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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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  • how to fast compute distance between high dimension vectors

    - by chyojn
    assume there are three group of high dimension vectors: {a_1, a_2, ..., a_N}, {b_1, b_2, ... , b_N}, {c_1, c_2, ..., c_N}. each of my vector can be represented as: x = a_i + b_j + c_k, where 1 <=i, j, k <= N. then the vector is encoded as (i, j, k) wich is then can be decoded as x = a_i + b_j + c_k. my question is, if there are two vector: x = (i_1, j_1, k_1), y = (i_2, j_2, k_2), is there a method to compute the euclidian distance of these two vector without decode x and y.

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  • Show me some cool python list comprehensions

    - by christangrant
    One of the major strengths of python and a few other (functional) programming languages are the list comprehension. They allow programmers to write complex expressions in 1 line. They may be confusing at first but if one gets used to the syntax, it is much better than nested complicated for loops. With that said, please share with me some of the coolest uses of list comprehensions. (By cool, I just mean useful) It could be for some programming contest, or a production system. For example: To do the transpose of a matrix mat >>> mat = [ ... [1, 2, 3], ... [4, 5, 6], ... [7, 8, 9], ... ] >>> [[row[i] for row in mat] for i in [0, 1, 2]] [[1, 4, 7], [2, 5, 8], [3, 6, 9]] Please include a description of the expression and where it was used (if possible).

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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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  • Data structure name: combination array/linked list

    - by me_and
    I have come up with a data structure that combines some of the advantages of linked lists with some of the advantages of fixed-size arrays. It seems very obvious to me, and so I'd expect someone to have thought of it and named it already. Does anyone know what this is called: Take a small fixed-size array. If the number of elements you want to put in your array is greater than the size of the array, add a new array and whatever pointers you like between the old and the new. Thus you have: Static array ————————————————————————— |1|2|3|4|5|6|7|8|9|a|b|c| ————————————————————————— Linked list ———— ———— ———— ———— ———— |1|*->|2|*->|3|*->|4|*->|5|*->NULL ———— ———— ———— ———— ———— My thing: ———————————— ———————————— |1|2|3|4|5|*->|6|7|8|9|a|*->NULL ———————————— ————————————

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  • Find all A^x in a given range

    - by Austin Henley
    I need to find all monomials in the form AX that when evaluated falls within a range from m to n. It is safe to say that the base A is greater than 1, the power X is greater than 2, and only integers need to be used. For example, in the range 50 to 100, the solutions would be: 2^6 3^4 4^3 My first attempt to solve this was to brute force all combinations of A and X that make "sense." However this becomes too slow when used for very large numbers in a big range since these solutions are used in part of much more intensive processing. Here is the code: def monoSearch(min, max): base = 2 power = 3 while 1: while base**power < max: if base**power > min: print "Found " + repr(base) + "^" + repr(power) + " = " + repr(base**power) power = power + 1 base = base + 1 power = 3 if base**power > max: break I could remove one base**power by saving the value in a temporary variable but I don't think that would make a drastic effect. I also wondered if using logarithms would be better or if there was a closed form expression for this. I am open to any optimizations or alternatives to finding the solutions.

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  • more efficient version of this?

    - by john connor
    i have this thingy here : function numOfPackets(bufferSize, packetSize) { if (bufferSize <= 0 || packetSize > bufferSize) return 0; if (packetSize < 0) throw Error(); var out = 0; for(;;){ out++; bufferSize = bufferSize - packetSize; if( packetSize > bufferSize ) break; } return out; } which i run at often , can u give me more efficent variant of it?

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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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  • Enumerating large (20-digit) [probable] prime numbers

    - by Paul Baker
    Given A, on the order of 10^20, I'd like to quickly obtain a list of the first few prime numbers greater than A. OK, my needs aren't quite that exact - it's alright if occasionally a composite number ends up on the list. What's the fastest way to enumerate the (probable) primes greater than A? Is there a quicker way than stepping through all of the integers greater than A (other than obvious multiples of say, 2 and 3) and performing a primality test for each of them? If not, and the only method is to test each integer, what primality test should I be using?

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  • Help to learn Image Search algorithm

    - by R Manu
    I am a beginner in image processing. I want to write an application in C++ or in C# for Searching an image in a list of images Searching for a particular feature (for e.g. face) in a list of images. Can anybody suggest where should I start from? What all should I learn before doing this? Where can I find the correct information regarding this?

