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  • algorithm - How to sort a 0/1 array with 2n/3 comparisons?

    - by Jackson Tale
    In Algorithm Design Manual, there is such an excise 4-26 Consider the problem of sorting a sequence of n 0’s and 1’s using comparisons. For each comparison of two values x and y, the algorithm learns which of x < y, x = y, or x y holds. (a) Give an algorithm to sort in n - 1 comparisons in the worst case. Show that your algorithm is optimal. (b) Give an algorithm to sort in 2n/3 comparisons in the average case (assuming each of the n inputs is 0 or 1 with equal probability). Show that your algorithm is optimal. For (a), I think it is fairly easy. I can choose a[n-1] as pivot, then do something like in quicksort partition, scan 0 to n - 2, find the middle point where left side is all 0 and right side is all 1, this take n - 1 comparisons. But for (b), I can't get a clue. It says "each of the n inputs is 0 or 1 with equal probability", so I guess I can assume the numbers of 0 and 1 equal? But how can I get a result which is related to 1/3? divide the whole array into 3 groups? Thanks

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  • Is there an efficient algorithm to distribute resources in a way that both avoids conflict and allows bias?

    - by Steve V.
    Background (Skip this if you only care about the algorithm) At the university where I work, one of the biggest hassles in our department is classroom scheduling. For illustration purposes and to lay out the scope of the problem, here's how we do scheduling now: Professors give us a list of the classes they're teaching with the time slots they'd prefer to teach, ranked in order of priority (most desired to least desired). Administration gives us a list of the rooms we may assign along with the times those rooms are available for our department's use. We start assigning professors to rooms trying (at first) to take into account the preferences of the various professors. Inevitably, conflicts arise, professors start asking for changes, and the plan falls to pieces somewhere around professor number 30, at which point we start assigning rooms basically wherever we can fit them in, crumpled pieces of paper are everywhere, and nobody's happy. (If you've ever wondered why your class was at 9.30 in the morning on Thursday but 4 pm every other day, now you know) I have been asked to quietly investigate whether software could do this more optimally. The Actual Question Is there an algorithm to efficiently schedule a set of resources such that the following criteria are met: The algorithm must never assign two professors to the same room at the same time. The task is not complete until every professor has been assigned a room / time. The algorithm need not worry about having too many professors for the amount of time slots available. (We're not that well funded.) As much as is possible the algorithm should respect the scheduling preferences of the individual professors. I feel like I can't be the first one to ask this. Is there a efficient algorithm for this, or is this the sort of problem that can only be brute-forced?

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  • How to optimize neural network by using genetic algorithm?

    - by Billy Coen
    I'm quite new with this topic so any help would be great. What i need is to optimize a neural network in MATLAB by using GA. My network has [2x98] input and [1x98] target, i've tried consulting matlab help but im still kind of clueless about what to do :( so, any help would be appreciated. Thanks in advance. edit: i guess i didn't say what is there to be optimized as Dan said in the 1st answer. I guess most important thing is number of hidden neurons. And maybe number of hidden layers and training parameters like number of epochs or so. Sorry for not providing enough info, i'm still learning about this.

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  • Rather than sending in numbers, having code passed to an individual in genetic programming? ECJ

    - by sieve411
    I'm using ECJ with Java. I have an army of individuals who I all want to have the same brain. Basically, I'd like to evolve the brains using GP. I want things like "if-on-enemy-territory" and "if-sense-target" for if statements and "go-home" or "move-randomly" or "shoot" for terminals. However, these statements need to be full executable Java code. How can I do this with ECJ?

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  • How do you avoid an invalid search space in a genetic algorithm?

    - by Dave
    I am developing a GA for a school project and I've noticed that upon evaluating my functions for fitness, an individual is equivalent to its inverse. For example, the set (1, 1, -1, 1) is equivalent to (-1, -1, 1, -1). To shrink my search space and reach a solution more efficiently, how can I avoid my crossovers from searching in this second half of the search space?

