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  • Given a string of letters from alphabet insert frequency of each character in the string.in O(n) time and O(1) space [on hold]

    - by learner
    Below is my attempt void str_freq(char *str, int len) { char c; int cnt=0; c=str[0]; int i,j=0; for(i=0;i<len;i++) { if(c==str[i]) { cnt++; } else { c = str[i]; // printf(" %d ",cnt); str[j] = str[i-1]; str[j+1] = (char)(((int)'0')+cnt); j++; cnt=0; } } str[j+1]='\0'; printf("%s",str); } int main() { char str[] = "aaabbccccdeffgggg"; int length=strlen(str); str_freq(str,length); } I am getting wrong answer abcdef1 instead of a3b2c4d1e1f2g4. Please let me know where I am going wrong.

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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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  • 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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  • 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 project euler problem no 18

    - by Valentino Ru
    Problem number 18 from Project Euler's site is as follows: By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23. 3 7 4 2 4 6 8 5 9 3 That is, 3 + 7 + 4 + 9 = 23. Find the maximum total from top to bottom of the triangle below: 75 95 64 17 47 82 18 35 87 10 20 04 82 47 65 19 01 23 75 03 34 88 02 77 73 07 63 67 99 65 04 28 06 16 70 92 41 41 26 56 83 40 80 70 33 41 48 72 33 47 32 37 16 94 29 53 71 44 65 25 43 91 52 97 51 14 70 11 33 28 77 73 17 78 39 68 17 57 91 71 52 38 17 14 91 43 58 50 27 29 48 63 66 04 68 89 53 67 30 73 16 69 87 40 31 04 62 98 27 23 09 70 98 73 93 38 53 60 04 23 NOTE: As there are only 16384 routes, it is possible to solve this problem by trying every route. However, Problem 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o) The formulation of this problems does not make clear if the "Traversor" is greedy, meaning that he always choosed the child with be higher value the maximum of every single walkthrough is asked The NOTE says, that it is possible to solve this problem by trying every route. This means to me, that is is also possible without! This leads to my actual question: Assumed that not the greedy one is the max, is there any algorithm that finds the max walkthrough value without trying every route and that doesn't act like the greedy algorithm? I implemented an algorithm in Java, putting the values first in a node structure, then applying the greedy algorithm. The result, however, is cosidered as wrong by Project Euler. sum = 0; void findWay(Node node){ sum += node.value; if(node.nodeLeft != null && node.nodeRight != null){ if(node.nodeLeft.value > node.nodeRight.value){ findWay(node.nodeLeft); }else{ findWay(node.nodeRight); } } }

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  • C# 5 Async, Part 3: Preparing Existing code For Await

    - by Reed
    While the Visual Studio Async CTP provides a fantastic model for asynchronous programming, it requires code to be implemented in terms of Task and Task<T>.  The CTP adds support for Task-based asynchrony to the .NET Framework methods, and promises to have these implemented directly in the framework in the future.  However, existing code outside the framework will need to be converted to using the Task class prior to being usable via the CTP. Wrapping existing asynchronous code into a Task or Task<T> is, thankfully, fairly straightforward.  There are two main approaches to this. Code written using the Asynchronous Programming Model (APM) is very easy to convert to using Task<T>.  The TaskFactory class provides the tools to directly convert APM code into a method returning a Task<T>.  This is done via the FromAsync method.  This method takes the BeginOperation and EndOperation methods, as well as any parameters and state objects as arguments, and returns a Task<T> directly. For example, we could easily convert the WebRequest BeginGetResponse and EndGetResponse methods into a method which returns a Task<WebResponse> via: Task<WebResponse> task = Task.Factory .FromAsync<WebResponse>( request.BeginGetResponse, request.EndGetResponse, null); .csharpcode, .csharpcode pre { font-size: small; color: black; font-family: consolas, "Courier New", courier, monospace; background-color: #ffffff; /*white-space: pre;*/ } .csharpcode pre { margin: 0em; } .csharpcode .rem { color: #008000; } .csharpcode .kwrd { color: #0000ff; } .csharpcode .str { color: #006080; } .csharpcode .op { color: #0000c0; } .csharpcode .preproc { color: #cc6633; } .csharpcode .asp { background-color: #ffff00; } .csharpcode .html { color: #800000; } .csharpcode .attr { color: #ff0000; } .csharpcode .alt { background-color: #f4f4f4; width: 100%; margin: 0em; } .csharpcode .lnum { color: #606060; } Event-based Asynchronous Pattern (EAP) code can also be wrapped into a Task<T>, though this requires a bit more effort than the one line of code above.  This is handled via the TaskCompletionSource<T> class.  MSDN provides a detailed example of using this to wrap an EAP operation into a method returning Task<T>.  It demonstrates handling cancellation and exception handling as well as the basic operation of the asynchronous method itself. The basic form of this operation is typically: Task<YourResult> GetResultAsync() { var tcs = new TaskCompletionSource<YourResult>(); // Handle the event, and setup the task results... this.GetResultCompleted += (o,e) => { if (e.Error != null) tcs.TrySetException(e.Error); else if (e.Cancelled) tcs.TrySetCanceled(); else tcs.TrySetResult(e.Result); }; // Call the asynchronous method this.GetResult(); // Return the task from the TaskCompletionSource return tcs.Task; } We can easily use these methods to wrap our own code into a method that returns a Task<T>.  Existing libraries which cannot be edited can be extended via Extension methods.  The CTP uses this technique to add appropriate methods throughout the framework. The suggested naming for these methods is to define these methods as “Task<YourResult> YourClass.YourOperationAsync(…)”.  However, this naming often conflicts with the default naming of the EAP.  If this is the case, the CTP has standardized on using “Task<YourResult> YourClass.YourOperationTaskAsync(…)”. Once we’ve wrapped all of our existing code into operations that return Task<T>, we can begin investigating how the Async CTP can be used with our own code.

