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  • Automated tests for differencing algorithm

    - by Matthew Rodatus
    We are designing a differencing algorithm (based on Longest Common Subsequence) that compares a source text and a modified copy to extract the new content (i.e. content that is only in the modified copy). I'm currently compiling a library of test case data. We need to be able to run automated tests that verify the test cases, but we don't want to verify strict accuracy. Given the heuristic nature of our algorithm, we need our test pass/failures to be fuzzy. We want to specify a threshold of overlap between the desired result and the actual result (i.e. the content that is extracted). I have a few sketches in my mind as to how to solve this, but has anyone done this before? Does anyone have guidance or ideas about how to do this effectively?

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  • Removing ocurrances 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?

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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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  • ConcurrentDictionary<TKey,TValue> used with Lazy<T>

    - by Reed
    In a recent thread on the MSDN forum for the TPL, Stephen Toub suggested mixing ConcurrentDictionary<T,U> with Lazy<T>.  This provides a fantastic model for creating a thread safe dictionary of values where the construction of the value type is expensive.  This is an incredibly useful pattern for many operations, such as value caches. The ConcurrentDictionary<TKey, TValue> class was added in .NET 4, and provides a thread-safe, lock free collection of key value pairs.  While this is a fantastic replacement for Dictionary<TKey, TValue>, it has a potential flaw when used with values where construction of the value class is expensive. The typical way this is used is to call a method such as GetOrAdd to fetch or add a value to the dictionary.  It handles all of the thread safety for you, but as a result, if two threads call this simultaneously, two instances of TValue can easily be constructed. If TValue is very expensive to construct, or worse, has side effects if constructed too often, this is less than desirable.  While you can easily work around this with locking, Stephen Toub provided a very clever alternative – using Lazy<TValue> as the value in the dictionary instead. This looks like the following.  Instead of calling: MyValue value = dictionary.GetOrAdd( key, () => new MyValue(key)); .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; } We would instead use a ConcurrentDictionary<TKey, Lazy<TValue>>, and write: MyValue value = dictionary.GetOrAdd( key, () => new Lazy<MyValue>( () => new MyValue(key))) .Value; This simple change dramatically changes how the operation works.  Now, if two threads call this simultaneously, instead of constructing two MyValue instances, we construct two Lazy<MyValue> instances. However, the Lazy<T> class is very cheap to construct.  Unlike “MyValue”, we can safely afford to construct this twice and “throw away” one of the instances. We then call Lazy<T>.Value at the end to fetch our “MyValue” instance.  At this point, GetOrAdd will always return the same instance of Lazy<MyValue>.  Since Lazy<T> doesn’t construct the MyValue instance until requested, the actual MyClass instance returned is only constructed once.

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  • Looking for a non-cryptographic hash function that returns a single character

    - by makerofthings7
    Suppose I have a dictionary of ASCII words stored in uppercase. I also want to save those words into separate files so that the total word count of each file is approximately the same. By simply looking at the word I need to know which file it should be in (if it's there at all). Duplicate words should go into the same file and overwrite the last one. My first attempt at solving this problem is to use .NET's object.GetHashCode() function and .Trim() to get one of the "random" characters that pop up. I asked a similar question here If I only use one character of object.GetHashCode() I would get a hash code character of A..Z or 0..9. However saving the result of GetHashCode to disk is a no-no so I need a substitute. Question: What algorithm (or subset of an algorithm) is appropriate for pigeonholing strings into a single character or range of characters (Like hex 0..F offers 16 chars)? Real world usage: I'll use this answer to modify the Partition key used in Azure Table storage as described here

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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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  • Name of the Countdown Numbers round problem - and algorithmic solutions?