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  • Designing for an algorithm that reports progress

    - by Stefano Borini
    I have an iterative algorithm and I want to print the progress. However, I may also want it not to print any information, or to print it in a different way, or do other logic. In an object oriented language, I would perform the following solutions: Solution 1: virtual method have the algorithm class MyAlgoClass which implements the algo. The class also implements a virtual reportIteration(iterInfo) method which is empty and can be reimplemented. Subclass the MyAlgoClass and override reportIteration so that it does what it needs to do. This solution allows you to carry additional information (for example, the file unit) in the reimplemented class. I don't like this method because it clumps together two functionalities that may be unrelated, but in GUI apps it may be ok. Solution 2: observer pattern the algorithm class has a register(Observer) method, keeps a list of the registered observers and takes care of calling notify() on each of them. Observer::notify() needs a way to get the information from the Subject, so it either has two parameters, one with the Subject and the other with the data the Subject may pass, or just the Subject and the Observer is now in charge of querying it to fetch the relevant information. Solution 3: callbacks I tend to see the callback method as a lightweight observer. Instead of passing an object, you pass a callback, which may be a plain function, but also an instance method in those languages that allow it (for example, in python you can because passing an instance method will remain bound to the instance). C++ however does not allow it, because if you pass a pointer to an instance method, this will not be defined. Please correct me on this regard, my C++ is quite old. The problem with callbacks is that generally you have to pass them together with the data you want the callback to be invoked with. Callbacks don't store state, so you have to pass both the callback and the state to the Subject in order to find it at callback execution, together with any additional data the Subject may provide about the event is reporting. Question My question is relative to the fact that I need to implement the opening problem in a language that is not object oriented, namely Fortran 95, and I am fighting with my usual reasoning which is based on python assumptions and style. I think that in Fortran the concept is similar to C, with the additional trouble that in C you can store a function pointer, while in Fortran 95 you can only pass it around. Do you have any comments, suggestions, tips, and quirks on this regard (in C, C++, Fortran and python, but also in any other language, so to have a comparison of language features that can be exploited on this regard) on how to design for an algorithm that must report progress to some external entity, using state from both the algorithm and the external entity ?

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  • Is there any super fast algorithm for finding LINES on picture?

    - by Ole Jak
    So I have Image like this I need some super fast algorithm for finding all straight lines on it. I want to give to algorithm parameters like min length and max line distortion. I want to get relative to picture pixel coords start and end points of lines. So on this picture to find all lines between dalles and thouse 2 black lines on top. So I need algorithm for super fast finding straight lines of different colors on picture. Is there any such algorithm? (super duper fast=)

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  • Algorithm for nice graph labels for time/date axis?

    - by Aaron
    Hello, I'm looking for a "nice numbers" algorithm for determining the labels on a date/time value axis. I'm familar with Paul Heckbert's Nice Numbers algorithm (http://tinyurl.com/5gmk2c). I have a plot that displays time/date on the X axis and the user can zoom in and look at a smaller time frame. I'm looking for an algorithm that picks nice dates to display on the ticks. For example: Looking at a day or so: 1/1 12:00, 1/1 4:00, 1/1 8:00... Looking at a week: 1/1, 1/2, 1/3... Looking at a month: 1/09, 2/09, 3/09... The nice label ticks don't need to correspond to the first visible point, but close to it. Is anybody familar with such an algorithm? Thanks

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  • Algorithm for a lucky game [on hold]

    - by Ronnie
    Assume we have the following Keno(lottery type) game: From 80 numbers(from 1 to 80), 20 are being drawn. The players choose 1 or 2 or 3..... or 12 numbers to play(12 categories). If they choose for example 4 then they win if they predict correctly a certain amount of numbers(2,3 or 4) from the 4 they have played and lose if the predict only 1 or 0 numbers. They win X times their money accordingly to some predefined factor depending on how many numbers they predict from each category. The same with the other categories. And e.g 11 out of 11 gives 250000 times your money and 12 out of 12 gives 1000000 your money. So the company would want to avoid winnings so high. Every draw by the company is being made every 5 minutes and in each draw around 120000 (let's say) different predictions(Keno tickets) are being played. Let's assume 12000 are being played in category 10 and 12000 in category 11 and also 12000 in category 12. I'm wondering if there is an algorithm to allow the company that provides the game in the 5 minutes between the drawings, to find a 20 number set, in order to avoid any "12 out of 12" and "11 out of 11" and "11 out of 12" and "10 out of 11" and "10 out of 10" winning ticket. That means is there any algorithm, where in a time of less than 1 minute approximately(in todays hardware), to be able to find a 20 number set so that none of the 12000 12 and 11 and 10 number sets that the players played(in categories 10,11 and 12) contains any winning of "12 out of 12" and "11 out of 11" and "11 out of 12" and "10 out of 11" and "10 out of 10"? Or even better the generalization of the problem: What is the best algorithm(from a perspective of minimal time), to be able to find a Y number set from numbers 1 to Z(e.g Y=20, Z=80) so that none of the X sets of K-numbers that are being played(in category K) contains more than K-m numbers from the Y-set? (Note that for Y=K and m=1 there is a practical algorithm.)