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  • GWT Calendrical Calculations

    - by Kyle Hayes
    We have a GWT application that needs to display various holidays. Is there a library available to do these calendrical calculations? If not, we'll have to do our own that we can ingest a set of rules to. Cheers

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  • Pointer mysteriously moves

    - by Armen Ablak
    Hi, I have this code for Node rotation and in a line which is marked something happens and I don't really know what and why :). //Test case 30 \ 16 / 29 RotationRight(node->mParent); //call template<class T> void SplayTree<T>::RotationRight(SplayNode<T> *&node) const { SplayNode<T> *left = node->mLeft; SplayNode<T> *parent = node->mParent; node->mLeft = left->mRight; if(left->HasRight()) left->mRight->mParent = node; left->mRight = node; //node in this line points to 0x00445198 {30} left->mParent = node->mParent; //and in this line it points to 0x00444fb8 {16} (node, not node->mParent) node->mParent = left; node = left; } Well, left-mParent points to node also, so I basically do node = node-mParent. The problem is I can't find a work around - how to unpin in from node and change it's pointing address without changing it's.

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  • How to find same-value rectangular areas of a given size in a matrix most efficiently?

    - by neo
    My problem is very simple but I haven't found an efficient implementation yet. Suppose there is a matrix A like this: 0 0 0 0 0 0 0 4 4 2 2 2 0 0 4 4 2 2 2 0 0 0 0 2 2 2 1 1 0 0 0 0 0 1 1 Now I want to find all starting positions of rectangular areas in this matrix which have a given size. An area is a subset of A where all numbers are the same. Let's say width=2 and height=3. There are 3 areas which have this size: 2 2 2 2 0 0 2 2 2 2 0 0 2 2 2 2 0 0 The result of the function call would be a list of starting positions (x,y starting with 0) of those areas. List((2,1),(3,1),(5,0)) The following is my current implementation. "Areas" are called "surfaces" here. case class Dimension2D(width: Int, height: Int) case class Position2D(x: Int, y: Int) def findFlatSurfaces(matrix: Array[Array[Int]], surfaceSize: Dimension2D): List[Position2D] = { val matrixWidth = matrix.length val matrixHeight = matrix(0).length var resultPositions: List[Position2D] = Nil for (y <- 0 to matrixHeight - surfaceSize.height) { var x = 0 while (x <= matrixWidth - surfaceSize.width) { val topLeft = matrix(x)(y) val topRight = matrix(x + surfaceSize.width - 1)(y) val bottomLeft = matrix(x)(y + surfaceSize.height - 1) val bottomRight = matrix(x + surfaceSize.width - 1)(y + surfaceSize.height - 1) // investigate further if corners are equal if (topLeft == bottomLeft && topLeft == topRight && topLeft == bottomRight) { breakable { for (sx <- x until x + surfaceSize.width; sy <- y until y + surfaceSize.height) { if (matrix(sx)(sy) != topLeft) { x = if (x == sx) sx + 1 else sx break } } // found one! resultPositions ::= Position2D(x, y) x += 1 } } else if (topRight != bottomRight) { // can skip x a bit as there won't be a valid match in current row in this area x += surfaceSize.width } else { x += 1 } } } return resultPositions } I already tried to include some optimizations in it but I am sure that there are far better solutions. Is there a matlab function existing for it which I could port? I'm also wondering whether this problem has its own name as I didn't exactly know what to google for. Thanks for thinking about it! I'm excited to see your proposals or solutions :)

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  • A question about matrix manipulation

    - by appi
    Given a 1*N matrix or an array, how do I find the first 4 elements which have the same value and then store the index for those elements? PS: I'm just curious. What if we want to find the first 4 elements whose value differences are within a certain range, say below 2? For example, M=[10,15,14.5,9,15.1,8.5,15.5,9.5], the elements I'm looking for will be 15,14.5,15.1,15.5 and the indices will be 2,3,5,7.

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  • Efficient determination of which strings in an array are substrings of the others?

