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  • What is the better approach to find if a given set is a perfect subset of a set - If given subset is

    - by Microkernel
    Hi guys, What is the best approach to find if a given set(unsorted) is a perfect subset of a main set. I got to do some validation in my program where I got to compare the clients request set with the registered internal capability set. I thought of doing by having internal capability set sorted(will not change once registered) and do Binary search for each element in the client's request set. Is it the best I could get? I suspected that there might be better approach. Any idea? Regards, Microkernel

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  • PHP Modify Array

    - by Ozzy
    Hi all, I have the following array: array(a, a, a, b, b, c, c, c, c, d, d); When I loop through it and echo it, the result is: a a a b b c c c c d d How ever I want to echo it in such a way that it displays: a b c d a b c d a c c Here is the array in a grid to better explain what im trying to achieve Current a a a b b c c c c d d What im tryin to do a b c d a b c d a c c How would I do this?

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  • Lexographical sorting problem

    - by Shawn Mclean
    I'm doing a problem that says concatenate the words to generate the lexicographically lowest possible string. from a competition. Take for example this string: jibw ji jp bw jibw The actual output turns out to be: bw jibw jibw ji jp When I do sorting on this, I get: bw ji jibw jibw jp. Does this mean that this is not sorting? If it is sorting, does lexicographic sorting take into consideration pushing the shorter strings to the back or something? I've been doing some reading on lexigographical order and I dont see any point or scenarios on which this is used, do you have any?

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  • 'Fixed' for loop - what is more efficient?

    - by pimvdb
    I'm creating a tic-tac-toe game, and one of the functions has to iterate through each of the 9 fields (tic-tac-toe is played on a 3x3 grid). I was wondering what is more efficient (which one is perhaps faster, or what is the preferred way of scripting in such situation) - using two for nested loops like this: for(var i=0; i<3; i++) { for(var j=0; j<3; j++) { checkField(i, j); } } or hard-coding it like this: checkField(0, 0); checkField(0, 1); checkField(0, 2); checkField(1, 0); checkField(1, 1); checkField(1, 2); checkField(2, 0); checkField(2, 1); checkField(2, 2); As there are only 9 combinations, it would be perhaps overkill to use two nested for loops, but then again this is clearer to read. The for loop, however, will increment variables and check whether i and j are smaller than 3 every time as well. In this example, the time saving at least might be negligible, but what is the preferred way of coding in this case? Thanks.

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  • What is it about Fibonacci numbers?

    - by Ian Bishop
    Fibonacci numbers have become a popular introduction to recursion for Computer Science students and there's a strong argument that they persist within nature. For these reasons, many of us are familiar with them. They also exist within Computer Science elsewhere too; in surprisingly efficient data structures and algorithms based upon the sequence. There are two main examples that come to mind: Fibonacci heaps which have better amortized running time than binomial heaps. Fibonacci search which shares O(log N) running time with binary search on an ordered array. Is there some special property of these numbers that gives them an advantage over other numerical sequences? Is it a density quality? What other possible applications could they have? It seems strange to me as there are many natural number sequences that occur in other recursive problems, but I've never seen a Catalan heap.

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  • Moving a unit precisely along a path in x,y coordinates

