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  • What programming concept is used in Nokia Lumina City Lens application [closed]

    - by gowri
    I am totally impressed about the Nokia City Lens application. How does the Nokia Lumia City Lens app work? Nokia Lumia City Lens app detects shops, restaurants, etc. by scanning the visual environment. But how can it detect shops or anything by only scanning visual information? Because we need a 360 degree view to detect a location. Because we can't simply match visual information and get that data. The visuals will change proportionally with distance and angle. So how does this app match the location and retrieve the information? Can anyone explain the concept What technology or algorithm is used in this app?

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  • How to solve linear recurrences involving two functions?

    - by Aditya Bahuguna
    Actually I came across a question in Dynamic Programming where we need to find the number of ways to tile a 2 X N area with tiles of given dimensions.. Here is the problem statement Now after a bit of recurrence solving I came out with these. F(n) = F(n-1) + F(n-2) + 2G(n-1), and G(n) = G(n-1) + F(n-1) I know how to solve LR model where one function is there.For large N as is the case in the above problem we can do the matrix exponentiation and achieve O(k^3log(N)) time where k is the minimum number such that for all km F(n) does not depend on F(n-k). The method of solving linear recurrence with matrix exponentiation as it is given in that blog. Now for the LR involving two functions can anyone suggest an approach feasible enough for large N.

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  • "Bad apple" algorithm, or process crashes shared sandbox

    - by Roger Lipscombe
    I'm looking for an algorithm to handle the following problem, which I'm (for now) calling the "bad apple" algorithm. The problem I've got a N processes running in M sandboxes, where N M. It's impractical to give each process its own sandbox. At least one of those processes is badly-behaved, and is bringing down the entire sandbox, thus killing all of the other processes. If it was a single badly-behaved process, then I could use a simple bisection to put half of the processes in one sandbox, and half in another sandbox, until I found the miscreant. This could probably be extended by partitioning the set into more than two pieces until the badly-behaved process was found. For example, partitioning into 8 sets allows me to eliminate 7/8 of the search space at each step, and so on. The question If more than one process is badly-behaved -- including the possibility that they're all badly-behaved -- does this naive algorithm "work"? Is it guaranteed to work within some sensible bounds?

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  • How does one unit test an algorithm

    - by Asa Baylus
    I was recently working on a JS slideshow which rotates images using a weighted average algorithm. Thankfully, timgilbert has written a weighted list script which implements the exact algorithm I needed. However in his documentation he's noted under todos: "unit tests!". I'd like to know is how one goes about unit testing an algorithm. In the case of a weighted average how would you create a proof that the averages are accurate when there is the element of randomness? Code samples of similar would be very helpful to my understanding.

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  • Is there a phrase or word to describe an algorithim or programme is complete in that given any value for its arguments there is a predictable outcome?

    - by Mrk Mnl
    Is there a phrase to describe an algorithim or programme is complete in that given any possible value for its arguments there is a predicatable outcome? i.e. all the ramifications have been considered whatever the context? A simple example would be the below function: function returns string get_item_type(int type_no) { if(type_no < 10) return "hockey stick" else if (type_no < 20) return "bulldozer" else return "unknown" } (excuse the dismal pseudo code) No matter what number is supplied all possibiblites are catered for. My question is: is there a word to fill the blank here: "get_item_type() is ______ complete" ? (The answer is not Turing Complete - that is something quite different - but I annoyingly always think of something as "Turing Complete" when I am thinking of the above).

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  • When module calling gets ugly

    - by Pete
    Has this ever happened to you? You've got a suite of well designed, single-responsibility modules, covered by unit tests. In any higher-level function you code, you are (95% of the code) simply taking output from one module and passing it as input to the next. Then, you notice this higher-level function has turned into a 100+ line script with multiple responsibilities. Here is the problem. It is difficult (impossible) to test that script. At least, it seems so. Do you agree? In my current project, all of the bugs came from this script. Further detail: each script represents a unique solution, or algorithm, formed by using different modules in different ways. Question: how can you remedy this situation? Knee-jerk answer: break the script up into single-responsibility modules. Comment on knee-jerk answer: it already is! Best answer I can come up with so far: create higher-level connector objects which "wire" modules together in particular ways (take output from one module, feed it as input to another module). Thus if our script was: FooInput fooIn = new FooInput(1, 2); FooOutput fooOutput = fooModule(fooIn); Double runtimevalue = getsomething(fooOutput.whatever); BarInput barIn = new BarInput( runtimevalue, fooOutput.someOtherValue); BarOutput barOut = barModule(BarIn); It would become with a connector: FooBarConnectionAlgo fooBarConnector = new fooBarConnector(fooModule, barModule); FooInput fooIn = new FooInput(1, 2); BarOutput barOut = fooBarConnector(fooIn); So the advantage is, besides hiding some code and making things clearer, we can test FooBarConnectionAlgo. I'm sure this situation comes up a lot. What do you do?