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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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  • How to use TCP/IP Nagle algorithm at Apple Push Notification

    - by Mahbubur R Aaman
    From Apple's Developer Library The binary interface employs a plain TCP socket for binary content that is streaming in nature. For optimum performance, you should batch multiple notifications in a single transmission over the interface, either explicitly or using a TCP/IP Nagle algorithm. How to use TCP/IP Nagle algorithm in case Apple's Push Notification? How to batch multiple notification in a single transmission over the interface? Additional # In Apple's Push Notification Urban Airship is a familiar name to send large amount of push notification within several minutes. Does they use TCP/IP Nagle algorithm?

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  • How can I locate empty space next to polygon regions?

    - by Stephen
    Let's say I have the following area in a top-down map: The circle is the player, the black square is an obstacle, and the grey polygons with red borders are walk-able areas that will be used as a navigation mesh for enemies. Obstacles and grey polygons are always convex. The grey regions were defined using an algorithm when the world was generated at runtime. Notice the little white column. I need to figure out where any empty space like this is, if at all, after the algorithm builds the grey regions, so that I can fill the space with another region. Basically what I'm hoping for is an algorithm that can detect empty space next to a polygon.

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  • moore's law and quadratic algorithm

    - by damon
    I was going thru a video (from coursera - by sedgewick) in which he argues that you cannot sustain Moore's law using a quadratic algorithm.He elaborates like this In year 197* you build a computer of power X ,and need to count N objects.This takes M days According to Moore's law,you have a computer of power 2X after 1.5 years.But now you have 2N objects to count. If you use a quadratic algorithm, In year 197*+1.5 ,it takes (4M)/2 = 2M days 4M because the algorithm is quadratic,and division by 2 because of doubling computer power. I find this hard to understand.I tried to work thru this as below To count N objects using comp=X , it takes M days. -> N/X = M After 1.5 yrs ,you need to count 2N objects using comp=2X -> 2N/(2X) -> N/X -> M days where do I go wrong? can someone please help me understand?

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  • Tangent basis calculation problem

    - by Kirill Daybov
    I have the problem with seams with calculating a tangent basis in my application. I'm using a seems to be right algorithm, but it gives wrong result on the seams. What am I doing wrong? Is there a problem with an algorithm, or with the model? The designer says that our models with our normal maps are rendered correctly in Xoliul Shader Plugin in 3Ds Max, so there should be a way to calculate correct tangent basis programmatically. Here's an example of the problem I'm talking about. Steps, I've already taken: - Tried different algorithm (from Gamasutra, I can't post the link because I don't have enough reputation yet). I got wrong, much worse, results; - Tried to average basis vectors for vertexes are used in multiple faces; - Tried to average basis vectors for vertexes that have same world coordinates (this would be obviously wrong solution, but I've tried it anyway).

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  • Most efficient AABB - Ray intersection algorithm for input/output distance calculation

    - by Tobbey
    Thanks to the following thread : most efficient AABB vs Ray collision algorithms I have seen very fast algorithm for ray/AABB intersection point computation. Unfortunately, most of the recent algorithm are accelerated by omitting the "output" intersection point of the box. In my application, I would interested in getting both the the distance from source ray to input: t0 and source ray to output of bounding box: t1. I have seen for instance Eisemann designed a very fast version regarding plucker, smits, ... , but it does not compare the case when both input/output distance should be computed see: http://www.cg.cs.tu-bs.de/publications/Eisemann07FRA/ Does someone know where I can find more information on algorithm performances for the specific input/output problem ? Thank you in advance

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  • algorithm to print the digits in the correct order

    - by Aga Waw
    I've been trying to write an algorithm that will print separately the digits from an integer. I have to write it in Pseudocode. I know how to write an algorithm that reverse the digits. digi(n): while n != 0: x = n % 10 n = n // 10 print (x) But I don't know how to write an algorithm to print the digits in the correct order. f.eg. the input is integer 123467 and the output is: 1 2 3 4 6 7 The numbers will be input from the user, and we cannot convert them to a string. I just need help gettin started on writing algorithms. Thanks

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  • How does one unit test an algorithm

    - by Asa Baylus
    I was recently working on a JS slideshow which rotates images using a weighted average algorithm. Thankfully, timgilbert has written a weighted list script which implements the exact algorithm I needed. However in his documentation he's noted under todos: "unit tests!". I'd like to know is how one goes about unit testing an algorithm. In the case of a weighted average how would you create a proof that the averages are accurate when there is the element of randomness? Code samples of similar would be very helpful to my understanding.

