four integers, N, R, C and K. N - The number of heirs (2 <= N <= 100) R and C - The dimensions of the land. (2 <= R,C <= 100) K - Number of battles that are going to take place. (1 <= K <= 100) Heirs are identified by sequential integers starting from zero. Each of the next R lines contains C integers HeirIdentificationNumber (saying what heir owns this land) separated by single spaces. This is to layout the initial land. The last test case is a line separated by four zeroes separated by single spaces. (To exit the program so to speak) Output For each test case your program must print R lines with C integers each, separated by single spaces in the same format as the input, representing the land distribution after all battles. Sample Input: Sample Output: 3 4 4 3 2 2 2 0 0 1 2 0 2 1 0 1 1 0 2 0 2 2 2 0 0 1 2 0 0 2 0 0 0 1 2 2 Another example: Sample Input: Sample Output: 4 2 3 4 1 0 3 1 0 3 2 1 2 2 1 2

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• polynomial multiplication using fastfourier transform

  - by mawia

  i am going through the above topic from CLRS(CORMEN) (page 834) and I got stuck at this point. Can anybody please explain how the following expression, A(x)=A^{[0]}(x^2) +xA^{[1]}(x^2) follows from, n-1 ` S a_j x^j j=0 Where, A^{[0]} = a_0 + a_2x + a_4a^x ... a_{n-2}x^{\frac{n}{2-1}} A^{[1]} = a_1 + a_3x + a_5a^x ... a_{n-1}x^{\frac{n}{2-1}} WITH REGARDS THANKS

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• Anyone got a nifty credit expiry algorithm?

  - by garethkeenan

  Our website uses a credit system to allow users to purchase inexpensive digital goods (eg. photos). We use credits, rather than asking the user to pay for items individually, because the items are cheap and we are trying to keep our credit-card/PayPal overhead low. Because we aren't a bank, we have to expire credits after a certain amount of time. We expire deposit credits after a year, but other types of credits (bonuses, prizes, refunds) may have a different shelf-life. When a buyer buys an item, we spend the credit that is going to expire first. Our current system keeps track of every deposit by storing the original value and the remainder to be spent. We keep a list of all purchases as well, of course. I am currently moving to a system which is much more like a traditional double-entry accounting system. A deposit will create a ledger item, increasing the user's 'spending' account balance. Every purchase will also create a ledger item, decreasing the user's 'spending' account balance. The new system has running balances, while the old system does not, which greatly improves our ability to find problems and do reconciliations. We do not want to use the old system of keeping a 'remainder' value attached to each deposit record because it is inefficient to replay a user's activities to calculate what the remainder of each deposit is over time (for the user's statement). So, after all of this verbose introduction, my question is "Does anyone else out there have a similar system of expiring credits?" If you could describe how you calculate expired credits it would be a great help. If all expired credits had the exact same shelf life, we would be able to calculate the expired amount using: Total Deposits - Total Spending - Deposits Not Due To Expire = Amount to Expire However, because deposits can have different shelf lives, this formula does not work because more than one deposit can be partially spent at any given time.

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• Binary Heap Traversal Proof by Induction

  - by Ahmet Alp Balkan

  How to prove that: Let's say we have two binary heap trees H1 and H2 with size N. If their inorder traversals are the same, prove that H1=H2 by induction on N.

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• Minimal-change algorithm which maximises 'swapping'

  - by Kim Bastin

  This is a question on combinatorics from a non-mathematician, so please try to bear with me! Given an array of n distinct characters, I want to generate subsets of k characters in a minimal-change order, i.e. an order in which generation n+1 contains exactly one character that was not in generation n. That's not too hard in itself. However, I also want to maximise the number of cases in which the character that is swapped out in generation n+1 is the same character that was swapped in in generation n. To illustrate, for n=7, k=3: abc abd abe* abf* abg* afg aeg* adg* acg* acd ace* acf* aef adf* ade bde bdf bef bcf* bce bcd* bcg* bdg beg* bfg* cfg ceg* cdg* cde cdf* cef def deg dfg efg The asterisked strings indicate the case I want to maximise; e.g. the e that is new in generation 3, abe, replaces a d that was new in generation 2, abd. It doesn't seem possible to have this happen in every generation, but I want it to happen as often as possible. Typical array sizes that I use are 20-30 and subset sizes around 5-8. I'm using an odd language, Icon (or actually its derivative Unicon), so I don't expect anyone to post code that I can used directly. But I will be grateful for answers or hints in pseudo-code, and will do my best to translate C etc. Also, I have noticed that problems of this kind are often discussed in terms of arrays of integers, and I can certainly apply solutions posted in such terms to my own problem. Thanks Kim Bastin

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• array interleaving problem

  - by Matt

  I was looking for something over the web when I came across this question. Have no idea of how to solve it. Help me out please. Suppose we have an array a1,a2,... ,an, b1,b2,..., bn How to change this array to a1,b1,a2,b2, ..., an,bn in O(n) time and in O(1) space.

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• how is google Calculator implemented ?