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  • Can a candidate be judged by asking to write a complex program on "paper"?

    - by iammilind
    Sometime back in an interview, I was asked to write following program: In a keypad of a mobile phone, there is a mapping between number and characters. e.g. 0 & 1 corresponds to nothing; 2 corresponds to 'a','b','c'; 3 corresponds to 'd','e','f'; ...; 9 corresponds to 'w','x','y','z'. User should input any number (e.g. 23, 389423, 927348923747293) and I should store all the combinations of these character mapping into some data structure. For example, if user enters "23" then possible character combinations are: ad, ae, af, bd, be, bf, cd, ce, cf or if user enters, "4676972" then it can be, gmpmwpa, gmpmwpb, ..., hnroxrc, ..., iosozrc Interviewer told that people have written code for this within 20-30 mins!! Also he insisted I have to write on paper. If I am writing a code then my tendency is as of I am writing production code, even though it may not be expected from me. So, I always try to think all the aspects like, optimization, readability, maintainability, extensible and so on. Considering all these, I felt that I should be writing on PC and it needs decent 2 hours. Finally after 25 mins, I was able to come up with just the concept and some shattered pieces of code (not to mention of my rejection). My question is not the answer for the above program. I want to know that is this a right way to judge the caliber of a person ? Am I wrong / too slow in the estimates ? Am I too idealistic ?

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  • One dimensional cutting algorithm with minimum waste

    - by jm666
    Can anybody point me to some resources about "cutting algorithm"? The problem: have rods with length of L meters, e.g. 6 m need cut smaller pieces of different lengths, e.g. need: 4 x 1.2m 8 x 0,9m etc... (many other lengths and counts) How to determine the optimal cutting, what will produce the minimum wasted material? I'm capable write an perl program, but haven't any idea about the algorithm. (if here is already some CPAN module what can help, would be nice). Alternatively, if someone can point me to some "spreadsheet" solution, or to anything what helps. Ps: in addition, need care about the "cutting line width" too, whats means than from the 6m long rod is impossible to cut 6 x 1m, because the cutting itself takes "3mm" width, so it is possible cut only 5 x 1m and the last piece will be only 98.5 cm (1m minus 5 x 3mm cut-width) ;(.

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  • questions on a particular algorithm

    - by paul smith
    Upon searching for a fast primr algorithm, I stumbled upon this: public static boolean isP(long n) { if (n==2 || n==3) return true; if ((n&0x1)==0 || n%3==0 || n<2) return false; long root=(long)Math.sqrt(n)+1L; // we check just numbers of the form 6*k+1 and 6*k-1 for (long k=6;k<=root;k+=6) { if (n%(k-1)==0) return false; if (n%(k+1)==0) return false; } return true; } My questions are: Why is long being used everywhere instead of int? Because with a long type the argument could be much larger than Integer.MAX thus making the method more flexible? In the second 'if', is n&0x1 the same as n%2? If so why didn't the author just use n%2? To me it's more readable. The line that sets the 'root' variable, why add the 1L? What is the run-time complexity? Is it O(sqrt(n/6)) or O(sqrt(n)/6)? Or would we just say O(n)?

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  • Tournament bracket method to put distance between teammates

    - by Fred Thomsen
    I am using a proper binary tree to simulate a tournament bracket. It's preferred any competitors in the bracket that are teammates don't meet each other until the later rounds. What is an efficient method in which I can ensure that teammates in the bracket have as much distance as possible from each other? Are there any other data structures besides a tree that would be better for this purpose? EDIT: There can be more than 2 teams represented in a bracket.

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  • How to avoid or minimise use of check/conditional statement in my scenario?

