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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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• Partitioning set into subsets with respect to equality of sum among subsets

  - by Al.Net

  let say i have {3, 1, 1, 2, 2, 1,5,2,7} set of numbers, I need to split the numbers such that sum of subset1 should be equal to sum of subset2 {3,2,7} {1,1,2,1,5,2}. First we should identify whether we can split number(one way might be dividable by 2 without any remainder) and if we can, we should write our algorithm two create s1 and s2 out of s. How to proceed with this approach? I read partition problem in wiki and even in some articles but i am not able to get anything. Can someone help me to find the right algorithm and its explanation in simple English?

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• Is there a word or description for this type of query?

  - by Nick

  We have the requirement to find a result in a collection of records based on a prioritised set of search criteria against a relational db (I'm talking indexed field matching here rather than text search). The way we are thinking about designing the query is to begin with a highly refined and specific set of criteria. If there are no results for this initial query we want to progressively reduce the criteria one by one in order of reducing priority, querying each time such a less specific set of criteria until we find a result we can accept. Alternatively, we have considered starting with a smaller set of criteria and increasing until we have reduced number of results down to the last set. What I would like to know is if an existing term to describe this type of query exists? So that we can look to model our own on existing patterns and use best practice.

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• How to avoid oscillation by async event based systems?

  - by inf3rno

  Imagine a system where there are data sources which need to be kept in sync. A simple example is model - view data binding by MVC. Now I intend to describe these kind of systems with data sources and hubs. Data sources are publishing and subscribing for events and hubs are relaying events to data sources. By handling an event a data source will change it state described in the event. By publishing an event the data source puts its current state to the event, so other data sources can use that information to change their state accordingly. The only problem with this system, that events can be reflected from the hub or from the other data sources, and that can put the system into an infinite oscillation (by async or infinite loop by sync). For example A -- data source B -- data source H -- hub A -> H -> A -- reflection from the hub A -> H -> B -> H -> A -- reflection from another data source By sync it is relatively easy to solve this issue. You can compare the current state with the event, and if they are equal, you don't change the state and raise the same event again. By async I could not find a solution yet. The state comparison does not work by async event handling because there is eventual consistency, and new events can be published in an inconsistent state causing the same oscillation. For example: A(*->x) -> H -> B(y->x) -- can go parallel with B(*->y) -> H -> A(x->y) -- so first A changes to x state while B changes to y state -- then B changes to x state while A changes to y state -- and so on for eternity... What do you think is there an algorithm to solve this problem? If there is a solution, is it possible to extend it to prevent oscillation caused by multiple hubs, multiple different events, etc... ? update: I don't think I can make this work without a lot of effort. I think this problem is just the same as we have by syncing multiple databases in a distributed system. So I think what I really need is constraints if I want to prevent this problem in an automatic way. What constraints do you suggest?

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• Construct an array from an existing array

  - by Luv

  Given an array of integers A[1...n-1] where 'N' is the length of array A[ ]. Construct an array B such that B[i] = min(A[i], A[i+1], ..., A[i+K-1]), where K will be given. Array B will have N-K+1 elements. We can solve the problem using min-heaps Construct min-heap for k elements - O(k) For every next element delete the first element and insert the new element and heapify Hence Worst Case Time - O( (n-k+1)*k ) + O(k) Space - O(k) Can we do it better?

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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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• 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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• Amazon Kindle - Whispersync implementation?

  - by Bala

  For those who are not aware of Kindle's whispersync, here is how it works (from amazon.com): "...Whispersync synchronizes the bookmarks and furthest page read among devices registered to the same account. Whispersync is on by default to ensure a seamless reading experience for a book read across multiple Kindles." Can anyone give some details on how the Whispersync feature is implemented in Kindle and in the Backend of Amazon? I am guessing this implementation involves a very simple hashmap for each user account. Each hashmap maps Books with satellite information about the book. Satellite information contains bookmarks, furthest page read, device on which it was read, etc.. Thanks!

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• Performing a Depth First Search iteratively using async/parallel processing?

