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• How to judge the relative efficiency of algorithms given runtimes as functions of 'n'?

  - by Lopa

  Consider two algorithms A and B which solve the same problem, and have time complexities (in terms of the number of elementary operations they perform) given respectively by a(n) = 9n+6 b(n) = 2(n^2)+1 (i) Which algorithm is the best asymptotically? (ii) Which is the best for small input sizes n, and for what values of n is this the case? (You may assume where necessary that n0.) i think its 9n+6. guys could you please help me with whether its right or wrong?? and whats the answer for part b. what exactly do they want?

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• What's the best way to normalize scores for ranking things?

  - by beagleguy

  hi all, I'm curious how to do normalizing of numbers for a ranking algorithm let's say I want to rank a link based on importance and I have two columns to work with so a table would look like url | comments | views now I want to rank comments higher than views so I would first think to do comments*3 or something to weight it, however if there is a large view number like 40,000 and only 4 comments then the comments weight gets dropped out. So I'm thinking I have to normalize those scores down to a more equal playing field before I can weight them. Any ideas or pointers to how that's usually done? thanks

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• Popularity Algorithm - SQL / Django

  - by RadiantHex

  Hi folks, I've been looking into popularity algorithms used on sites such as Reddit, Digg and even Stackoverflow. Reddit algorithm: t = (time of entry post) - (Dec 8, 2005) x = upvotes - downvotes y = {1 if x > 0, 0 if x = 0, -1 if x < 0) z = {1 if x < 0, otherwise x} log(z) + (y * t)/45000 I have always performed simple ordering within SQL, I'm wondering how I should deal with such ordering. Should it be used to define a table, or could I build an SQL with the ordering within the formula (without hindering performance)? I am also wondering, if it is possible to use multiple ordering algorithms in different occasions, without incurring into performance problems. I'm using Django and PostgreSQL. Help would be much appreciated! ^^

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• How do people prove the correctness of Computer Vision methods?

  - by solvingPuzzles

  I'd like to pose a few abstract questions about computer vision research. I haven't quite been able to answer these questions by searching the web and reading papers. How does someone know whether a computer vision algorithm is correct? How do we define "correct" in the context of computer vision? Do formal proofs play a role in understanding the correctness of computer vision algorithms? A bit of background: I'm about to start my PhD in Computer Science. I enjoy designing fast parallel algorithms and proving the correctness of these algorithms. I've also used OpenCV from some class projects, though I don't have much formal training in computer vision. I've been approached by a potential thesis advisor who works on designing faster and more scalable algorithms for computer vision (e.g. fast image segmentation). I'm trying to understand the common practices in solving computer vision problems.

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• Explaining training method for AdaBoost algorithm

  - by konzti8

  Hi, I'm trying to understand the Haar feature method used for the training step in the AdaBoost algorithm. I don't understand the math that well so I'd appreciate more of a conceptual answer (as much as possible, anyway). Basically, what does it do? How do you choose positive and negative sets for what you want to select? Can it be generalized? What I mean by that is, can you choose it to find any kind of feature that you want no matter what the background is? So, for example, if I want to find some kind of circular blob - can I do that? I've also read that it is used on small patches for the images around the possible feature - does that mean you have to manually select that image patch or can it be automated to process the entire image? Is there matlab code for the training step? Thanks for any help...

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• Searching Techniques/Algorithms for Resources over a given area

  - by Raydon

  I have a flat area with nodes randomly placed on this flat surface. I need techniques which are able to take a starting point, move in a certain way (the algorithm), find nodes and continue searching. I do not have an overall view of the surface (i.e. I cannot see everything), only a limited view (i.e. 4 cells in any direction). Ideally, these methods would be efficient in the way that they work. Any points in the right direction would be greatly appreciated.

