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• O(log N) == O(1) - Why not?

  - by phoku

  Whenever I consider algorithms/data structures I tend to replace the log(N) parts by constants. Oh, I know log(N) diverges - but does it matter in real world applications? log(infinity) < 100 for all practical purposes. I am really curious for real world examples where this doesn't hold. To clarify: I understand O(f(N)) I am curious about real world examples where the asymptotic behaviour matters more than the constants of the actual performance. If log(N) can be replaced by a constant it still can be replaced by a constant in O( N log N). This question is for the sake of (a) entertainment and (b) to gather arguments to use if I run (again) into a controversy about the performance of a design.

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• arbitrary vire connection / search and replace

  - by fatai

  input :["vire_connection",[1, 2, [ 3, [ 4, "connect"]]], ["connect", [3 , 5] ] ] output:["vire_connection",[ 1, 2, [ 3, [ 4, [ 3, 5 ] ] ] ] ], [ [ 3 , 5] ] ] after connection ( simply copying [3,5] to other wanted position ) , remove connect word input :["vire_connection", [ [ [ ["connect", [ 3, 4 ] ] ] ] ], [ 2, "connect"]] output :["vire_connection",[[[[[3,4]]]]], [ 2, [ 3 , 4 ]]] after connection ( simply copying [3,4] to other wanted position ) , remove connect word how can I do ?

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• Finding patterns in Puzzle games.

  - by José Joel.

  I was wondering, which are the most commonly used algorithms applied to finding patterns in puzzle games conformed by grids of cells. I know that depends of many factors, like the kind of patterns You want to detect, or the rules of the game...but I wanted to know which are the most commonly used algorithms in that kind of problems... For example, games like columns, bejeweled, even tetris. I also want to know if detecting patterns by "brute force" ( like , scanning all the grid trying to find three adyacent cells of the same color ) is significantly worst that using particular algorithms in very small grids, like 4 X 4 for example ( and again, I know that depends of the kind of game and rules ...) Which structures are commonly used in this kind of games ?

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• Big-O for Eight Year Olds?

  - by Jason Baker

  I'm asking more about what this means to my code. I understand the concepts mathematically, I just have a hard time wrapping my head around what they mean conceptually. For example, if one were to perform an O(1) operation on a data structure, I understand that the amount of operations it has to perform won't grow because there are more items. And an O(n) operation would mean that you would perform a set of operations on each element. Could somebody fill in the blanks here? Like what exactly would an O(n^2) operation do? And what the heck does it mean if an operation is O(n log(n))? And does somebody have to smoke crack to write an O(x!)?

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• A quick way to map unordered list of longs to buffer location ?

  - by alhazen

  I have a large number of points (indexed by long) that are processed by multiple threads and I'm using a buffer to hold the output results in order. As the number of points processed is huge, what would be an efficient way to map the indexes of the points to the corresponding ordered position in the buffer ? Example: long bufferIndex bufferIndex index (if BufferSize = 2) (if BufferSize = 4) ---------------------------------------------- 2938 0 0 2939 1 1 2941 1 3 2940 0 2 Thanks.

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• Space requirements of a merge-sort

  - by Arkaitz Jimenez

  I'm trying to understand the space requirements for a Mergesort, O(n). I see that time requirements are basically, amount of levels(logn) * merge(n) so that makes (n log n). Now, we are still allocating n per level, in 2 different arrays, left and right. I do understand that the key here is that when the recursive functions return the space gets deallocated, but I'm not seeing it too obvious. Besides, all the info I find, just states space required is O(n) but don't explain it. Any hint? function merge_sort(m) if length(m) = 1 return m var list left, right, result var integer middle = length(m) / 2 for each x in m up to middle add x to left for each x in m after middle add x to right left = merge_sort(left) right = merge_sort(right) result = merge(left, right) return result

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• Determining the order of a list of numbers (possibly without sorting)

  - by Victor Liu

  I have an array of unique integers (e.g. val[i]), in arbitrary order, and I would like to populate another array (ord[i]) with the the sorted indexes of the integers. In other words, val[ord[i]] is in sorted order for increasing i. Right now, I just fill in ord with 0, ..., N, then sort it based on the value array, but I am wondering if we can be more efficient about it since ord is not populated to begin with. This is more of a question out of curiousity; I don't really care about the extra overhead from having to prepopulate a list and then sort it (it's small, I use insertion sort). This may be a silly question with an obvious answer, but I couldn't find anything online.

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• Recursion - Ship Battle

  - by rgorrosini

  I'm trying to write a little ship battle game in java. It is 100% academic, I made it to practice recursion, so... I want to use it instead of iteration, even if it's simpler and more efficient in most some cases. Let's get down to business. These are the rules: Ships are 1, 2 or 3 cells wide and are placed horizontally only. Water is represented with 0, non-hit ship cells are 1, hit ship cells are 2 and sunken ships have all it's cells in 3. With those rules set, I'm using the following array for testing: int[][] board = new int[][] { {0, 1, 2, 0, 1, 0}, {0, 0, 1, 1, 1, 0}, {0, 3, 0, 0, 0, 0}, {0, 0, 2, 1, 2, 0}, {0, 0, 0, 1, 1, 1}, }; It works pretty good so far, and to make it more user-friendly I would like to add a couple of reports. these are the methods I need for them: Given the matrix, return the amount of ships in it. Same as a), but separating them by state (amount of non-hit ships, hit and sunken ones). I will need a hand with those reports, and I would like to get some ideas. Remember it must be done using recursion, I want to understand this, and the only way to go is practice! Thanks a lot for your time and patience :).