    - by Adam Eberbach
    I am playing around with a strategy game where squads move around a map. Each turn a certain amount of movement is allocated to a squad and if the squad has a destination the points are applied each turn until the destination is reached. Actual distance is used so if a squad moves one position in the x or y direction it uses one point, but moving diagonally takes ~1.4 points. The squad maintains actual position as float which is then rounded to allow drawing the position on the map. The path is described by touching the squad and dragging to the end position then lifting the pen or finger. (I'm doing this on an iPhone now but Android/Qt/Windows Mobile would work the same) As the pointer moves x, y points are recorded so that the squad gains a list of intermediate destinations on the way to the final destination. I'm finding that the destinations are not evenly spaced but can be further apart depending on the speed of the pointer movement. Following the path is important because obstacles or terrain matter in this game. I'm not trying to remake Flight Control but that's a similar mechanic. Here's what I've been doing, but it just seems too complicated (pseudocode): getDestination() { - self.nextDestination = remove_from_array(destinations) - self.gradient = delta y to destination / delta x to destination - self.angle = atan(self.gradient) - self.cosAngle = cos(self.angle) - self.sinAngle = sin(self.angle) } move() { - get movement allocation for this turn - if self.nextDestination not valid - - getNextDestination() - while(nextDestination valid) && (movement allocation remains) { - - find xStep and yStep using movement allocation and sinAngle/cosAngle calculated for current self.nextDestination - - if current position + xStep crosses the destination - - - find x movement remaining after self.nextDestination reached - - - calculate remaining direct path movement allocation (xStep remaining / cosAngle) - - - make self.position equal to self.nextDestination - - else - - - apply xStep and yStep to current position - } - round squad's float coordinates to integer screen coordinates - draw squad image on map } That's simplified of course, stuff like sign needs to be tweaked to ensure movement is in the right direction. If trig is the best way to do it then lookup tables can be used or maybe it doesn't matter on modern devices like it used to. Suggestions for a better way to do it? an update - iPhone has zero issues with trig and tracking tens of positions and tracks implemented as described above and it draws in floats anyway. The Bresenham method is more efficient, trig is more precise. If I was to use integer Bresenham I would want to multiply by ten or so to maintain a little more positional accuracy to benefit collisions/terrain detection.

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  • Finding the largest subtree in a BST

    - by rakeshr
    Given a binary tree, I want to find out the largest subtree which is a BST in it. Naive approach: I have a naive approach in mind where I visit every node of the tree and pass this node to a isBST function. I will also keep track of the number of nodes in a sub-tree if it is a BST. Is there a better approach than this ?

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  • How to generate a number in arbitrary range using random()={0..1} preserving uniformness and density?

    - by psihodelia
    Generate a random number in range [x..y] where x and y are any arbitrary floating point numbers. Use function random(), which returns a random floating point number in range [0..1] from P uniformly distributed numbers (call it "density"). Uniform distribution must be preserved and P must be scaled as well. I think, there is no easy solution for such problem. To simplify it a bit, I ask you how to generate a number in interval [-0.5 .. 0.5], then in [0 .. 2], then in [-2 .. 0], preserving uniformness and density? Thus, for [0 .. 2] it must generate a random number from P*2 uniformly distributed numbers. The obvious simple solution random() * (x - y) + y will generate not all possible numbers because of the lower density for all abs(x-y)>1.0 cases. Many possible values will be missed. Remember, that random() returns only a number from P possible numbers. Then, if you multiply such number by Q, it will give you only one of P possible values, scaled by Q, but you have to scale density P by Q as well.

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  • incremental way of counting quantiles for large set of data

    - by Gacek
    I need to count the quantiles for a large set of data. Let's assume we can get the data only through some portions (i.e. one row of a large matrix). To count the Q3 quantile one need to get all the portions of the data and store it somewhere, then sort it and count the quantile: List<double> allData = new List<double>(); foreach(var row in matrix) // this is only example. In fact the portions of data are not rows of some matrix { allData.AddRange(row); } allData.Sort(); double p = 0.75*allData.Count; int idQ3 = (int)Math.Ceiling(p) - 1; double Q3 = allData[idQ3]; Now, I would like to find a way of counting this without storing the data in some separate variable. The best solution would be to count some parameters od mid-results for first row and then adjust it step by step for next rows. Note: These datasets are really big (ca 5000 elements in each row) The Q3 can be estimated, it doesn't have to be an exact value. I call the portions of data "rows", but they can have different leghts! Usually it varies not so much (+/- few hundred samples) but it varies! This question is similar to this one: http://stackoverflow.com/questions/1058813/on-line-iterator-algorithms-for-estimating-statistical-median-mode-skewness But I need to count quantiles. ALso there are few articles in this topic, i.e.: http://web.cs.wpi.edu/~hofri/medsel.pdf http://portal.acm.org/citation.cfm?id=347195&dl But before I would try to implement these, I wanted to ask you if there are maybe any other, qucker ways of counting the 0.25/0.75 quantiles?

