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  • How to find the number of inversions in an array ?

    - by Michael
    This is an phone interview question: "Find the number of inversions in an array". I guess they mean O(N*log N) solution since O(N^2) is trivial. I guess it cannot be better than O(N*log N) since sorting is O(N*log N) I have checked a similar question from SO and can summarize the answers as follows: Calculate half the distance the elements should be moved to sort the array : copy the array and sort the copy. For each element of the original array a[i] find it's position j in the sorted copy (binary search) and sum abs(i - j)/2. Modify merge sort : modify merge to count inversions between two sorted arrays (it takes O(N)) and run merge sort with the modified merge. Does it make sense ? Are there other (maybe simpler) solution ? Isn't it too hard for a phone interview ?

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  • Generate sample XML from composite hierarchical structure

    - by Jevgenij Nekrasov
    Let's say I have composite hierarchical structure. Each object in the structure has child collection of the same objects. Each object has XPath property, which stores the exact xpath to the element inside XML file. Right now I am trying to create an extension, which can generate XML string from that hierarchical structure, but first I want to make some sort of research what is the most efficient way to do that? ant what is the easiest way?

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  • Purpose of IF, ELSE, FOR macros ?

    - by psihodelia
    I have a source code of a library which has a lot of strange IF, ELSE, FOR, etc. macros for all common C-keywords instead of using just usual if,else,for,while keywords. These macros are defined like this: #define IF( a) if( increment_if(), a) where increment_if() function is defined so: static __inline void increment_if( void) { // If the "IF" operator comes just after an "ELSE", its counter // must not be incremented. ... //implementation } I don't really understand, what is the purpose of such macros? This library is for a real-time application and I suppose that using such macros must slow-down an application.

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  • What are the core mathematical concepts a good developer should know?

    - by Jose B.
    Since Graduating from a very small school in 2006 with a badly shaped & outdated program (I'm a foreigner & didn't know any better school at the time) I've come to realize that I missed a lot of basic concepts from a mathematical & software perspective that are mostly the foundations of other higher concepts. I.e. I tried to listen/watch the open courseware from MIT on Introduction to Algorithms but quickly realized I was missing several mathematical concepts to better understand the course. So what are the core mathematical concepts a good software engineer should know? And what are the possible books/sites you will recommend me?

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  • What is the best book for learning about Algorithms?

    - by sheats
    I know what algorithms are, but I have never consciously used or created one for any of the programming that I have done. So I'd like to get a book about the subject - I'd prefer if it was in python but that's not a strict requirement. What book about algorithms helped you most to understand, use, and create algorithms? One book per answer so they can be voted on...

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  • How to Implement AutoSize

    - by TheCloudlessSky
    I'm trying to figure out a good way to auto-size a Rectangle that has text drawn inside of it. I basically want the size to have a ratio of width/height and then "grow" according to that ratio to fit the text. I've looked at Graphics.MeasureString but I don't think it does what I'm looking for (maybe it does and I'm just using it wrong). I don't want to specify a specific width of the rectangle to be drawn, instead I want to say find the smallest width/height to fit this text but the found rectangle must have some specific ratio of width and height. This doesn't have to be specific to C#, any idea for solving this problem I'm sure can be mapped to C#. Thanks!

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  • How to find patterns (lines, circles,...) from a list of points?

    - by Burkhard
    I have a list of points. Each point being an x and y coordinate (both of which are integers). Now I'm trying to find known patterns, such as lines, arcs or circles, knowing that the points are not perfectly on the pattern. What's the best way to do it? I don't have many clues to get started. Edit: the points are ordered. The user is drawing something and the program should detect the best patterns. For instance, if a triangle is drawn, it should detect three lines.

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  • How do I find the next multiple of 10 of any integer?

    - by Tommy
    Dynamic integer will be any number from 0 to 150. i.e. - number returns 41, need to return 50. If number is 10 need to return 10. Number is 1 need to return 10. Was thinking I could use the ceiling function if I modify the integer as a decimal...? then use ceiling function, and put back to decimal? Only thing is would also have to know if the number is 1, 2 or 3 digits (i.e. - 7 vs 94 vs 136) Is there a better way to achieve this? Thank You,

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  • Fast ceiling of an integer division in C / C++

    - by andand
    Given integer values x and y, C and C++ returns as the quotient q = x/y the floor of the floating point valued equivalent. I'm interestd in a method of returning the ceiling instead? For example, ceil(10/5) = 2 and ceil(11/5) = 3. The obvious approach involves something like: q = x / y; if (q * y < x) ++q; This requires an extra comparison and multiplication; and other methods I've seen (used in fact) involve casting as a float or double. Is there a more direct method that avoids the additional multiplication (or a second division) and branch, and that also avoids casting as a floating point number?