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• align graph nodes in several swimlines

  - by jonny

  I want to align certain graph nodes into several 'lanes' like this Any suitable algorithms (like force-based algorithms in general graph drawing)?

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• help implementing algorithm

  - by davit-datuashvili

  http://en.wikipedia.org/wiki/All_nearest_smaller_values this is site of the problem and here is my code but i have some trouble to implement it import java.util.*; public class stack{ public static void main(String[]args){ int x[]=new int[]{ 0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15 }; Stack<Integer> st=new Stack<Integer>(); for (int a:x){ while (!st.empty() && st.pop()>=a){ System.out.println( st.pop()); if (st.empty()){ break; } else{ st.push(a); } } } } } and here is pseudo code from site S = new empty stack data structure for x in the input sequence: while S is nonempty and the top element of S is greater than or equal to x: pop S if S is empty: x has no preceding smaller value else: the nearest smaller value to x is the top element of S push x onto S

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• Find the centroid of a polygon with weighted vertices

  - by Calle Kabo

  Hi, I know how to find the centroid (center of mass) of a regular polygon. This assumes that every part of the polygon weighs the same. But how do I calculate the centroid of a weightless polygon (made from aerogel perhaps :), where each vertex has a weight? Simplified illustration of what I mean using straight line: 5kg-----------------5kg ^center of gravity 10kg---------------5kg ^center of gravity offset du to weight of vertices Of course, I know how to calculate the center of gravity on a straight line with weighted vertices, but how do I do it on a polygon with weighted vertices? Thanks for your time!

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• What Software Engineering Areas should be stressed upon while Interviewing Candidate for Fulltime So

  - by Rachel

  Hi, This question is somewhat related to other posts which I found on Stackoverflow but not exactly and so am prompted to ask about it. I know we must ask for Data-Structures and Algorithms but what specific data-structures or Algorithms or other CS Concepts should be asked while interviewing Sr. Software Engineering Fulltime Position as compared with Software Engineering Position. Thanks.

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• Unit Testing - Algorithm or Sample based ?

  - by ohadsc

  Say I'm trying to test a simple Set class public IntSet : IEnumerable<int> { Add(int i) {...} //IEnumerable implementation... } And suppose I'm trying to test that no duplicate values can exist in the set. My first option is to insert some sample data into the set, and test for duplicates using my knowledge of the data I used, for example: //OPTION 1 void InsertDuplicateValues_OnlyOneInstancePerValueShouldBeInTheSet() { var set = new IntSet(); //3 will be added 3 times var values = new List<int> {1, 2, 3, 3, 3, 4, 5}; foreach (int i in values) set.Add(i); //I know 3 is the only candidate to appear multiple times int counter = 0; foreach (int i in set) if (i == 3) counter++; Assert.AreEqual(1, counter); } My second option is to test for my condition generically: //OPTION 2 void InsertDuplicateValues_OnlyOneInstancePerValueShouldBeInTheSet() { var set = new IntSet(); //The following could even be a list of random numbers with a duplicate var values = new List<int> { 1, 2, 3, 3, 3, 4, 5}; foreach (int i in values) set.Add(i); //I am not using my prior knowledge of the sample data //the following line would work for any data CollectionAssert.AreEquivalent(new HashSet<int>(values), set); } Of course, in this example, I conveniently have a set implementation to check against, as well as code to compare collections (CollectionAssert). But what if I didn't have either ? This is the situation when you are testing your real life custom business logic. Granted, testing for expected conditions generically covers more cases - but it becomes very similar to implementing the logic again (which is both tedious and useless - you can't use the same code to check itself!). Basically I'm asking whether my tests should look like "insert 1, 2, 3 then check something about 3" or "insert 1, 2, 3 and check for something in general" EDIT - To help me understand, please state in your answer if you prefer OPTION 1 or OPTION 2 (or neither, or that it depends on the case, etc )

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• Given a word, how do I get the list of all words, that differ by one letter?

  - by user187809

  Let's say I have the word "CAT". These words differ from "CAT" by one letter (not the full list) CUT CAP PAT FAT COT etc. Is there an elegant way to generate this? Obviously, one way to do it is through brute force. pseduo code: while (0 to length of word) while (A to Z) replace one letter at a time, and check if the resulting word is a valid word If I had a 10 letter word, the loop would run 26 * 10 = 260 times. Is there a better, elegant way to do this?

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• How to find the number of inversions in an array ?