  - by Prabhu

  Here is a method that does a DFS search and returns a list of all items given a top level item id. How could I modify this to take advantage of parallel processing? Currently, the call to get the sub items is made one by one for each item in the stack. It would be nice if I could get the sub items for multiple items in the stack at the same time, and populate my return list faster. How could I do this (either using async/await or TPL, or anything else) in a thread safe manner? private async Task<IList<Item>> GetItemsAsync(string topItemId) { var items = new List<Item>(); var topItem = await GetItemAsync(topItemId); Stack<Item> stack = new Stack<Item>(); stack.Push(topItem); while (stack.Count > 0) { var item = stack.Pop(); items.Add(item); var subItems = await GetSubItemsAsync(item.SubId); foreach (var subItem in subItems) { stack.Push(subItem); } } return items; } I was thinking of something along these lines, but it's not coming together: var tasks = stack.Select(async item => { items.Add(item); var subItems = await GetSubItemsAsync(item.SubId); foreach (var subItem in subItems) { stack.Push(subItem); } }).ToList(); if (tasks.Any()) await Task.WhenAll(tasks); The language I'm using is C#.

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• reference list for non-IT driven algorithmic patterns

  - by Quicker

  I am looking for a reference list for non-IT driven algorithmic patterns (which still can be helped with IT implementations of IT). An Example List would be: name; short desc; reference Travelling Salesman; find the shortest possible route on a multiple target path; http://en.wikipedia.org/wiki/Travelling_salesman_problem Ressource Disposition (aka Regulation); Distribute a limited/exceeding input on a given number output receivers based on distribution rules; http://database-programmer.blogspot.de/2010/12/critical-analysis-of-algorithm-sproc.html If there is no such list, but you instantly think of something specific, please 'put it on the desk'. Maybe I can compile something out of the input I get here (actually I am very frustrated as I did not find any such list via research by myself). Details on Scoping: I found it very hard to formulate what I want in a way everything is out that I do not need (which may be the issue why I did not find anything at google). There is a database centric definition for what I am looking for in the section 'Processes' of the second example link. That somehow fits, but the database focus sort of drifts away from the pattern thinking, which I have in mind. So here are my own thoughts around what's in and what's out: I am NOT looking for a foundational algo ref list, which is implemented as basis for any programming language. Eg. the php reference describes substr and strlen. That implements algos, but is not what I am looking for. the problem the algo does address would even exist, if there were no computers (or other IT components) the main focus of the algo is NOT to help other algo's chances are high, that there are implementions of the solution or any workaround without any IT support out there in the world however the algo could be benefitialy implemented/fully supported by a software application = means: the problem of the algo has to be addressed anyway, but running an algo implementation with software automates the process (that is why I posted it on stackoverflow and not somewhere else) typically such algo implementations have more than one input field value and more than one output field value - which implies it could not be implemented as simple function (which is fixed to produce not more than one output value) in a normalized data model often times such algo implementation outputs span accross multiple rows (sometimes multiple tables), whereby the number of output rows depends on the input paraters and rows in the table(s) at start time - which implies that any algo implementation/procedure must interact with a database (read and/or write) I am mainly looking for patterns, not for specific implementations. Example: The Travelling Salesman assumes any coordinates, however it does not say: You need a table targets with fields x and y. - however sometimes descriptions are focussed on examples with specific implementations very much - no worries, as long as the pattern gets clear

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• How to find optimal path visit every node with parallel workers complicated by dynamic edge costs?

  - by Aaron Anodide

  Say you have an acyclic directed graph with weighted edges and create N workers. My goal is to calculate the optimal way those workers can traverse the entire graph in parralel. However, edge costs may change along the way. Example: A -1-> B A -2-> C B -3-> C (if A has already been visited) B -5-> C (if A has not already been visited) Does what I describe lend itself to a standard algorithmic approach, or alternately can someone suggest if I'm looking at this in an inherently flawed way (i have an intuition I might be)?

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• How should I compress a file with multiple bytes that are the same with Huffman coding?