    - by Muneeb Nasir
    I have scenario, where I got stream and I need to check for some value. If I got any new value I have to store it in any of data structure. It seems very easy, I can place conditional statement if-else or can use contain method of set/map to check either received is new or not. But the problem is checking will effect my application performance, in stream I will receive hundreds for value in second, if I start checking each and every value I received then for sure it effect performance. Anybody can suggest me any mechanism or algorithm to solve my issue, either by bypassing checks or at least minimize them?

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  • Conflict resolution for two-way sync

    - by K.Steff
    How do you manage two-way synchronization between a 'main' database server and many 'secondary' servers, in particular conflict resolution, assuming a connection is not always available? For example, I have an mobile app that uses CoreData as the 'database' on the iOS and I'd like to allow users to edit the contents without Internet connection. In the same time, this information is available on a website the devices will connect to. What do I do if/when the data on the two DB servers is in conflict? (I refer to CoreData as a DB server, though I am aware it is something slightly different.) Are there any general strategies for dealing with this sort of issue? These are the options I can think of: 1. Always use the client-side data as higher-priority 2. Same for server-side 3. Try to resolve conflicts by marking each field's edit timestamp and taking the latest edit Though I'm certain the 3rd option will open room for some devastating data corruption. I'm aware that the CAP theorem concerns this, but I only want eventual consistency, so it doesn't rule it out completely, right? Related question: Best practice patterns for two-way data synchronization. The second answer to this question says it probably can't be done.

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  • algorithm for Virtual Machine(VM) Consolidation in Cloud

    - by devansh dalal
    PROBLEM: We have N physical machines(PMs) each with ram Ri, cpu Ci and a set of currently scheduled VMs each with ram requirement ri and ci respectively Moving(Migrating) any VM from one PM to other has a cost associated which depends on its ram ri. A PM with no VMs is shut down to save power. Our target is to minimize the weighted sum of (N,migration cost) by migrating some VMs i.e. minimize the number of working PMs as well as not to degrade the service level due to excessive migrations. My Approach: Brute Force approach is choosing the minimum loaded PM and try to fit its VMs to other PMs by First Fit Decreasing algorithm or we can select the victim PMs and target PMs based on their loading level and shut down victims if possible by moving their VMs to targets. I tried this Greedy approach on the Data of Baadal(IIT-D cloud) but It isn't giving promising results. I have also tried to study the Ant colony optimization for dynamic VM consolidating but was unable to understand very much. I used the links. http://dumas.ccsd.cnrs.fr/docs/00/72/52/15/PDF/Esnault.pdf http://hal.archives-ouvertes.fr/docs/00/72/38/56/PDF/RR-8032.pdf Would anyone please explain the solution or suggest any new approach for better performance soon. Thanks in advance.

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  • Need help on a problemset in a programming contest

    - by topher
    I've attended a local programming contest on my country. The name of the contest is "ACM-ICPC Indonesia National Contest 2013". The contest has ended on 2013-10-13 15:00:00 (GMT +7) and I am still curious about one of the problems. You can find the original version of the problem here. Brief Problem Explanation: There are a set of "jobs" (tasks) that should be performed on several "servers" (computers). Each job should be executed strictly from start time Si to end time Ei Each server can only perform one task at a time. (The complicated thing goes here) It takes some time for a server to switch from one job to another. If a server finishes job Jx, then to start job Jy it will need an intermission time Tx,y after job Jx completes. This is the time required by the server to clean up job Jx and load job Jy. In other word, job Jy can be run after job Jx if and only if Ex + Tx,y = Sy. The problem is to compute the minimum number of servers needed to do all jobs. Example: For example, let there be 3 jobs S(1) = 3 and E(1) = 6 S(2) = 10 and E(2) = 15 S(3) = 16 and E(3) = 20 T(1,2) = 2, T(1,3) = 5 T(2,1) = 0, T(2,3) = 3 T(3,1) = 0, T(3,2) = 0 In this example, we need 2 servers: Server 1: J(1), J(2) Server 2: J(3) Sample Input: Short explanation: The first 3 is the number of test cases, following by number of jobs (the second 3 means that there are 3 jobs for case 1), then followed by Ei and Si, then the T matrix (sized equal with number of jobs). 3 3 3 6 10 15 16 20 0 2 5 0 0 3 0 0 0 4 8 10 4 7 12 15 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 8 10 4 7 12 15 1 4 0 50 50 50 50 0 50 50 50 50 0 50 50 50 50 0 Sample Output: Case #1: 2 Case #2: 1 Case #3: 4 Personal Comments: The time required can be represented as a graph matrix, so I'm supposing this as a directed acyclic graph problem. Methods I tried so far is brute force and greedy, but got Wrong Answer. (Unfortunately I don't have my code anymore) Could probably solved by dynamic programming too, but I'm not sure. I really have no clear idea on how to solve this problem. So a simple hint or insight will be very helpful to me.