    - by byte
    In C#, Say you have an array of strings, which contain only characters '0' and '1': string[] input = { "0101", "101", "11", "010101011" }; And you'd like to build a function: public void IdentifySubstrings(string[] input) { ... } That will produce the following: "0101 is a substring of 010101011" "101 is a substring of 0101" "101 is a substring of 010101011" "11 is a substring of 010101011" And you are NOT able to use built-in string functionality (such as String.Substring). How would one efficiently solve this problem? Of course you could plow through it via brute force, but it just feels like there ought to be a way to accomplish it with a tree (since the only values are 0's and 1's, it feels like a binary tree ought to fit somehow). I've read a little bit about things like suffix trees, but I'm uncertain if that's the right path to be going down. Any efficient solutions you can think of?

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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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  • 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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  • Generate a valid array key from an URL string in PHP

    - by John Riche
    I have a PHP array with some predefined values: $aArray = array( 0 => 'value0', 1 => 'value1' ); I need to create a function where the string input will always return the same, valid, array key so that when I call: GiveMeAKey('http://www.google.com'); // May return 0 or 1 I receive always the same key (I don't care which one) from the array. Obvisously I can't store the relationship in a database and the string passed to the GiveMeAKey method can be any URL. I wonder if there is a way of doing that ?

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  • Python threading question (Working with a method that blocks forever)

    - by Nix
    I am trying to wrap a thread around some receiving logic in python. Basically we have an app, that will have a thread in the background polling for messages, the problem I ran into is that piece that actually pulls the messages waits forever for a message. Making it impossible to terminate... I ended up wrapping the pull in another thread, but I wanted to make sure there wasn't a better way to do it. Original code: class Manager: def __init__(self): receiver = MessageReceiver() receiver.start() #do other stuff... class MessageReceiver(Thread): receiver = Receiver() def __init__(self): Thread.__init__(self) def run(self): #stop is a flag that i use to stop the thread... while(not stopped ): #can never stop because pull below blocks message = receiver.pull() print "Message" + message What I refectored to: class Manager: def __init__(self): receiver = MessageReceiver() receiver.start() class MessageReceiver(Thread): receiver = Receiver() def __init__(self): Thread.__init__(self) def run(self): pullThread = PullThread(self.receiver) pullThread.start() #stop is a flag that i use to stop the thread... while(not stopped and pullThread.last_message ==None): pass message = pullThread.last_message print "Message" + message class PullThread(Thread): last_message = None def __init__(self, receiver): Thread.__init(self, target=get_message, args=(receiver)) def get_message(self, receiver): self.last_message = None self.last_message = receiver.pull() return self.last_message I know the obvious locking issues exist, but is this the appropriate way to control a receive thread that waits forever for a message? One thing I did notice was this thing eats 100% cpu while waiting for a message... **If you need to see the stopping logic please let me know and I will post.

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  • Minimize the sequence by putting appropriate operations ' DP'

    - by Vikas
    Given a sequence,say, 222 We have to put a '+' or '* ' between each adjacent pair. '* ' has higher precedence over '+' We have to o/p the string whose evaluation leads to minimum value. O/p must be lexicographically smallest if there are more than one. inp:222 o/p: 2*2+2 Explaination: 2+2+2=6 2+2*2=6 2*2+2=6 of this 3rd is lexicographically smallest. I was wondering how to construct a DP solution for this.

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  • How to read arbitrary number of values using std::copy?

    - by Miro Kropacek
    Hi, I'm trying to code opposite action to this: std::ostream outs; // properly initialized of course std::set<int> my_set; // ditto outs << my_set.size(); std::copy( my_set.begin(), my_set.end(), std::ostream_iterator<int>( outs ) ); it should be something like this: std::istream ins; std::set<int>::size_type size; ins >> size; std::copy( std::istream_iterator<int>( ins ), std::istream_iterator<int>( ins ) ???, std::inserter( my_set, my_set.end() ) ); But I'm stuck with the 'end' iterator -- input interators can't use std::advance and neither I can use two streams with the same source... Is there any elegant way how to solve this? Of course I can use for loop, but maybe there's something nicer :)

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  • Algorithms for finding the intersections of intervals

    - by tomwu
    I am wondering how I can find the number of intervals that intersect with the ones before it. for the intervals [2, 4], [1, 6], [5, 6], [0, 4], the output should be 2. from [2,4] [5,6] and [5,6] [0,4]. So now we have 1 set of intervals with size n all containing a point a, then we add another set of intervals size n as well, and all of the intervals are to the right of a. Can you do this in O(nlgn) and O(nlg^2n)?

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