  - by Omega

  On my great quest for compressing/decompressing files with a Java implementation of Huffman coding (http://en.wikipedia.org/wiki/Huffman_coding) for a school assignment, I am now at the point of building a list of prefix codes. Such codes are used when decompressing a file. Basically, the code is made of zeroes and ones, that are used to follow a path in a Huffman tree (left or right) for, ultimately, finding a byte. In this Wikipedia image, to reach the character m the prefix code would be 0111 The idea is that when you compress the file, you will basically convert all the bytes of the file into prefix codes instead (they tend to be smaller than 8 bits, so there's some gain). So every time the character m appears in a file (which in binary is actually 1101101), it will be replaced by 0111 (if we used the tree above). Therefore, 1101101110110111011011101101 becomes 0111011101110111 in the compressed file. I'm okay with that. But what if the following happens: In the file to be compressed there exists only one unique byte, say 1101101. There are 1000 of such byte. Technically, the prefix code of such byte would be... none, because there is no path to follow, right? I mean, there is only one unique byte anyway, so the tree has just one node. Therefore, if the prefix code is none, I would not be able to write the prefix code in the compressed file, because, well, there is nothing to write. Which brings this problem: how would I compress/decompress such file if it is impossible to write a prefix code when compressing? (using Huffman coding, due to the school assignment's rules) This tutorial seems to explain a bit better about prefix codes: http://www.cprogramming.com/tutorial/computersciencetheory/huffman.html but doesn't seem to address this issue either.

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• Finding the median of the merged array of two sorted arrays in O(logN)?

  - by user176517

  Refering to the solution present at MIT handout I have tried to figure out the solution myself but have got stuck and I believe I need help to understand the following points. In the function header used in the solution MEDIAN -SEARCH (A[1 . . l], B[1 . . m], max(1,n/2 - m), min(l, n/2)) I do not understand the last two arguments why not simply 1, l why the max and min respectively. Thanking You.

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• how to avoid or minimise use of check/conditional statement?

  - by Muneeb Nasir

  I have scenario, where i got stream and i need to check for some value. if i got my any new value i have to store it in any of data structure. well 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'll receive hundreds for value in second, if i start checking each and every value i received than for sure it effect performance. Any body can suggest me any mechanism or algorithm that solve my issue. either by bypassing checks or atleast minimize them?

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• Algorithm to increase odds of matching when randomly selecting

  - by Bryan

  I am building a mobile game loosely based on dual n-back http://brainworkshop.sourceforge.net/tutorial.html Now with the game I have 9 squares (numbered 1 through 9) and 9 letters (A through K) In the current code, I randomly select a square (e.g. 3) and a letter (e.g. C), then repeat the random selection for the next turn. For 1-back, I test whether either, neither or both match the previous turn. The problem with my current code is I get very few matches - I can go through many turns without having either match. How can I increase the match frequency, or alternatively decrease the randomness so a match is more likely? I am not looking for specific code (but pseudo-code would be fine) - just more an approach to increase match frequency.

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• Structuring Access Control In Hierarchical Object Graph

  - by SB2055

  I have a Folder entity that can be Moderated by users. Folders can contain other folders. So I may have a structure like this: Folder 1 Folder 2 Folder 3 Folder 4 I have to decide how to implement Moderation for this entity. I've come up with two options: Option 1 When the user is given moderation privileges to Folder 1, define a moderator relationship between Folder 1 and User 1. No other relationships are added to the db. To determine if the user can moderate Folder 3, I check and see if User 1 is the moderator of any parent folders. This seems to alleviate some of the complexity of handling updates / moved entities / additions under Folder 1 after the relationship has been defined, and reverting the relationship means I only have to deal with one entity. Option 2 When the user is given moderation privileges to Folder 1, define a new relationship between User 1 and Folder 1, and all child entities down to the grandest of grandchildren when the relationship is created, and if it's ever removed, iterate back down the graph to remove the relationship. If I add something under Folder 2 after this relationship has been made, I just copy all Moderators into the new Entity. But when I need to show only the top-level Folders that a user is Moderating, I need to query all folders that have a parent folder that the user does not moderate, as opposed to option 1, where I just query any items that the user is moderating. Thoughts I think it comes down to determining if users will be querying for all parent items more than they'll be querying child items... if so, then option 1 seems better. But I'm not sure. Is either approach better than the other? Why? Or is there another approach that's better than both? I'm using Entity Framework in case it matters.