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  • Create a fast algorithm for a "weighted" median

    - by Hameer Abbasi
    Suppose we have a set S with k elements of 2-dimensional vectors, (x, n). What would be the most efficient algorithm to calculate the median of the weighted set? By "weighted set", I mean that the number x has a weight n. Here is an example (inefficient due to sorting) algorithm, where Sx is the x-part, and Sn is the n-part. Assume that all co-ordinate pairs are already arranged in Sx, with the respective changes also being done in Sn, and the sum of n is sumN: sum <= 0; i<= 0 while(sum < sumN) sum <= sum + Sn(i) ++i if(sum > sumN/2) return Sx(i) else return (Sx(i)*Sn(i) + Sx(i+1)*Sn(i+1))/(Sn(i) + Sn(i+1)) EDIT: Would this hold in two or more dimensions, if we were to calculate the median first in one dimension, then in another, with n being the sum along that dimension in the second pass?

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  • Why did visual programming never take off and what future paradigms might change that?

    - by Rego
    As the number of "visual" OS's such as Android, iOS and the promised Windows 8 are becoming more popular, it does not seem to me that we programmers have new ways to code using these new technologies, due to a possible lack in new visual programming languages paradigms. I've seen several discussions about incompatibilities between the current coding development environment, and the new OS approaches from Windows 8, Android and other tablets OS's. I mean, today if we have a new tablet, it's almost a requirement for coding, to have, for instance, an external keyboard (due it seems to me it's very difficult to program using the touch screen), exactly because the coding assistance is not conceived to "write" thousands of lines of code. So, how advanced should be the "new" visual programming languages paradigms? Which characteristics these new paradigms would be required?

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  • Calculating WPM given a variable stream of input

    - by Jaxo
    I'm creating an application that sits in the background and records all key presses (currently this is done and working; an event is fired every keydown/keyup). I want to offer a feature for the user that will show them their WPM over the entire session the program has been running for. This would be easy if I added a "Start" and "End" button to activate a timer, but I need to detect only when the user is typing continuously - ignoring all one-time keyboard shortcuts and breaks the user takes from typing. How in the world do I approach this? Is this even realistically & accurately possible?

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  • Any algorithm to dedicate a set of known resources to a set of known requirements (scheduling)

    - by Saeed Neamati
    I'm developing an application to help school principals in dedicating teachers to classes and courses over the hours of a week (scheduling). The scenario is roughly something like this: User enters the list of teachers and their free times into the system User enters the list of courses for this semester User enters the list of available classes into the system Well, up to here, there is no big deal. Just simple CRUD operations and nothing extraordinary. However, now what makes this system useful is that the application should automatically and based on an algorithm create the semester scheduling. I think you've got the main idea here. For example application should suggest that teacher A should go to class 1 for mathematics, and at the same time teacher B should go to class 2 for physics. This way all of the classes would be dedicated to lessons and teacher times won't overlap each other. Piece a cake for school principal. However, I can't find a good algorithm for this resource dedication. I mean it seems hard to me. Searching Google resulted in articles from different websites, but they are of no help and use to me. For example: http://en.wikipedia.org/wiki/Resource_allocation or http://en.wikipedia.org/wiki/Scheduling_(production_processes) Is there any algorithm out there, or any application or engine which can help me here? Does this requirements have a known name, like for example time scheduling engine? Any help would be appreciated.