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  • Travelling Salesman Problem Constraint Representation

    - by alex25
    Hey! I read a couple of articles and sample code about how to solve TSP with Genetic Algorithms and Ant Colony Optimization etc. But everything I found didn't include time (window) constraints, eg. "I have to be at customer x before 12am)" and assumed symmetry. Can somebody point me into the direction of some sample code or articles that explain how I can add constraints to TSP and how I can represent those in code. Thanks!

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  • Compact data structure for storing a large set of integral values

    - by Odrade
    I'm working on an application that needs to pass around large sets of Int32 values. The sets are expected to contain ~1,000,000-50,000,000 items, where each item is a database key in the range 0-50,000,000. I expect distribution of ids in any given set to be effectively random over this range. The operations I need on the set are dirt simple: Add a new value Iterate over all of the values. There is a serious concern about the memory usage of these sets, so I'm looking for a data structure that can store the ids more efficiently than a simple List<int>or HashSet<int>. I've looked at BitArray, but that can be wasteful depending on how sparse the ids are. I've also considered a bitwise trie, but I'm unsure how to calculate the space efficiency of that solution for the expected data. A Bloom Filter would be great, if only I could tolerate the false negatives. I would appreciate any suggestions of data structures suitable for this purpose. I'm interested in both out-of-the-box and custom solutions. EDIT: To answer your questions: No, the items don't need to be sorted By "pass around" I mean both pass between methods and serialize and send over the wire. I clearly should have mentioned this. There could be a decent number of these sets in memory at once (~100).

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  • Find the element with the most "neighbors" in a sequence

    - by Bao An
    Assume that we have a sequence S with n elements <x1,x2,...,xn>. A pair of elements xi,xj are considered neighbors if |xi-xj|<d, with d a given distance between two neighbors. So how can find out the element that has most neighbors in the sequence? (A simply way is sorting the sequence and then calculating number of each element but it's time complexity is quite large): O(nlogn) May you please help me find a better way to reduce time complexity?

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  • Revisions: algorithm and data structure

    - by SODA
    Hi, I need ideas for structuring and processing data with revisions. For example, I have a database of objects (e.g. cars). Each object has a number of properties, which can be arbitrary, so there's no a set schema to describe these objects. These objects are probably saved as key-value pairs. Now I need to change property of an object. I don't want to completely rewrite it - I want to be able to go back and see history of changes to these properties, that's why I want to add new property and keep the old one (so I guess a timestamp would do the job of telling which property is the latest). At the same time I want to be able to get info about any object in a snap, with only latest versions of each of the properties. Any ideas what would be the best approach? At least please point me in the right direction. Thanks!

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  • Is there a name for the technique of using base-2 numbers to encode a list of unique options?

    - by Lunatik
    Apologies for the rather vague nature of this question, I've never been taught programming and Google is rather useless to a self-help guy like me in this case as the key words are pretty ambiguous. I am writing a couple of functions that encode and decode a list of options into a Long so they can easily be passed around the application, you know this kind of thing: 1 - Apple 2 - Orange 4 - Banana 8 - Plum etc. In this case the number 11 would represent Apple, Orange & Plum. I've got it working but I see this used all the time so assume there is a common name for the technique, and no doubt all sorts of best practice and clever algorithms that are at the moment just out of my reach.

