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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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  • Count double palindromes in given int sequence

    - by jakubmal
    For a given int sequence check number of double palindromes, where by double palindrome we mean sequence of two same palindromes without break between them. So for example: in 1 0 1 1 0 1 we have 1 0 1 as a palindrome which appears 2 times without a break, in 1 0 1 5 1 0 1 we have 1 0 1 but it's separated (apart from the other palindromes in these sequences) Problem example test data is: 3 12 0 1 1 0 0 1 1 0 0 1 1 0 12 1 0 1 0 1 0 1 0 1 0 1 0 6 3 3 3 3 3 3 with answers 8 0 9 Manacher is obvious for the begging, but I'm not sure what to do next. Any ideas appreciated. Complexity should be below n^2 I guess. EDIT: int is here treated as single element of alphabet

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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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  • Solving the problem of finding parts which work well with each other

    - by dotnetdev
    Hi, I have a database of items. They are for cars and similar parts (eg cam/pistons) work better than others in different combinations (eg one product will work well with another, while another combination of 2 parts may not). There are so many possible permutations, what solutions apply to this problem? So far, I feel that these are possible approaches (Where I have question marks, something tells me these are solutions but I am not 100% confident they are). Neural networks (?) Collection-based approach (selection of parts in a collection for cam, and likewise for pistons in another collection, all work well with each other) Business rules engine (?) What are good ways to tackle this sort of problem? Thanks

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  • Did I implement this correctly?

    - by user146780
    I'm trying to implement line thickness as denoted here: start = line start = vector(x1, y1) end = line end = vector(x2, y2) dir = line direction = end - start = vector(x2-x1, y2-y1) ndir = normalized direction = dir*1.0/length(dir) perp = perpendicular to direction = vector(dir.x, -dir.y) nperp = normalized perpendicular = perp*1.0/length(perp) perpoffset = nperp*w*0.5 diroffset = ndir*w*0.5 p0, p1, p2, p3 = polygon points: p0 = start + perpoffset - diroffset p1 = start - perpoffset - diroffset p2 = end + perpoffset + diroffset p3 = end - perpoffset + diroffset I'v implemented this like so: void OGLENGINEFUNCTIONS::GenerateLinePoly(const std::vector<std::vector<GLdouble>> &input, std::vector<GLfloat> &output, int width) { output.clear(); float temp; float dirlen; float perplen; POINTFLOAT start; POINTFLOAT end; POINTFLOAT dir; POINTFLOAT ndir; POINTFLOAT perp; POINTFLOAT nperp; POINTFLOAT perpoffset; POINTFLOAT diroffset; POINTFLOAT p0, p1, p2, p3; for(int i = 0; i < input.size() - 1; ++i) { start.x = input[i][0]; start.y = input[i][1]; end.x = input[i + 1][0]; end.y = input[i + 1][1]; dir.x = end.x - start.x; dir.y = end.y - start.y; dirlen = sqrt((dir.x * dir.x) + (dir.y * dir.y)); ndir.x = dir.x * (1.0 / dirlen); ndir.y = dir.y * (1.0 / dirlen); perp.x = dir.x; perp.y = -dir.y; perplen = sqrt((perp.x * perp.x) + (perp.y * perp.y)); nperp.x = perp.x * (1.0 / perplen); nperp.y = perp.y * (1.0 / perplen); perpoffset.x = nperp.x * width * 0.5; perpoffset.y = nperp.y * width * 0.5; diroffset.x = ndir.x * width * 0.5; diroffset.y = ndir.x * width * 0.5; // p0 = start + perpoffset - diroffset //p1 = start - perpoffset - diroffset //p2 = end + perpoffset + diroffset // p3 = end - perpoffset + diroffset p0.x = start.x + perpoffset.x - diroffset.x; p0.y = start.y + perpoffset.y - diroffset.y; p1.x = start.x - perpoffset.x - diroffset.x; p1.y = start.y - perpoffset.y - diroffset.y; p2.x = end.x + perpoffset.x + diroffset.x; p2.y = end.y + perpoffset.y + diroffset.y; p3.x = end.x - perpoffset.x + diroffset.x; p3.y = end.y - perpoffset.y + diroffset.y; output.push_back(p0.x); output.push_back(p0.y); output.push_back(p1.x); output.push_back(p1.y); output.push_back(p2.x); output.push_back(p2.y); output.push_back(p3.x); output.push_back(p3.y); } } But right now the lines look perpendicular and wrong, it should be giving me quads to render which is what i'm rendering, but the points it is outputing are strange. Have I done this wrong? Thanks

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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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  • R implementation of sorting by reversals

    - by user1357015
    I was wondering if there is an implementation in R where it sorts a permutation of n numbers into the original 1...n sequence and provides the number of reversals needed. Eg an implementation of the "sorting by reversals" or "sorting by translocation" as outlined in this ppt. Specifically, I have a permutation of a sequence of n elements, pi(n), and I want to figure out how close it is to the original sequence. The number of reversals seems a good metric. Thanks!