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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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  • "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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  • What is the runtime of this program

    - by grebwerd
    I was wondering what the run time of this small program would be? #include <stdio.h> int main(int argc, char* argv[]) { int i; int j; int inputSize; int sum = 0; if(argc == 1) inputSize = 16; else inputSize = atoi(argv[i]); for(i = 1; i <= inputSize; i++){ for(j = i; j < inputSize; j *=2 ){ printf("The value of sum is %d\n",++sum); } } } n S floor(log n - log (n-i)) = ? i =1 and that each summation would be the floor value between log(n) - log(n-i). Would the run time be n log n?

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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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  • Finding "spare time" in a day from within a list of events

    - by MFB
    I have a list of events which is always sorted chronologically. The start time is always followed by the end time. Times are strings formatted as 'HHmmss'. // list of events var events = [ '010000', // start '013000', // end... '053000', '060000', '161500', '184500'] // desired output var spares = [ '000000', // start '010000', // end... '013000', '053000', '060000', '161500', '184500', '235959'] How can I programmatically create a new list of "spare time" from 000000 to 235959? PS I'm trying to do this in Javascript, but any conceptual answer or pseudo code would be helpful too.

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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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  • Simple algorithm for a sudoku solver java

    - by user142050
    just a quick note first, I originally asked this question on stack overflow but was refered here instead. I've been stuck on this thing for a while, I just can't wrap my head around it. For a homework, I have to produce an algorithm for a sudoku solver that can check what number goes in a blank square in a row, in a column and in a block. It's a regular 9x9 sudoku and I'm assuming that the grid is already printed so I have to produce the part where it solves it. I've read a ton of stuff on the subject I just get stuck expressing it. I want the solver to do the following: If the value is smaller than 9, increase it by 1 If the value is 9, set it to zero and go back 1 If the value is invalid, increase by 1 I've already read about backtracking and such but I'm in the early stage of the class so I'd like to keep it as simple as possible. I'm more capable of writing in pseudo code but not so much with the algorithm itself and it's the algorithm that is needed for this exercise. Thanks in advance for your help guys.

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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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  • 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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  • What is an appropriate language for expressing initial stages of algorithm refinement?

    - by hydroparadise
    First, this is not a homework assignment, but you can treat it as such ;). I found the following question in the published paper The Camel Has Two Humps. I was not a CS major going to college (I majored in MIS/Management), but I have a job where I find myself coding quite often. For a non-trivial programming problem, which one of the following is an appropriate language for expressing the initial stages of algorithm refinement? (a) A high-level programming language. (b) English. (c) Byte code. (d) The native machine code for the processor on which the program will run. (e) Structured English (pseudocode). What I do know is that you usually want to start your design implementation by writing down pseuducode and then moving/writing in the desired technology (because we all do that, right?) But I never thought about it in terms of refinement. I mean, if you were the original designer, then you might have access to the original pseudocode. But realisticly, when I have to maintain/refactor/refine somebody elses code, I just keep trucking with the language it currently resides in. Anybody have a definitive answer to this? As a side note, I did a quick scan of the paper as I havn't read every single detail. It presents various score statistics, can't find where the answers are with the paper.