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  • Avoiding dog-piling or thundering herd in a memcached expiration scenario

    - by Quintin Par
    I have the result of a query that is very expensive. It is the join of several tables and a map reduce job. This is cached in memcached for 15 minutes. Once the cache expires the queries are obviously run and the cache warmed again. But at the point of expiration the thundering herd problem issue can happen. One way to fix this problem, that I do right now is to run a scheduled task that kicks in the 14th minute. But somehow this looks very sub optimal to me. Another approach I like is nginx’s proxy_cache_use_stale updating; mechanism. The webserver/machine continues to deliver stale cache while a thread kicks in the moment expiration happens and updates the cache. Has someone applied this to memcached scenario though I understand this is a client side strategy? If it benefits, I use Django.

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  • Pecking order of pigeons?

    - by sc_ray
    I was going though problems on graph theory posted by Prof. Ericksson from my alma-mater and came across this rather unique question about pigeons and their innate tendency to form pecking orders. The question goes as follows: Whenever groups of pigeons gather, they instinctively establish a pecking order. For any pair of pigeons, one pigeon always pecks the other, driving it away from food or potential mates. The same pair of pigeons always chooses the same pecking order, even after years of separation, no matter what other pigeons are around. Surprisingly, the overall pecking order can contain cycles—for example, pigeon A pecks pigeon B, which pecks pigeon C, which pecks pigeon A. Prove that any finite set of pigeons can be arranged in a row from left to right so that every pigeon pecks the pigeon immediately to its left. Since this is a question on Graph theory, the first things that crossed my mind that is this just asking for a topological sort of a graphs of relationships(relationships being the pecking order). What made this a little more complex was the fact that there can be cyclic relationships between the pigeons. If we have a cyclic dependency as follows: A-B-C-A where A pecks on B,B pecks on C and C goes back and pecks on A If we represent it in the way suggested by the problem, we have something as follows: C B A But the above given row ordering does not factor in the pecking order between C and A. I had another idea of solving it by mathematical induction where the base case is for two pigeons arranged according to their pecking order, assuming the pecking order arrangement is valid for n pigeons and then proving it to be true for n+1 pigeons. I am not sure if I am going down the wrong track here. Some insights into how I should be analyzing this problem will be helpful. Thanks

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  • How does Amazon's Statistically Improbable Phrases work?

    - by ??iu
    How does something like Statistically Improbable Phrases work? According to amazon: Amazon.com's Statistically Improbable Phrases, or "SIPs", are the most distinctive phrases in the text of books in the Search Inside!™ program. To identify SIPs, our computers scan the text of all books in the Search Inside! program. If they find a phrase that occurs a large number of times in a particular book relative to all Search Inside! books, that phrase is a SIP in that book. SIPs are not necessarily improbable within a particular book, but they are improbable relative to all books in Search Inside!. For example, most SIPs for a book on taxes are tax related. But because we display SIPs in order of their improbability score, the first SIPs will be on tax topics that this book mentions more often than other tax books. For works of fiction, SIPs tend to be distinctive word combinations that often hint at important plot elements. For instance, for Joel's first book, the SIPs are: leaky abstractions, antialiased text, own dog food, bug count, daily builds, bug database, software schedules One interesting complication is that these are phrases of either 2 or 3 words. This makes things a little more interesting because these phrases can overlap with or contain each other.

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  • Typecasting a floating value or using the math.h floor* functions?

    - by nobody
    Hi, I am coding up an implementation of Interpolation Search in C. The question is actually rather simple, I need to use the floating operations to do linear interpolation to find the correct index which will eventually be an integer result. In particular my probe index is: t = i + floor((((k-low)/(high-low)) * (j-i))); where, i,j,k,t are unsigned ints, and high,low are doubles. Would this be equivalent to: t = i + (unsigned int)(((k-low)/(high-low)) * (j-i)); Is there any reason I would actually want to use math.h floor* functions over just a simple (int) typecast?

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  • How can I test if a point lies within a 3d shape with its surface defined by a point cloud?