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  • Searching for entity awareness in 3D space algorithm and data structure

    - by Khanser
    I'm trying to do some huge AI system just for the fun and I've come to this problem. How can I let the AI entities know about each other without getting the CPU to perform redundant and costly work? Every entity has a spatial awareness zone and it has to know what's inside when it has to decide what to do. First thoughts, for every entity test if the other entities are inside the first's reach. Ok, so it was the first try and yep, that is redundant and costly. We are working with real time AI over 10000+ entities so this is not a solution. Second try, calculate some grid over the awareness zone of every entity and test whether in this zones are entities (we are working with 3D entities with float x,y,z location coordinates) testing every point in the grid with the indexed-by-coordinate entities. Well, I don't like this because is also costly, but not as the first one. Third, create some multi linked lists over the x's and y's indexed positions of the entities so when we search for an interval between x,y and z,w positions (this interval defines the square over the spatial awareness zone) over the multi linked list, we won't have 'voids'. This has the problem of finding the nearest proximity value if there isn't one at the position where we start the search. I'm not convinced with any of the ideas so I'm searching for some enlightening. Do you people have any better ideas?

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  • Inexpensive generation of hierarchical unique IDs

    - by romaninsh
    My application is building a hierarchical structure like this: root = { 'id': 'root', 'children': [ { 'name': 'root_foo', 'children': [] }, { 'id': 'root_foo2', 'children': [ { 'id': 'root_foo2_bar', 'children': [] } ] } ] } in other words, it's a tree of nodes, where each node might have child elements and unique identifier I call "id". When a new child is added, I need to generate a unique identifier for it, however I have two problems: identifiers are getting too long adding many children takes slower, as I need to find first available id My requirement is: naming of a child X must be determined only from the state in their ancestors When I re-generate tree with same contents, the IDs must be same or in other words, when we have nodes A and B, creating child in A, must not affect the name given to children of B. I know that one way to optimize would be to introduce counter in each node and append it to the names which will solve my performance issue, but will not address the issue with the "long identifiers". Could you suggest me the algorithm for quickly coming up with new IDs?

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  • How can I permute pairs across a set?

    - by sila
    I am writing a bet settling app in C# and WinForms. I have 6 selections, 4 of them have won. I know that using the following formula from Excel: =FACT(selections)/(FACT(selections-doubles))/FACT(doubles) This is coded into my app and working well: I can work out how many possible doubles (e.g., AB, AC, AD, AE, BC, BD, BE, etc.) need to be resolved. But what I can't figure out is how to do the actual calculation. How can I efficiently code it so that every combination of A, B, C, and D has been calculated? All my efforts thus far on paper have proved to be ugly and verbose: is there an elegant solution to this problem?

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  • How to make a queue switches from FIFO mode to priority mode?

    - by enzom83
    I would like to implement a queue capable of operating both in the FIFO mode and in the priority mode. This is a message queue, and the priority is first of all based on the message type: for example, if the messages of A type have higher priority than the messages of the B type, as a consequence all messages of A type are dequeued first, and finally the messages of B type are dequeued. Priority mode: my idea consists of using multiple queues, one for each type of message; in this way, I can manage a priority based on the message type: just take first the messages from the queue at a higher priority and progressively from lower priority queues. FIFO mode: how to handle FIFO mode using multiple queues? In other words, the user does not see multiple queues, but it uses the queue as if it were a single queue, so that the messages leave the queue in the order they arrive when the priority mode is disabled. In order to achieve this second goal I have thought to use a further queue to manage the order of arrival of the types of messages: let me explain better with the following code snippet. int NUMBER_OF_MESSAGE_TYPES = 4; int CAPACITY = 50; Queue[] internalQueues = new Queue[NUMBER_OF_MESSAGE_TYPES]; Queue<int> queueIndexes = new Queue<int>(CAPACITY); void Enqueue(object message) { int index = ... // the destination queue (ie its index) is chosen according to the type of message. internalQueues[index].Enqueue(message); queueIndexes.Enqueue(index); } object Dequeue() { if (fifo_mode_enabled) { // What is the next type that has been enqueued? int index = queueIndexes.Dequeue(); return internalQueues[index].Dequeue(); } if (priority_mode_enabled) { for(int i=0; i < NUMBER_OF_MESSAGE_TYPES; i++) { int currentQueueIndex = i; if (!internalQueues[currentQueueIndex].IsEmpty()) { object result = internalQueues[currentQueueIndex].Dequeue(); // The following statement is fundamental to a subsequent switching // from priority mode to FIFO mode: the messages that have not been // dequeued (since they had lower priority) remain in the order in // which they were queued. queueIndexes.RemoveFirstOccurrence(currentQueueIndex); return result; } } } } What do you think about this idea? Are there better or more simple implementations?