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• What are startups expecting when they ask you to solve a programming challenge before interviewing? [closed]

  - by Swapnil Tailor

  I have applied to couple of startups and most of them are asking to solve programming challenge before they start on the interviewing candidate. I have submitted couple of the solutions and all the time getting rejected in the initial screening. Now what I think is, they will see my coding style, algorithm and OOD concepts that I have used to solve the problem. Can you guys input more on it as what other details are taken into consideration and how can I improve my coding for getting selected. By the way, I did all my coding in either Java/Perl. EDIT I feel the biggest reason for rejection is code didn't work for couple of use cases.

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• Writing a spell checker similar to "did you mean"

  - by user888734

  I'm hoping to write a spellchecker for search queries in a web application - not unlike Google's "Did you mean?" The algorithm will be loosely based on this: http://catalog.ldc.upenn.edu/LDC2006T13 In short, it generates correction candidates and scores them on how often they appear (along with adjacent words in the search query) in an enormous dataset of known n-grams - Google Web 1T - which contains well over 1 billion 5-grams. I'm not using the Web 1T dataset, but building my n-gram sets from my own documents - about 200k docs, and I'm estimating tens or hundreds of millions of n-grams will be generated. This kind of process is pushing the limits of my understanding of basic computing performance - can I simply load my n-grams into memory in a hashtable or dictionary when the app starts? Is the only limiting factor the amount of memory on the machine? Or am I barking up the wrong tree? Perhaps putting all my n-grams in a graph database with some sort of tree query optimisation? Could that ever be fast enough?

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• Find possible variations of one item out of multiple baskets.

  - by tugberk

  I have three baskets of balls and each of them has 10 balls which have the following numbers: Basket 1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Basket 2: 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 Basket 3: 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 What would be the possible variations If I were to pick one ball from each basket? I guess this is called as Probability in Mathematics but not sure. How would you write this code in C# (or any other programming language) to get the correct results? Edit: Based on @Kilian Foth's comment, here is the solution in C#: class Program { static void Main(string[] args) { IEnumerable<string> basket1 = new List<string> { "1", "2", "3", "4", "5", "6", "7", "8", "9", "10" }; IEnumerable<string> basket2 = new List<string> { "11", "12", "13", "14", "15", "16", "17", "18", "19", "20" }; IEnumerable<string> basket3 = new List<string> { "21", "22", "23", "24", "25", "26", "27", "28", "29", "30" }; foreach (var item1 in basket1) foreach (var item2 in basket2) foreach (var item3 in basket3) { Console.WriteLine("{0}, {1}, {2}", item1, item2, item3); } Console.ReadLine(); } }

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• Approach to Authenticate Clients to TCP Server

  - by dab

  I'm writing a Server/Client application where clients will connect to the server. What I want to do, is make sure that the client connecting to the server is actually using my protocol and I can "trust" the data being sent from the client to the server. What I thought about doing is creating a sort of hash on the client's machine that follows a particular algorithm. What I did in a previous version was took their IP address, the client version, and a few other attributes of the client and sent it as a calculated hash to the server, who then took their IP, and the version of the protocol the client claimed to be using, and calculated that number to see if they matched. This works ok until you get clients that connect from within a router environment where their internal IP is different from their external IP. My fix for this was to pass the client's internal IP used to calculate this hash with the authentication protocol. My fear is this approach is not secure enough. Since I'm passing the data used to create the "auth hash". Here's an example of what I'm talking about: Client IP: 192.168.1.10, Version: 2.4.5.2 hash = 2*4*5*1 * (1+9+2) * (1+6+8) * (1) * (1+0) Client Connects to Server client sends: auth hash ip version Server calculates that info, and accepts or denies the hash. Before I go and come up with another algorithm to prove a client can provide data a server (or use this existing algorithm), I was wondering if there are any existing, proven, and secure systems out there for generating a hash that both sides can generate with general knowledge. The server won't know about the client until the very first connection is established. The protocol's intent is to manage a network of clients who will be contributing data to the server periodically. New clients will be added simply by connecting the client to the server and "registering" with the server. So a client connects to the server for the first time, and registers their info (mac address or some other kind of unique computer identifier), then when they connect again, the server will recognize that client as a previous person and associate them with their data in the database.