    - by Ben
    Hi I have a collection of points which describe the surface of a shape that should be roughly spherical, and I need a method with which to determine if any other given point lies within this shape. I've previously been approximating the shape as an exact sphere, but this has proven too inaccurate and I need a more accurate method. Simplicity and speed is favourable over complete accuracy, a good approximation will suffice. I've come across techniques for converting a point cloud to a 3d mesh, but most things I have found have been very complicated, and I am looking for something as simple as possible. Any ideas? Many thanks, Ben.

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  • How can I group an array of rectangles into "Islands" of connected regions?

    - by Eric
    The problem I have an array of java.awt.Rectangles. For those who are not familiar with this class, the important piece of information is that they provide an .intersects(Rectangle b) function. I would like to write a function that takes this array of Rectangles, and breaks it up into groups of connected rectangles. Lets say for example, that these are my rectangles (constructor takes the arguments x, y, width,height): Rectangle[] rects = new Rectangle[] { new Rectangle(0, 0, 4, 2), //A new Rectangle(1, 1, 2, 4), //B new Rectangle(0, 4, 8, 2), //C new Rectangle(6, 0, 2, 2) //D } A quick drawing shows that A intersects B and B intersects C. D intersects nothing. A tediously drawn piece of ascii art does the job too: +-------+ +---+ ¦A+---+ ¦ ¦ D ¦ +-+---+-+ +---+ ¦ B ¦ +-+---+---------+ ¦ +---+ C ¦ +---------------+ Therefore, the output of my function should be: new Rectangle[][]{ new Rectangle[] {A,B,C}, new Rectangle[] {D} } The failed code This was my attempt at solving the problem: public List<Rectangle> getIntersections(ArrayList<Rectangle> list, Rectangle r) { List<Rectangle> intersections = new ArrayList<Rectangle>(); for(Rectangle rect : list) { if(r.intersects(rect)) { list.remove(rect); intersections.add(rect); intersections.addAll(getIntersections(list, rect)); } } return intersections; } public List<List<Rectangle>> mergeIntersectingRects(Rectangle... rectArray) { List<Rectangle> allRects = new ArrayList<Rectangle>(rectArray); List<List<Rectangle>> groups = new ArrayList<ArrayList<Rectangle>>(); for(Rectangle rect : allRects) { allRects.remove(rect); ArrayList<Rectangle> group = getIntersections(allRects, rect); group.add(rect); groups.add(group); } return groups; } Unfortunately, there seems to be an infinite recursion loop going on here. My uneducated guess would be that java does not like me doing this: for(Rectangle rect : allRects) { allRects.remove(rect); //... } Can anyone shed some light on the issue?

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  • Aligning music notes using String matching algorithms or Dynamic Programming

    - by Dolphin
    Hi I need to compare 2 sets of musical pieces (i.e. a playing-taken in MIDI format-note details extracted and saved in a database table, against sheet music-taken into XML format). When evaluating playing against sheet music (i.e.note details-pitch, duration, rhythm), note alignment needs to be done - to identify missed/extra/incorrect/swapped notes that from the reference (sheet music) notes. I have like 1800-2500 notes in one piece approx (can even be more-with polyphonic, right now I'm doing for monophonic). So will I have to have all these into an array? Will it be memory overloading or stack overflow? There are string matching algorithms like KMP, Boyce-Moore. But note alignment can also be done through Dynamic Programming. How can I use Dynamic Programming to approach this? What are the available algorithms? Is it about approximate string matching? Which approach is much productive? String matching algos like Boyce-Moore, or dynamic programming? How can I assess which is more effective? Greatly appreciate any insight or suggestions Thanks in advance

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  • Most Frequent 3 page sequence in a weblog

    - by Sundararajan S
    Given a web log which consists of fields 'User ' 'Page url'. We have to find out the most frequent 3-page sequence that users takes. There is a time stamp. and it is not guaranteed that the single user access will be logged sequentially it could be like user1 Page1 user2 Pagex user1 Page2 User10 Pagex user1 Page 3 her User1s page sequence is page1- page2- page 3

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