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  • Does LINQ require significantly more processing cycles and memory than lower-level data iteration techniques?

    - by Matthew Patrick Cashatt
    Background I am recently in the process of enduring grueling tech interviews for positions that use the .NET stack, some of which include silly questions like this one, and some questions that are more valid. I recently came across an issue that may be valid but I want to check with the community here to be sure. When asked by an interviewer how I would count the frequency of words in a text document and rank the results, I answered that I would Use a stream object put the text file in memory as a string. Split the string into an array on spaces while ignoring punctuation. Use LINQ against the array to .GroupBy() and .Count(), then OrderBy() said count. I got this answer wrong for two reasons: Streaming an entire text file into memory could be disasterous. What if it was an entire encyclopedia? Instead I should stream one block at a time and begin building a hash table. LINQ is too expensive and requires too many processing cycles. I should have built a hash table instead and, for each iteration, only added a word to the hash table if it didn't otherwise exist and then increment it's count. The first reason seems, well, reasonable. But the second gives me more pause. I thought that one of the selling points of LINQ is that it simply abstracts away lower-level operations like hash tables but that, under the veil, it is still the same implementation. Question Aside from a few additional processing cycles to call any abstracted methods, does LINQ require significantly more processing cycles to accomplish a given data iteration task than a lower-level task (such as building a hash table) would?

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  • Removing occurrences of characters in a string

    - by DmainEvent
    I am reading this book, programming Interviews exposed by John Wiley and sons and in chapter 6 they are discussing removing all instances of characters in a src string using a removal string... so removeChars(string str, string remove) In there writeup they sey the steps to accomplish this are to have a boolean lookup array with all values initially set to false, then loop through each character in remove setting the corresponding value in the lookup array to true (note: this could also be a hash if the possible character set where huge like Unicode-16 or something like that or if str and remove are both relatively small... < 100 characters I suppose). You then iterate through the str with a source and destination index, copying each character only if its corresponding value in the lookup array is false... Which makes sense... I don't understand the code that they use however... They have for(src = 0; src < len; ++src){ flags[r[src]] == true; } which is turning the flag value at the remove string indexed at src to true... so if you start out with PLEASE HELP as your str and LEA as your remove you will be setting in your flag table at 0,1,2... t|t|t but after that you will get an out of bounds exception because r doesn't have have anything greater than 2 in it... even using there example you get an out of bounds exception... Am is there code example unworkable? Entire function string removeChars( string str, string remove ){ char[] s = str.toCharArray(); char[] r = remove.toCharArray(); bool[] flags = new bool[128]; // assumes ASCII! int len = s.Length; int src, dst; // Set flags for characters to be removed for( src = 0; src < len; ++src ){ flags[r[src]] = true; } src = 0; dst = 0; // Now loop through all the characters, // copying only if they aren’t flagged while( src < len ){ if( !flags[ (int)s[src] ] ){ s[dst++] = s[src]; } ++src; } return new string( s, 0, dst ); } as you can see, r comes from the remove string. So in my example the remove string has only a size of 3 while my str string has a size of 11. len is equal to the length of the str string. So it would be 11. How can I loop through the r string since it is only size 3? I haven't compiled the code so I can loop through it, but just looking at it I know it won't work. I am thinking they wanted to loop through the r string... in other words they got the length of the wrong string here.

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  • How to calculate Sin function quicker and more precisely?

    - by user1297181
    I want to calculate y(n)=32677Sin(45/1024•n), where y is an integer and n ranges from 0 to 2048. How can I make this process quicker and more precisely? Now I want to show you a reference answer: Since Sin(a+b)=Sin(a)Cos(b)+Cos(a)Sin(b) And Cos(a+b)=Cos(a)Cos(b)-Sin(a)Cos(b). So I can store Sin(45/1024•1) andCos(45/1024•1) ` only.Then use this formula: Sin(45/1024•2)=Sin(45/1024•1+45/1024•1), Cos(45/1024•2)=Cos(45/1024•1+45/1024•1), .... `Sin(45/1024•n)=Sin(45/1024•(n-1)+45/1024•1) `, `Cos(45/1024•n)=Cos(45/1024•(n-1)+45/1024•1) `, This way maybe quicker without storing large array.

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