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  • "Bad apple" algorithm, or process crashes shared sandbox

    - by Roger Lipscombe
    I'm looking for an algorithm to handle the following problem, which I'm (for now) calling the "bad apple" algorithm. The problem I've got a N processes running in M sandboxes, where N M. It's impractical to give each process its own sandbox. At least one of those processes is badly-behaved, and is bringing down the entire sandbox, thus killing all of the other processes. If it was a single badly-behaved process, then I could use a simple bisection to put half of the processes in one sandbox, and half in another sandbox, until I found the miscreant. This could probably be extended by partitioning the set into more than two pieces until the badly-behaved process was found. For example, partitioning into 8 sets allows me to eliminate 7/8 of the search space at each step, and so on. The question If more than one process is badly-behaved -- including the possibility that they're all badly-behaved -- does this naive algorithm "work"? Is it guaranteed to work within some sensible bounds?

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  • Nearest color algorithm using Hex Triplet

    - by Lijo
    Following page list colors with names http://en.wikipedia.org/wiki/List_of_colors. For example #5D8AA8 Hex Triplet is "Air Force Blue". This information will be stored in a databse table (tbl_Color (HexTriplet,ColorName)) in my system Suppose I created a color with #5D8AA7 Hex Triplet. I need to get the nearest color available in the tbl_Color table. The expected anaser is "#5D8AA8 - Air Force Blue". This is because #5D8AA8 is the nearest color for #5D8AA7. Do we have any algorithm for finding the nearest color? How to write it using C# / Java? REFERENCE http://stackoverflow.com/questions/5440051/algorithm-for-parsing-hex-into-color-family http://stackoverflow.com/questions/6130621/algorithm-for-finding-the-color-between-two-others-in-the-colorspace-of-painte Suggested Formula: Suggested by @user281377. Choose the color where the sum of those squared differences is minimal (Square(Red(source)-Red(target))) + (Square(Green(source)-Green(target))) +(Square(Blue(source)-Blue(target)))

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  • How to find 2D grid cells swept by a moving circle?

    - by Nevermind
    I'm making a game based on a 2D grid, with some cells passable and some not. Dynamic objects can move continuously, independent of the grid, but need to collide with impassable cells. I wrote an algorithm to trace a ray against the grid, that gives me all cells that ray intersects. However, actual object are not point-sized; I'm currently representing them as circles. But I can't figure out an effective algorithm to trace a moving circle. Here's a picture of what I need: The numbers show in what order the circle collides with grid cells. Does anybody know the algorithm to find these collisions? Preferably in C#. Update The circle can be bigger than a single grid cell.

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  • Bracketing algorithm when root finding. Single root in "quadratic" function