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  • Recursive breadth-first travel function in Java or C++?

    - by joejax
    Here is a java code for breadth-first travel: void breadthFirstNonRecursive(){ Queue<Node> queue = new java.util.LinkedList<Node>(); queue.offer(root); while(!queue.isEmpty()){ Node node = queue.poll(); visit(node); if (node.left != null) queue.offer(node.left); if (node.right != null) queue.offer(node.right); } } Is it possible to write a recursive function to do the same? At first, I thought this would be easy, so I came out with this: void breadthFirstRecursive(){ Queue<Node> q = new LinkedList<Node>(); breadthFirst(root, q); } void breadthFirst(Node node, Queue<Node> q){ if (node == null) return; q.offer(node); Node n = q.poll(); visit(n); if (n.left != null) breadthFirst(n.left, q); if (n.right != null) breadthFirst(n.right, q); } Then I found it doesn't work. It is actually does the same thing as this: void preOrder(Node node) { if (node == null) return; visit(node); preOrder(node.left); preOrder(node.right); } Has any one thought about this before?

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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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  • Finding users near other user

    - by Bunny Rabbit
    what algorithms should I explore to implement a feature which lets a user find other user located near him , the latitude and the longitudes of all the user are known in advance and are fixed [not dynamic]. Also i believe that there should be a better way to store such data then simply storing the lat , long of the user against his user id in a database.What are the efficient ways to handle this ?

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  • Lists Hash function

    - by John Retallack
    I'm trying to make a hash function so I can tell if too lists with same sizes contain the same elements. For exemple this is what I want: f((1 2 3))=f((1 3 2))=f((2 1 3))=f((2 3 1))=f((3 1 2))=f((3 2 1)). Any ideea how can I approch this problem ? I've tried doing the sum of squares of all elements but it turned out that there are collisions,for exemple f((2 2 5))=33=f((1 4 4)) which is wrong as the lists are not the same. I'm looking for a simple approach it there are any.

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  • Comparing two speech sounds

    - by JessicaB
    I need to be able to determine if two sounds are very similar. The goal is to have a very limited vocabulary (10 or 15) of short one or two syllable words, then compare a captured sound to determine if it is one of those items with all the usual variability in environmental and capture conditions. The idea is that the user can issue a few simple commands by voice instead of keyboard or mouse. Does anyone know the best approach to this? I don't want to do full blown speech recognition, just something much more limited.

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  • Function for creating color wheels

    - by lbrandy
    This is something I've pseudo-solved many times and never quite found a solution that's stuck with me. The problem is to come up with a way to generate N colors that are as distinguishable as possible where N is a parameter.

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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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  • Determining the best audio quality.

    - by The Rook
    How can you determine the best audio quality in a list of audio files, with out looking at the audio file's header. What if all of the files came from differnt encoding types and they where all transcoded to the same format and bit rate.

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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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  • How does pattern matching work behind the scenes in F#?

    - by kryptic
    Hello Everyone, I am completely new to F# (and functional programming in general) but I see pattern matching used everywhere in sample code. I am wondering for example how pattern matching actually works? For example, I imagine it working the same as a for loop in other languages and checking for matches on each item in a collection. This is probably far from correct, how does it actually work behind the scenes?

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  • How would I use for_each to delete every value in an STL map?

    - by stusmith
    Suppose I have a STL map where the values are pointers, and I want to delete them all. How would I represent the following code, but making use of std::for_each? I'm happy for solutions to use Boost. for( stdext::hash_map<int, Foo *>::iterator ir = myMap.begin(); ir != myMap.end(); ++ir ) { delete ir->second; // delete all the (Foo *) values. } (I've found Boost's checked_delete, but I'm not sure how to apply that to the pair<int, Foo *> that the iterator represents). (Also, for the purposes of this question, ignore the fact that storing raw pointers that need deleting in an STL container isn't very sensible).

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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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  • 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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  • 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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  • 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 calculate the state of a graph?

    - by zcb
    Given a graph G=(V,E), each node i is associated with 'Ci' number of objects. At each step, for every node i, the Ci objects will be taken away by the neighbors of i equally. After K steps, output the number of objects of the top five nodes which has the most objects. Some Constrains: |V|<10^5, |E|<2*10^5, K<10^7, Ci<1000 My current idea is: represent the transformation in each step with a matrix. This problem is converted to the calculation of the power of matrix. But this solution is much too slow considering |V| can be 10^5. Is there any faster way to do it?

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