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• Spatial Index for Rectangles With Fast Insert

  - by TheCloudlessSky

  Hello, I'm looking for a data structure that provides indexing for Rectangles. I need the insert algorithm to be as fast as possible since the rectangles will be moving around the screen (think of dragging a rectangle with your mouse to a new position). I've looked into R-Trees, R+Trees, kD-Trees, Quad-Trees and B-Trees but from my understanding insert's are usually slow. I'd prefer to have inserts at sub-linear time complexity so maybe someone can prove me wrong about either of the listed data structures. I should be able to query the data structure for what rectangles are at point(x, y) or what rectangles intersect rectangle(x, y, width, height). EDIT: The reason I want insert so fast is because if you think of a rectangle being moved around the screen, they're going to have to be removed and then re-inserted. Thanks!

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• Generate 10-digit number using a phone keypad

  - by srikfreak

  Given a phone keypad as shown below: 1 2 3 4 5 6 7 8 9 0 How many different 10-digit numbers can be formed starting from 1? The constraint is that the movement from 1 digit to the next is similar to the movement of the Knight in a chess game. For eg. if we are at 1 then the next digit can be either 6 or 8 if we are at 6 then the next digit can be 1, 7 or 0. Repetition of digits are allowed - 1616161616 is a valid number. Is there a polynomial time algorithm which solves this problem? The problem requires us to just give the count of 10-digit numbers and not necessarily list the numbers.

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• Simple Python Challenge: Fastest Bitwise XOR on Data Buffers

  - by user213060

  Challenge: Perform a bitwise XOR on two equal sized buffers. The buffers will be required to be the python str type since this is traditionally the type for data buffers in python. Return the resultant value as a str. Do this as fast as possible. The inputs are two 1 megabyte (2**20 byte) strings. The challenge is to substantially beat my inefficient algorithm using python or existing third party python modules (relaxed rules: or create your own module.) Marginal increases are useless. from os import urandom from numpy import frombuffer,bitwise_xor,byte def slow_xor(aa,bb): a=frombuffer(aa,dtype=byte) b=frombuffer(bb,dtype=byte) c=bitwise_xor(a,b) r=c.tostring() return r aa=urandom(2**20) bb=urandom(2**20) def test_it(): for x in xrange(1000): slow_xor(aa,bb)

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• Correct algorith for checking leap year

  - by Debanjan

  What will be the exact definition of leap year ? AFAIK "A year which is divisible by 4 is a leap year.But for century years' the years which are divisible by 400 is a leap year." But that definition makes 100, 200, 300, 400.... upto 1700 NOT LEAP years! But in Gregorian calender all of them are all leap year,check this out. You can also try "call 1700" in Linux to verify. So the correct algorithm foe leap year would be if ( (year % 4 == 0) && ( year <= 1700 || year % 100 != 0 || year % 400 == 0 )) printf("%d is a leap year.\n", year); else printf("%d is not a leap year.\n", year); But is this specific to Gregorian calender ? Even if that is the case why is it not mentioned here ? Regards, PS:The history of Gregorian callender seems interesting check out the September month of 1752.

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• number of days in a period that fall within another period

  - by thomas

  I have 2 independent but contiguous date ranges. The first range is the start and end date for a project. Lets say start = 3/21/10 and end = 5/16/10. The second range is a month boundary (say 3/1/10 to 3/31/10, 4/1/10 to 4/30/10, etc.) I need to figure out how many days in each month fall into the first range. The answer to my example above is March = 10, April = 30, May = 16. I am trying to figure out an excel formula or VBA function that will give me this value. Any thoughts on an algorithm for this? I feel it should be rather easy but I can't seem to figure it out. I have a formula which will return TRUE/FALSE if ANY part of the month range is within the project start/end but not the number of days. That function is below. return month_start <= project_end And month_end >= project_start

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• Minimizing the number of boxes that cover a given set of intervals

  - by fortran

  Hi, this is a question for the algorithms gurus out there :-) Let S be a set of intervals of the natural numbers that might overlap and b a box size. Assume that for each interval, the range is strictly less than b. I want to find the minimum set of intervals of size b (let's call it M) so all the intervals in S are contained in the intervals of M. Trivial example: S = {[1..4], [2..7], [3..5], [8..15], [9..13]} b = 10 M = {[1..10], [8..18]} // so ([1..4], [2..7], [3..5]) are inside [1..10] and ([8..15], [9..13]) are inside [8..18] I think a greedy algorithm might not work always, so if anybody knows of a solution of this problem (or a similar one that can be converted into), that would be great. Thanks!