    - by Ander Biguri
    I am trying to implement a root finding algorithm. I am using the hybrid Newton-Raphson algorithm found in numerical recipes that works pretty nicely. But I have a problem in bracketing the root. While implementing the root finding algorithm I realised that in several cases my functions have 1 real root and all the other imaginary (several of them, usually 6 or 9). The only root I am interested is in the real one so the problem is not there. The thing is that the function approaches the root like a cubic function, touching with the point the y=0 axis... Newton-Rapson method needs some brackets of different sign and all the bracketing methods I found don't work for this specific case. What can I do? It is pretty important to find that root in my program... EDIT: more problems: sometimes due to reaaaaaally small numerical errors, say a variation of 1e-6 in some value the "cubic" function does NOT have that real root, it is just imaginary with a neglectable imaginary part... (checked with matlab) EDIT 2: Much more information about the problem. Ok, I need root finding algorithm. Info I have: The root I need to find is between [0-1] , if there are more roots outside that part I am not interested in them. The root is real, there may be imaginary roots, but I don't want them. Probably all the rest of the roots will be imaginary The root may be double in that point, but I think that actually doesn't mater in numerical analysis problems I need to use the root finding algorithm several times during the overall calculations, but the function will always be a polynomial In one of the particular cases of the root finding, my polynomial will be similar to a quadratic function that touches Y=0 with the point. Example of a real case: The coefficient may not be 100% precise and that really slight imprecision may make the function not to touch the Y=0 axis. I cannot solve for this specific case because in other cases it may be that the polynomial is pretty normal and doesn't make any "strange" thing. The method I am actually using is NewtonRaphson hybrid, where if the derivative is really small it makes a bisection instead of NewRaph (found in numerical recipes). Matlab's answer to the function on the image: roots: 0.853553390593276 + 0.353553390593278i 0.853553390593276 - 0.353553390593278i 0.146446609406726 + 0.353553390593273i 0.146446609406726 - 0.353553390593273i 0.499999999999996 + 0.000000040142134i 0.499999999999996 - 0.000000040142134i The function is a real example I prepared where I know that the answer I want is 0.5 Note: I still haven't check completely some of the answers I you people have give me (Thank you!), I am just trying to give al the information I already have to complete the question.

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  • Python: (sampling with replacement): efficient algorithm to extract the set of UNIQUE N-tuples from a set

    - by Homunculus Reticulli
    I have a set of items, from which I want to select DISSIMILAR tuples (more on the definition of dissimilar touples later). The set could contain potentially several thousand items, although typically, it would contain only a few hundreds. I am trying to write a generic algorithm that will allow me to select N items to form an N-tuple, from the original set. The new set of selected N-tuples should be DISSIMILAR. A N-tuple A is said to be DISSIMILAR to another N-tuple B if and only if: Every pair (2-tuple) that occurs in A DOES NOT appear in B Note: For this algorithm, A 2-tuple (pair) is considered SIMILAR/IDENTICAL if it contains the same elements, i.e. (x,y) is considered the same as (y,x). This is a (possible variation on the) classic Urn Problem. A trivial (pseudocode) implementation of this algorithm would be something along the lines of def fetch_unique_tuples(original_set, tuple_size): while True: # randomly select [tuple_size] items from the set to create first set # create a key or hash from the N elements and store in a set # store selected N-tuple in a container if end_condition_met: break I don't think this is the most efficient way of doing this - and though I am no algorithm theorist, I suspect that the time for this algorithm to run is NOT O(n) - in fact, its probably more likely to be O(n!). I am wondering if there is a more efficient way of implementing such an algo, and preferably, reducing the time to O(n). Actually, as Mark Byers pointed out there is a second variable m, which is the size of the number of elements being selected. This (i.e. m) will typically be between 2 and 5. Regarding examples, here would be a typical (albeit shortened) example: original_list = ['CAGG', 'CTTC', 'ACCT', 'TGCA', 'CCTG', 'CAAA', 'TGCC', 'ACTT', 'TAAT', 'CTTG', 'CGGC', 'GGCC', 'TCCT', 'ATCC', 'ACAG', 'TGAA', 'TTTG', 'ACAA', 'TGTC', 'TGGA', 'CTGC', 'GCTC', 'AGGA', 'TGCT', 'GCGC', 'GCGG', 'AAAG', 'GCTG', 'GCCG', 'ACCA', 'CTCC', 'CACG', 'CATA', 'GGGA', 'CGAG', 'CCCC', 'GGTG', 'AAGT', 'CCAC', 'AACA', 'AATA', 'CGAC', 'GGAA', 'TACC', 'AGTT', 'GTGG', 'CGCA', 'GGGG', 'GAGA', 'AGCC', 'ACCG', 'CCAT', 'AGAC', 'GGGT', 'CAGC', 'GATG', 'TTCG'] Select 3-tuples from the original list should produce a list (or set) similar to: [('CAGG', 'CTTC', 'ACCT') ('CAGG', 'TGCA', 'CCTG') ('CAGG', 'CAAA', 'TGCC') ('CAGG', 'ACTT', 'ACCT') ('CAGG', 'CTTG', 'CGGC') .... ('CTTC', 'TGCA', 'CAAA') ] [[Edit]] Actually, in constructing the example output, I have realized that the earlier definition I gave for UNIQUENESS was incorrect. I have updated my definition and have introduced a new metric of DISSIMILARITY instead, as a result of this finding.

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