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• Logic or Algorithm to solve this problem [closed]

  - by jade

  I have two lists. List1 {a,b,c,d,e} and List2 {f,g,h,i,j} The relation between the two list is as follows a->g,a->h,h->c,h->d,d->i,d->j Now I have these two lists displayed. Based on the relation above on selecting element a from List1, List2 shows g,h. On selecting h from List2, in List1 c,d are shown in List1. On selecting d from List1 it shows i,j in List2. How to trace back to initial state by deselecting the elements in reverse order in which they have been selected?

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• booth multiplication algorithm

  - by grassPro

  Is booth algorithm for multiplication only for multiplying 2 negative numbers (-3 * -4) or one positive and one negative number (-3 * 4) ? Whenever i multiply 2 positive numbers using booth algorithm i get a wrong result. example : 5 * 4 A = 101 000 0 // binary of 5 is 101 S = 011 000 0 // 2's complement of 5 is 011 P = 000 100 0 // binary of 4 is 100 x = 3 y = 3 m = 5 -m = 2's complement of m r = 4 After right shift of P by 1 bit 0 000 100 After right shift of P by 1 bit 0 000 010 P+S = 011 001 0 After right shift by 1 bit 0 011 001 Discarding the LSB 001100 But that comes out to be the binary of 12 . It should have been 20(010100)

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• Where would you start if you were trying to solve this PDF classification problem?

  - by burtonic

  We are crawling and downloading lots of companies' PDFs and trying to pick out the ones that are Annual Reports. Such reports can be downloaded from most companies' investor-relations pages. The PDFs are scanned and the database is populated with, among other things, the: Title Contents (full text) Page count Word count Orientation First line Using this data we are checking for the obvious phrases such as: Annual report Financial statement Quarterly report Interim report Then recording the frequency of these phrases and others. So far we have around 350,000 PDFs to scan and a training set of 4,000 documents that have been manually classified as either a report or not. We are experimenting with a number of different approaches including Bayesian classifiers and weighting the different factors available. We are building the classifier in Ruby. My question is: if you were thinking about this problem, where would you start?

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• An algorithm for finding subset matching criteria?

  - by Macin

  I recently came up with a problem which I would like to share some thoughts about with someone on this forum. This relates to finding a subset. In reality it is more complicated, but I tried to present it here using some simpler concepts. To make things easier, I created this conceptual DB model: Let's assume this is a DB for storing recipes. Recipe can have many instructions steps and many ingredients. Ingredients are stored in a cupboard and we know how much of each ingredient we have. Now, when we create a recipe, we have to define how much of each ingredient we need. When we want to use a recipe, we would just check if required amount is less than available amount for each product and then decide if we can cook a dinner - if amount required for at least one ingredient is less than available amount - recipe cannot be cooked. Simple sql query to get the result. This is straightforward, but I'm wondering, how should I work when the problem is stated the other way round, i.e. how to find recipies which can be cooked only from ingredients that are available? I hope my explanation is clear, but if you need any more clarification, please ask.

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• Looking for a dynamic programming solution

  - by krammer

  Given a sequence of integers in range 1 to n. Each number can appear at most once. Let there be a symbol X in the sequence which means remove the minimum element from the list. There can be an arbitrarily number of X in the sequence. Example: 1,3,4,X,5,2,X The output is 1,2. We need to find the best way to perform this operation. The solution I have been thinking is: Scan the sequence from left to right and count number of X which takes O(n) time. Perform partial sorting and find the k smallest elements (k = number of X) which takes O(n+klogk) time using median of medians. Is there a better way to solve this problem using dynamic programming or any other way ?

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