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  • What is the Big-O time complexity of this algorithm

    - by grebwerd
    I was wondering what the run time of this small program would be? #include <stdio.h> int main(int argc, char* argv[]) { int i; int j; int inputSize; int sum = 0; if(argc == 1) inputSize = 16; else inputSize = atoi(argv[i]); for(i = 1; i <= inputSize; i++){ for(j = i; j < inputSize; j *=2 ){ printf("The value of sum is %d\n",++sum); } } } n S floor(log n - log (n-i)) = ? i =1 and that each summation would be the floor value between log(n) - log(n-i). Would the run time be n log n?

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  • Defining formula through user interface in user form

    - by BriskLabs Pakistan
    I am a student and developing a simple assignment - windows form application in visual studio 2010. The application is suppose to construct formulas as per user requirement. The process: It has to pick data from columns of Microsoft Access database and the user should be able to pick the data by column name like we do in a drop down menu. and create reusable formulas in it ( configure it once and can change it again). followings are column titles from database that can be picked for example. e.g Col -1 : Marks in Maths Col -2 : Total Marks in Maths Col -3 : Marks in science Col -4 : Total marks in science Finally we should be able to construct any formula in the UI like (Col 1 + Col 3 ) / ( col 2 + col 4) = Formula 1 once this is formula is set saved and a name is assigned to it by user. he/she can use the formula and results shall appear in a window below. i.e He would be able to calculate his desired figures (formula) by only manipulating underlying data on the UI layer....choose the data for a period and apply the formula and get the answer Problem: It looks like I have to create an app where rules are set through UI....... this means no stored procedures are required in SQL.... please suggest the right approach.

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  • Algorithm to match timestamped events from two sources

    - by urza.cc
    I have two different physical devices (one is camera, one is other device) that observe the same scene and mark when a specified event occures. (record timestamp) So they each produce a serie of timestamps "when the event was observed". Theoretically the recorded timestamps should be very well aligned: Visualized ideal situation on two time lines "s" and "r" as recorded from the two devices: but more likely they will not be so nicely aligned and there might be missing events from timeline s or r: I am looking for algorithm to match events from "s" and "r" like this: So that the result will be something like: (s1,null); (s2,r1); (s3,null); (s4,r2); (s5,r3); (null,r4); (s6,r5); Or something similar. Maybe with some "confidence" rating. I have some ideas, but I feel that this might be probably a well known problem, that has some good known solutions, but I don't know the right terminology. I am a little bit out of my element here, this is not my primary area of programming.. Any helps, suggestions etc will be appreciated.

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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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  • 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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  • 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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  • 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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  • 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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  • Finding the shortest path through a digraph that visits all nodes

    - by Boluc Papuccuoglu
    I am trying to find the shortest possible path that visits every node through a graph (a node may be visited more than once, the solution may pick any node as the starting node.). The graph is directed, meaning that being able to travel from node A to node B does not mean one can travel from node B to node A. All distances between nodes are equal. I was able to code a brute force search that found a path of only 27 nodes when I had 27 nodes and each node had a connection to 2 or 1 other node. However, the actual problem that I am trying to solve consists of 256 nodes, with each node connecting to either 4 or 3 other nodes. The brute force algorithm that solved the 27 node graph can produce a 415 node solution (not optimal) within a few seconds, but using the processing power I have at my disposal takes about 6 hours to arrive at a 402 node solution. What approach should I use to arrive at a solution that I can be certain is the optimal one? For example, use an optimizer algorithm to shorten a non-optimal solution? Or somehow adopt a brute force search that discards paths that are not optimal? EDIT: (Copying a comment to an answer here to better clarify the question) To clarify, I am not saying that there is a Hamiltonian path and I need to find it, I am trying to find the shortest path in the 256 node graph that visits each node AT LEAST once. With the 27 node run, I was able to find a Hamiltonian path, which assured me that it was an optimal solution. I want to find a solution for the 256 node graph which is the shortest.

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