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• New to AVL tree implementation.

  - by nn

  I am writing a sliding window compression algorithm (LZ77) that searches for phrases in a "moving" dictionary. So far I have written a BST where each node is stored in an array and it's index in the array is also the value of the starting position in the window itself. I am now looking at transforming the BST to an AVL tree. I am a little confused at the sample implementations I have seen. Some only appear to store the balance factors whereas others store the height of each tree. Are there any performance advantage/disadvantages of storing the height and/or balance factor for each node? Apologies if this is a very simple question, but I'm still not visualizing how I want to restructure my BST to implement height balancing. Thanks.

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• What are some good algorithms for drawing lines between graph nodes?

  - by ApplePieIsGood

  What I'm specifically grappling with is not just the layout of a graph, but when a user selects a graph node and starts to drag it around the screen area, the line has to constantly be redrawn to reflect what it would look like if the user were to release the node. I suppose this is part of the layout algorithm? Also some applications get a bit fancy and don't simply draw the line in a nice curvy way, but also bend the line around the square shaped node in almost right angles. See attached image and keep in mind that as a node is dragged, the line is drawn as marching ants, and re-arranged nicely, while retaining its curved style.

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• count of distinct acyclic paths from A[a,b] to A[c,d]?

  - by Sorush Rabiee

  I'm writing a sokoban solver for fun and practice, it uses a simple algorithm (something like BFS with a bit of difference). now i want to estimate its running time ( O and omega). but need to know how to calculate count of acyclic paths from a vertex to another in a network. actually I want an expression that calculates count of valid paths, between two vertices of a m*n matrix of vertices. a valid path: visits each vertex 0 or one times. have no circuits for example this is a valid path: but this is not: What is needed is a method to find count of all acyclic paths between the two vertices a and b. comments on solving methods and tricks are welcomed.

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• How to create a random string of characters in C#?

  - by Keltex

  I'm trying to create random strings of characters. I'm wondering if there might be a more efficient way. Here's my algorithm: string RANDOM = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz#@$^*()"; StringBuilder sb = new StringBuilder(); int length = rand.Next(10) + 1; for (int idx = 0; idx < length; ++idx) { sb.Append(RANDOM[rand.Next(RANDOM.Length)]); } string RandomString = sb.ToString(); I'm wondering if the StringBuilder is the best choice. Also if selecting a random character from my RANDOM string is the best way.

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• Genetics algorithms theoretical question

  - by mandelart

  Hi All! I'm currently reading "Artificial Intelligence: A Modern Approach" (Russell+Norvig) and "Machine Learning" (Mitchell) - and trying to learn basics of AINN. In order to understand few basic things I have two 'greenhorn' questions: Q1: In a genetic algorithm given the two parents A and B with the chromosomes 001110 and 101101, respectively, which of the following offspring could have resulted from a one-point crossover? a: 001101 b: 001110 Q2: Which of the above offspring could have resulted from a two-point crossover? and why? Please advise.

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• Finding backedges in a graph, with special conditions.

  - by Morteza M.

  There is a vertex v, such that from the subtree rooted at v, there are at least two backedges to proper ancestors of v. The problem is finding whether such backedges exist or not ( finding v is not important at all). I run DFS algorithm, I can find backedges and save them in an array. I know which backedges in this array belong to a common tree. but I have problem on matching this condition in O(E) time. can anyone help me with that?

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• Matlab postpones disp calls when doing demanding calculations why is that?

  - by Reed Richards

  I am implementing an algorithm in Matlab. Among other things it calculates shortest paths etc. so its quite demanding for my old computer. I've put out disp calls through out the program to see what's happening all the time. However when starting on a particulary heavy for loop the disp seemes not to be called until the loop is over even though it comes before the loop. Why is that? I though that Matlab was really linear or am I just choking it with to many calculations and the disp calls get the lowest priority?