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  • finding long repeated substrings in a massive string

    - by Will
    I naively imagined that I could build a suffix trie where I keep a visit-count for each node, and then the deepest nodes with counts greater than one are the result set I'm looking for. I have a really really long string (hundreds of megabytes). I have about 1 GB of RAM. This is why building a suffix trie with counting data is too inefficient space-wise to work for me. To quote Wikipedia's Suffix tree: storing a string's suffix tree typically requires significantly more space than storing the string itself. The large amount of information in each edge and node makes the suffix tree very expensive, consuming about ten to twenty times the memory size of the source text in good implementations. The suffix array reduces this requirement to a factor of four, and researchers have continued to find smaller indexing structures. And that was wikipedia's comments on the tree, not trie. How can I find long repeated sequences in such a large amount of data, and in a reasonable amount of time (e.g. less than an hour on a modern desktop machine)? (Some wikipedia links to avoid people posting them as the 'answer': Algorithms on strings and especially Longest repeated substring problem ;-) )

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  • What's a good way to add a large number of small floats together?

    - by splicer
    Say you have 100000000 32-bit floating point values in an array, and each of these floats has a value between 0.0 and 1.0. If you tried to sum them all up like this result = 0.0; for (i = 0; i < 100000000; i++) { result += array[i]; } you'd run into problems as result gets much larger than 1.0. So what are some of the ways to more accurately perform the summation?

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  • Optimality of Binary Search

    - by templatetypedef
    Hello all- This may be a silly question, but does anyone know of a proof that binary search is asymptotically optimal? That is, if we are given a sorted list of elements where the only permitted operation on those objects is a comparison, how do you prove that the search can't be done in o(lg n)? (That's little-o of lg n, by the way.) Note that I'm restricting this to elements where the only operation permitted operation is a comparison, since there are well-known algorithms that can beat O(lg n) on expectation if you're allowed to do more complex operations on the data (see, for example, interpolation search). Thanks so much! This has really been bugging me since it seems like it should be simple but has managed to resist all my best efforts. :-)

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  • Stuck on solving the Minimal Spanning Tree problem.

    - by kunjaan
    I have reduced my problem to finding the minimal spanning tree in the graph. But I want to have one more constraint which is that the total degree for each vertex shouldnt exceed a certain constant factor. How do I model my problem? Is MST the wrong path? Do you know any algorithms that will help me? One more problem: My graph has duplicate edge weights so is there a way to count the number of unique MSTs? Are there algorithms that do this? Thank You. Edit: By degree, I mean the total number of edges connecting the vertex. By duplicate edge weight I mean that two edges have the same weight.

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  • How to find kth minimal element in the union of two sorted arrays?

    - by Michael
    This is a homework question. They say it takes O(logN + logM) where N and M are the arrays lengths. Let's name the arrays a and b. Obviously we can ignore all a[i] and b[i] where i k. First let's compare a[k/2] and b[k/2]. Let b[k/2] a[k/2]. Therefore we can discard also all b[i], where i k/2. Now we have all a[i], where i < k and all b[i], where i < k/2 to find the answer. What is the next step?

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  • Using MySQL as a job queue

    - by user237815
    I'd like to use MySQL as a job queue. Multiple machines will be producing and consuming jobs. Jobs need to be scheduled; some may run every hour, some every day, etc. It seems fairly straightforward: for each job, have a "nextFireTime" column, and have worker machines search for the job with the nextFireTime, change the status of the record to "inProcess", and then update the nextFireTime when the job ends. The problem comes in when a worker dies silently. It won't be able to update the nextFireTime or set the status back to "idle". Unfortunately, jobs can be long-running, so a reaper thread that looks for jobs that have been inProcess too long isn't an option. There's no timeout value that would work. Can anyone suggest a design pattern that would properly handle unreliable worker machines?

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  • How to store and collect data for mining such information as most viewed for last 24 hours, last 7 d

    - by Kirzilla
    Hello, Let's imagine that we have high traffic project (a tube site) which should provide sorting using this options (NOT IN REAL TIME). Number of videos is about 200K and all information about videos is stored in MySQL. Number of daily video views is about 1.5KK. As instruments we have Hard Disk Drive (text files), MySQL, Redis. Views top viewed top viewed last 24 hours top viewed last 7 days top viewed last 30 days top rated last 365 days How should I store such information? The first idea is to log all visits to text files (single file per hour, for example visits_20080101_00.log). At the beginning of each hour calculate views per video for previous hour and insert this information into MySQL. Then recalculate totals (for last 24 hours) and update statistics in tables. At the beginning of every day we have to do the same but recalculate for last 7 days, last 30 days, last 365 days. This method seems to be very poor for me because we have to store information about last 365 days for each video to make correct calculations. Is there any other good methods? Probably, we have to choose another instruments for this? Thank you.