    - by Dai
    For the non-Brits in the audience, there's a segment of a daytime game-show where contestants have a set of 6 numbers and a randomly generated target number. They have to reach the target number using any (but not necessarily all) of the 6 numbers using only arithmetic operators. All calculations must result in positive integers. An example: Youtube: Countdown - The Most Extraordinary Numbers Game Ever? A detailed description is given on Wikipedia: Countdown (Game Show) For example: The contentant selects 6 numbers - two large (possibilities include 25, 50, 75, 100) and four small (numbers 1 .. 10, each included twice in the pool). The numbers picked are 75, 50, 2, 3, 8, 7 are given with a target number of 812. One attempt is (75 + 50 - 8) * 7 - (3 * 2) = 813 (This scores 7 points for a solution within 5 of the target) An exact answer would be (50 + 8) * 7 * 2 = 812 (This would have scored 10 points exactly matching the target). Obviously this problem has existed before the advent of TV, but the Wikipedia article doesn't give it a name. I've also saw this game at a primary school I attended where the game was called "Crypto" as an inter-class competition - but searching for it now reveals nothing. I took part in it a few times and my dad wrote an Excel spreadsheet that attempted to brute-force the problem, I don't remember how it worked (only that it didn't work, what with Excel's 65535 row limit), but surely there must be an algorithmic solution for the problem. Maybe there's a solution that works the way human cognition does (e.g. in-parallel to find numbers 'close enough', then taking candidates and performing 'smaller' operations).

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  • finding houses within a radius

    - by paul smith
    During an interview I was asked given the following: A real estate application that lists all houses that are currently on the market (i.e., for sale) within a given distance (say for example the user wants to find all houses within 20 miles), how would you design your application (both data structure and alogirithm) to build this type of service? Any ideas? How would you implement it? I told him I didn't know becaue I've never done any geo-related stuff before.

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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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  • Number Game Algorithm

    - by 7Aces
    Problem Link - http://www.iarcs.org.in/inoi/2011/zco2011/zco2011-1b.php The task is to find the maximum score you can get in the game. Such problems, based on games, where you have to simulate, predict the result, or obtain the maximum possible score always seem to puzzle me. I can do it with recursion by considering two cases - first number picked or last number picked, each of which again branches into two states similarly, and so on... which finally can yield the max possible result. But it's a very time-inefficient approach, since time increases exponentially, due to the large test cases. What is the most pragmatic approach to the problem, and to such problems in general?

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  • Algorithm for rating books: Relative perception

    - by suneet
    So I am developing this application for rating books (think like IMDB for books) using relational database. Problem statement : Let's say book "A" deserves 8.5 in absolute sense. In case if A is the best book I have ever seen, I'll most probably rate it 9.5 whereas for someone else, it might be just an average book, so he/they will rate it less (say around 8). Let's assume 4 such guys rate it 8. If there are 10 guys who are like me (who haven't ever read great literature) and they all rate it 9.5-10. This will effectively make it's cumulative rating greater than 9 (9.5*10 + 8*4) / 14 = 9.1 whereas we needed the result to be 8.5 ... How can I take care of(normalize) this bias due to incorrect perception of individuals. MyProposedSolution : Here's one of the ways how I think it could be solved. We can have a variable Lit_coefficient which tells us how much knowledge a user has about literature. If I rate "A"(the book) 9.5 and person "X" rates it 8, then he must have read books much better than "A" and thus his Lit_coefficient should be higher. And then we can normalize the ratings according to the Lit_coefficient of user. Could there be a better algorithm/solution for the same?

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  • Technique to Solve Hard Programming logic

    - by Paresh Mayani
    I have heard about many techniques which are used by developer/software manager to solve hard programming logic or to create flow of an application and this flow will be implemented by developers to create an actual application. Some of the technique which i know, are: Flowchart Screen-Layout Data Flow Diagram E-R Diagram Algorithm of every programs I'd like to know about two facts: (1) Are there any techniques other than this ? (2) Which one is the most suitable to solve hard programming logic and process of application creation?

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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 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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  • Finding maximum number of congruent numbers

    - by Stefan Czarnecki
    Let's say we have a multiset (set with possible duplicates) of integers. We would like to find the size of the largest subset of the multiset such that all numbers in the subset are congruent to each other modulo some m 1. For example: 1 4 7 7 8 10 for m = 2 the subsets are: (1, 7, 7) and (4, 8, 10), both having size 3. for m = 3 the subsets are: (1, 4, 7, 7, 10) and (8), the larger set of size 5. for m = 4 the subsets are: (1), (4, 8), (7, 7), (10), the largest set of size 2. At this moment it is evident that the best answer is 5 for m = 3. Given m we can find the size of the largest subset in linear time. Because the answer is always equal or larger than half of the size of the set, it is enough to check for values of m upto median of the set. Also I noticed it is necessary to check for only prime values of m. However if values in the set are large the algorithm is still rather slow. Does anyone have any ideas how to improve it?

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  • If your algorithm is correct, does it matter how long it took you to write it?