  - by AlgoMan

  When you search in Google "100F to C" how does it know to convert from Fahrenheit to Celsius. Similarly, conversion from different currencies and simple calculation. What is the data structure used. Or is it simple pattern matching the strings ?

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• good books on numerical computation with C

  - by yCalleecharan

  Hi, I've read the post "What is the best book on numerical methods?" and I wish to ask more or less the same question but in relation to C programming. Most of the time, C programming books on numerical methods are just another version of the author's previous Fortran book on the same subject. I've seen Applied numerical methods in C by Nakamura, Shoichiro and the C codes are not good programming practice. I've heard bad comments about Numerical Recipes by Press. Do you know good books on C that discusses numerical methods. It's seem better for me to ask about good books on C discussing numerical methods than rather asking books on numerical methods that discusses C. I've heard about Numerical Algorithms with C by Giesela Engeln-Müllges and A Numerical Library in C for Scientists and Engineers bu Lau but haven't read them. Good books will always have algorithms implemented in the programming language in a smart way. Thanks a lot...

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• Simple Fundamental Algorithm Question, binary tree traversal

  - by Ben

  I'm trying to explain to non-computer science major student with many questions. (1)What traverses tree? Is it just logic or actual on off switch generates 1s and 0s traveling the circuit board? where is this tree and node exists CPU/Memory in between? (2)If it is 1s and 0s HOW the circuits understand the line for example p=p.getLeft(); I said search the google or wiki.

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• Finding distance to the closest point in a point cloud on an uniform grid

  - by erik

  I have a 3D grid of size AxBxC with equal distance, d, between the points in the grid. Given a number of points, what is the best way of finding the distance to the closest point for each grid point (Every grid point should contain the distance to the closest point in the point cloud) given the assumptions below? Assume that A, B and C are quite big in relation to d, giving a grid of maybe 500x500x500 and that there will be around 1 million points. Also assume that if the distance to the nearest point exceds a distance of D, we do not care about the nearest point distance, and it can safely be set to some large number (D is maybe 2 to 10 times d) Since there will be a great number of grid points and points to search from, a simple exhaustive: for each grid point: for each point: if distance between points < minDistance: minDistance = distance between points is not a good alternative. I was thinking of doing something along the lines of: create a container of size A*B*C where each element holds a container of points for each point: define indexX = round((point position x - grid min position x)/d) // same for y and z add the point to the correct index of the container for each grid point: search the container of that grid point and find the closest point if no points in container and D > 0.5d: search the 26 container indices nearest to the grid point for a closest point .. continue with next layer until a point is found or the distance to that layer is greater than D Basically: put the points in buckets and do a radial search outwards until a points is found for each grid point. Is this a good way of solving the problem, or are there better/faster ways? A solution which is good for parallelisation is preferred.

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• longest string in texts

  - by davit-datuashvili

  ok i have meet following problem too for example there is given two text find longest string that occur in both i think we should cretate string array where we should put common srings and then compare their length and which length will be largest print it is there fast method?

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• longest string in texts

  - by davit-datuashvili

  Ihave following code in Java: import java.util.*; public class longest{ public static void main(String[] args){ int t=0;int m=0;int token1, token2; String words[]=new String[10]; String word[]=new String[10]; String common[]=new String[10]; String text="saqartvelo gabrwyindeba da gadzlierdeba aucileblad "; String text1="saqartvelo gamtliandeba da gadzlierdeba aucileblad"; StringTokenizer st=new StringTokenizer(text); StringTokenizer st1=new StringTokenizer(text1); token1=st.countTokens(); token2=st1.countTokens(); while (st.hasMoreTokens()){ words[t]=st.nextToken(); t++; } while (st1.hasMoreTokens()){ word[m]=st1.nextToken(); m++; } for (int k=0;k<token1;k++){ for (int f=0;f<token2;f++){ if (words[f].compareTo(word[f])==0){ common[f]=words[f]; } } } while (i<common.length){ System.out.println(common[i]); i++; } } } I want that in common array put elements which i in both text or these words saqartvelo (georgia in english) da (and in english) gadzlierdeba (will be stronger) aucileblad (sure) and then between these words find string which has maximum length but it does not work more correctly it show me these words and also many null elements. How do I correct it?

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• Mergesort : Revision

  - by stan

  Does merge sort work by; taking a list of values splitting it in to two take the first element of each list, the lowest value one goes in to a new list(and i guess removed from the original). comare the next two numbers - do this until one list is empty, then place the rest of the other list at the end ofthe nw list? Also, what are the ramifications of doing this on a linked list? Thanks

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• What are the CS fundamentals behind package/dependency management?

  - by Frep D-Oronge

  Often I hear about situations where companies are developing extensable in house software (the dreaded enterprise 'framework') which is supposed to support multiple 'plugins' from diffirent teams. Usually this ends up being a half baked solution that does not really work due to compatibility prolems between addins, or between addins and the framework itself. Usually this means QA have to 'rubber stamp' a global set of versions accross all plugins, or more usually plugins are released and stuff breaks in nasty ways. This problem has been solved before however, for example the package management systems like apt for debian linux. I suspect that the reason it works is that it is built from the start on a known 'Computer Science-y' concept. My question is what is it?

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