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  • List circular group membership from active directory

    - by KAPes
    We have 40K+ groups in our active directory and we are increasingly facing problem of circular nested groups which are creating problems for some applications. Does anyone know how to list down the full route through which a circular group membership exists ? e.g. G1 --> G2 --> G3 --> G4 --> G1 How do I list it down.

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  • Recursion - Ship Battle

    - by rgorrosini
    I'm trying to write a little ship battle game in java. It is 100% academic, I made it to practice recursion, so... I want to use it instead of iteration, even if it's simpler and more efficient in most some cases. Let's get down to business. These are the rules: Ships are 1, 2 or 3 cells wide and are placed horizontally only. Water is represented with 0, non-hit ship cells are 1, hit ship cells are 2 and sunken ships have all it's cells in 3. With those rules set, I'm using the following array for testing: int[][] board = new int[][] { {0, 1, 2, 0, 1, 0}, {0, 0, 1, 1, 1, 0}, {0, 3, 0, 0, 0, 0}, {0, 0, 2, 1, 2, 0}, {0, 0, 0, 1, 1, 1}, }; It works pretty good so far, and to make it more user-friendly I would like to add a couple of reports. these are the methods I need for them: Given the matrix, return the amount of ships in it. Same as a), but separating them by state (amount of non-hit ships, hit and sunken ones). I will need a hand with those reports, and I would like to get some ideas. Remember it must be done using recursion, I want to understand this, and the only way to go is practice! Thanks a lot for your time and patience :).

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  • Efficient way to get highly correlated pairs from large data set in Python or R

    - by Akavall
    I have a large data set (Let's say 10,000 variables with about 1000 elements each), we can think of it as 2D list, something like: [[variable_1], [variable_2], ............ [variable_n] ] I want to extract highly correlated variable pairs from that data. I want "highly correlated" to be a parameter that I can choose. I don't need all pairs to be extracted, and I don't necessarily want the most correlated pairs. As long as there is an efficient method that gets me highly correlated pairs I am happy. Also, it would be nice if a variable does not show up in more than one pair. Although this might not be crucial. Of course, there is a brute force way to finding such pairs, but it is too slow for me. I've googled around for a bit and found some theoretical work on this issue, but I wasn't able for find a package that could do what I am looking for. I mostly work in python, so a package in python would be most helpful, but if there exists a package in R that does what I am looking for it will be great. Does anyone know of a package that does the above in Python or R? Or any other ideas? Thank You in Advance

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  • Why is Dictionary.First() so slow?

    - by Rotsor
    Not a real question because I already found out the answer, but still interesting thing. I always thought that hash table is the fastest associative container if you hash properly. However, the following code is terribly slow. It executes only about 1 million iterations and takes more than 2 minutes of time on a Core 2 CPU. The code does the following: it maintains the collection todo of items it needs to process. At each iteration it takes an item from this collection (doesn't matter which item), deletes it, processes it if it wasn't processed (possibly adding more items to process), and repeats this until there are no items to process. The culprit seems to be the Dictionary.Keys.First() operation. The question is why is it slow? Stopwatch watch = new Stopwatch(); watch.Start(); HashSet<int> processed = new HashSet<int>(); Dictionary<int, int> todo = new Dictionary<int, int>(); todo.Add(1, 1); int iterations = 0; int limit = 500000; while (todo.Count > 0) { iterations++; var key = todo.Keys.First(); var value = todo[key]; todo.Remove(key); if (!processed.Contains(key)) { processed.Add(key); // process item here if (key < limit) { todo[key + 13] = value + 1; todo[key + 7] = value + 1; } // doesn't matter much how } } Console.WriteLine("Iterations: {0}; Time: {1}.", iterations, watch.Elapsed); This results in: Iterations: 923007; Time: 00:02:09.8414388. Simply changing Dictionary to SortedDictionary yields: Iterations: 499976; Time: 00:00:00.4451514. 300 times faster while having only 2 times less iterations. The same happens in java. Used HashMap instead of Dictionary and keySet().iterator().next() instead of Keys.First().

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  • 3-clique counting in a graph

    - by Legend
    I am operating on a (not so) large graph having about 380K edges. I wrote a program to count the number of 3-cliques in the graph. A quick example: List of edges: A - B B - C C - A C - D List of cliques: A - B - C A 3-clique is nothing but a triangle in a graph. Currently, I am doing this using PHP+MySQL. As expected, it is not fast enough. Is there a way to do this in pure MySQL? (perhaps a way to insert all 3-cliques into a table?)

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