    - by John Isaacks
    I recently found out that Facebook had a programming challenge that if completed correctly you automatically get a phone interview. There is a sample challenge that asks you to write an algorithm that can solve a Tower of Hanoi type problem. Given a number of pegs and discs, an initial and final configuration; Your algorithm must determine the fewest steps possible to get to the final configuration and output the steps. This sample challenge gives you a 45 minute time limit but allows you to still test your code to see if it passes once your time limit expires. I did not know of any cute math solution that could solve it, and I didn't want to look for one since I think that would be cheating. So I tried to solve the challenge the best I could on my own. I was able to make an algorithm that worked and passed. However, it took me over 4 hours to make, much longer than the 45 minute requirement. Since it took me so much longer than the allotted time, I have not attempted the actual challenge. This got me wondering though, in reality does it really matter that it took me that long? I mean is this a sign that I will not be able to get a job at a place like this (not just Facebook, but Google, Fog Creek, etc.) and need to lower my aspirations, or does the fact that I actually passed on my first attempt even though it took too long be taken as good?

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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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  • 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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  • Algorithm for flattening overlapping ranges

    - by Joseph
    I am looking for a nice way of flattening (splitting) a list of potentially-overlapping numeric ranges. The problem is very similar to that of this question: Fastest way to split overlapping date ranges, and many others. However, the ranges are not only integers, and I am looking for a decent algorithm that can be easily implemented in Javascript or Python, etc. Example Data: Example Solution: Apologies if this is a duplicate, but I am yet to find a solution.

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  • Refactoring While Programming

    - by Kirby
    When posed with a problem, particularly when it is complicated in nature, I try to take some time to think about the approach I am going to take to solve the problem. Despite this, what often happens is, as I am programming the solution, I start to think of details of the problem that I missed, and I adjust the code accordingly. What results is a mess of code that needs to be refactored. I want to "refactor as I go," but while it sounds easy enough to do, I have a really hard time doing it. When the detail that I missed is small, it is tempting to make a small update to my design, rather than erase what I've already written and write it the way it is supposed to be. It sounds like a question with an obvious answer, but are there any techniques to use to better "refactor as you go"? I know that this is a good principle, but I fail with it time and time again.

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  • How to manually detect deadlocks

    - by Dawson
    I understand the concepts of deadlock well enough, but when I'm given a problem like the one below I'm not sure how to go about solving it. I can draw a resource allocation graph, but I'm not sure how to solve it from there. Is there a better more formal way of solving this? Consider a system with five processes, P1 through P5, and five resources, R1 through R5. Resource ownership is as follows. • P1 holds R1 and wants R3 • P2 holds R2 and wants R1 • P3 holds R3 and wants R5 • P4 holds R5 and wants R2 • P5 holds R4 and wants R2 Is this system deadlocked? Justify your answer. If the system is deadlocked, list the involved processes.

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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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  • 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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  • What is the name of this array transformation?

    - by Brandon Tilley
    Start with an array of arrays; in this case, they are different lengths in order to demonstrate the technique, but they do not have to be. [[1,2,3,4], [5,6,7], [8,9,10], [11,12,13,14,15]] At the other end of the transformation, you have an array of arrays where the first array contains the first element from each of the original arrays, the second array contains the second element from each of the original arrays, and so on. [[1,5,8,11], [2,6,9,12], [3,7,10,13], [4,14], [15]] Is there a mathematical or CS term for this operation?

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  • Sorting Algorithm : output

    - by Aaditya
    I faced this problem on a website and I quite can't understand the output, please help me understand it :- Bogosort, is a dumb algorithm which shuffles the sequence randomly until it is sorted. But here we have tweaked it a little, so that if after the last shuffle several first elements end up in the right places we will fix them and don't shuffle those elements furthermore. We will do the same for the last elements if they are in the right places. For example, if the initial sequence is (3, 5, 1, 6, 4, 2) and after one shuffle we get (1, 2, 5, 4, 3, 6) we will keep 1, 2 and 6 and proceed with sorting (5, 4, 3) using the same algorithm. Calculate the expected amount of shuffles for the improved algorithm to sort the sequence of the first n natural numbers given that no elements are in the right places initially. Input: 2 6 10 Output: 2 1826/189 877318/35343 For each test case output the expected amount of shuffles needed for the improved algorithm to sort the sequence of first n natural numbers in the form of irreducible fractions. I just can't understand the output.

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