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• How to calculate order (big O) for more complex algorithms (ie quicksort)

  - by bangoker

  I know there are quite a bunch of questions about big O notation, I have already checked Plain english explanation of Big O , Big O, how do you calculate/approximate it?, and Big O Notation Homework--Code Fragment Algorithm Analysis?, to name a few. I know by "intuition" how to calculate it for n, n^2, n! and so, however I am completely lost on how to calculate it for algorithms that are log n , n log n, n log log n and so. What I mean is, I know that Quick Sort is n log n (on average).. but, why? Same thing for merge/comb, etc. Could anybody explain me in a not to math-y way how do you calculate this? The main reason is that Im about to have a big interview and I'm pretty sure they'll ask for this kind of stuff. I have researched for a few days now, and everybody seem to have either an explanation of why bubble sort is n^2 or the (for me) unreadable explanation a la wikipedia Thanks!

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• Algorithms to find longest common prefix in a sliding window.

  - by nn

  Hi, I have written a Lempel Ziv compressor and decompressor. I am seeking to improve the time to search the dictionary for a phrase. I have considered K-M-P and Boyer-Moore, but I think an algorithm that adapts to changes in the dictionary would be faster. I've been reading that binary search trees (AVL or with splays) improve the performance of compression time considerably. What I fail to understand is how to bootstrap the binary search tree and insert/remove data. I'm not actually quite sure the significance of each node in the binary search. I am searching for phrases so will each character be considered a node? Also how and what is inserted/removed from the search tree as new data enters the dictionary and old data is removed? The binary search tree sounds like a good payoff since it can adapt to the dictionary, but I'm just not quite sure of how it's used.

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• Evaluating a function at a particular value in parallel

  - by Gaurav Kalra

  Hi. The question may seem vague, but let me explain it. Suppose we have a function f(x,y,z ....) and we need to find its value at the point (x1,y1,z1 .....). The most trivial approach is to just replace (x,y,z ...) with (x1,y1,z1 .....). Now suppose that the function is taking a lot of time in evaluation and I want to parallelize the algorithm to evaluate it. Obviously it will depend on the nature of function, too. So my question is: what are the constraints that I have to look for while "thinking" to parallelize f(x,y,z...)? If possible, please share links to study.

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• Algorithm for Source Control System?

  - by Michael Stum

  I need to write a simple source control system and wonder what algorithm I would use for file differences? I don't want to look into existing source code due to license concerns. I need to have it licensed under MPL so I can't look at any of the existing systems like CVS or Mercurial as they are all GPL licensed. Just to give some background, I just need some really simple functions - binary files in a folder. no subfolders and every file behaves like it's own repository. No Metadata except for some permissions. Overall really simple stuff, my single concern really is how to store only the differences of a file from revision to revision without wasting too much space but also without being too inefficient (Maybe store a full version every X changes, a bit like Keyframes in Videos?)

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• How to improve performance

  - by Ram

  Hi, In one of mine applications I am dealing with graphics objects. I am using open source GPC library to clip/merge two shapes. To improve accuracy I am sampling (adding multiple points between two edges) existing shapes. But before displaying back the merged shape I need to remove all the points between two edges. But I am not able to find an efficient algorithm that will remove all points between two edges which has same slope with minimum CPU utilization. Currently all points are of type PointF Any pointer on this will be a great help.

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• Counting problem: possible sudoko tables?

  - by Sorush Rabiee

  Hi, I'm working on a sudoko solver. my method is using a game tree and explore possible permutations for each set of digits by DFS Algorithm. in order to analyzing problem, i want to know what is the count of possible valid and invalid sudoko tables? - a 9*9 table that have 9 one, 9 two, ... , 9 nine. (this isn't exact duplicate by this question) my solution is: 1- First select 9 cells for 1s: (*) 2- and like (1) for other digits (each time, 9 cells will be deleted from remaining available cells): C(81-9,9) , C(81-9*2,9) .... = 3- finally multiply the result by 9! (permutation of 123456789 in (*)) this is not equal to accepted answer of this question but problems are equivalent. what did i do wrong?

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