  - by Michael

  This is an phone interview question: "Find the number of inversions in an array". I guess they mean O(N*log N) solution since O(N^2) is trivial. I guess it cannot be better than O(N*log N) since sorting is O(N*log N) I have checked a similar question from SO and can summarize the answers as follows: Calculate half the distance the elements should be moved to sort the array : copy the array and sort the copy. For each element of the original array a[i] find it's position j in the sorted copy (binary search) and sum abs(i - j)/2. Modify merge sort : modify merge to count inversions between two sorted arrays (it takes O(N)) and run merge sort with the modified merge. Does it make sense ? Are there other (maybe simpler) solution ? Isn't it too hard for a phone interview ?

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• help implementing All Nearest Smaller Values algorithm

  - by davit-datuashvili

  http://en.wikipedia.org/wiki/All_nearest_smaller_values this is site of the problem and here is my code but i have some trouble to implement it import java.util.*; public class stack{ public static void main(String[]args){ int x[]=new int[]{ 0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15 }; Stack<Integer> st=new Stack<Integer>(); for (int a:x){ while (!st.empty() && st.pop()>=a){ System.out.println( st.pop()); if (st.empty()){ break; } else{ st.push(a); } } } } } and here is pseudo code from site S = new empty stack data structure for x in the input sequence: while S is nonempty and the top element of S is greater than or equal to x: pop S if S is empty: x has no preceding smaller value else: the nearest smaller value to x is the top element of S push x onto S

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• Given a function which produces a random integer in the range 1 to 5, write a function which produce

  - by praveen

  what is simple solution what is effective solution to less minimum memory and(or) cpu speed?

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• Time complexity of a powerset generating function

  - by Lirik

  I'm trying to figure out the time complexity of a function that I wrote (it generates a power set for a given string): public static HashSet<string> GeneratePowerSet(string input) { HashSet<string> powerSet = new HashSet<string>(); if (string.IsNullOrEmpty(input)) return powerSet; int powSetSize = (int)Math.Pow(2.0, (double)input.Length); // Start at 1 to skip the empty string case for (int i = 1; i < powSetSize; i++) { string str = Convert.ToString(i, 2); string pset = str; for (int k = str.Length; k < input.Length; k++) { pset = "0" + pset; } string set = string.Empty; for (int j = 0; j < pset.Length; j++) { if (pset[j] == '1') { set = string.Concat(set, input[j].ToString()); } } powerSet.Add(set); } return powerSet; } So my attempt is this: let the size of the input string be n in the outer for loop, must iterate 2^n times (because the set size is 2^n). in the inner for loop, we must iterate 2*n times (at worst). 1. So Big-O would be O((2^n)*n) (since we drop the constant 2)... is that correct? And n*(2^n) is worse than n^2. if n = 4 then (4*(2^4)) = 64 (4^2) = 16 if n = 100 then (10*(2^10)) = 10240 (10^2) = 100 2. Is there a faster way to generate a power set, or is this about optimal?

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• How to perform a Depth First Search iteratively using async/parallel processing?

  - by Prabhu

  Here is a method that does a DFS search and returns a list of all items given a top level item id. How could I modify this to take advantage of parallel processing? Currently, the call to get the sub items is made one by one for each item in the stack. It would be nice if I could get the sub items for multiple items in the stack at the same time, and populate my return list faster. How could I do this (either using async/await or TPL, or anything else) in a thread safe manner? private async Task<IList<Item>> GetItemsAsync(string topItemId) { var items = new List<Item>(); var topItem = await GetItemAsync(topItemId); Stack<Item> stack = new Stack<Item>(); stack.Push(topItem); while (stack.Count > 0) { var item = stack.Pop(); items.Add(item); var subItems = await GetSubItemsAsync(item.SubId); foreach (var subItem in subItems) { stack.Push(subItem); } } return items; } EDIT: I was thinking of something along these lines, but it's not coming together: var tasks = stack.Select(async item => { items.Add(item); var subItems = await GetSubItemsAsync(item.SubId); foreach (var subItem in subItems) { stack.Push(subItem); } }).ToList(); if (tasks.Any()) await Task.WhenAll(tasks); UPDATE: If I wanted to chunk the tasks, would something like this work? foreach (var batch in items.BatchesOf(100)) { var tasks = batch.Select(async item => { await DoSomething(item); }).ToList(); if (tasks.Any()) { await Task.WhenAll(tasks); } } The language I'm using is C#.

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• Enumerating combinations in a distributed manner

  - by Reyzooti

  I have a problem where I must analyse 500C5 combinations (255244687600) of something. Distributing it over a 10 node cluster where each cluster processes roughly 10^6 combinations per second means the job will be complete in about 7hours. The problem I have is distributing the 255244687600 combinations over the 10 nodes. I'd like to present each node with 25524468760, however the algorithms I'm using can only produce the combinations sequentially, I'd like to be able to pass the set of elements and a range of combination indicies eg: [0-10^7) or [10^7,2.0 10^7) etc and have the nodes themselves figure out the combinations. The algorithms I'm using at the moment are from the following: http://home.roadrunner.com/~hinnant/combinations.html A logical question I've considered using a master node, that enumerates each of the combinations and sends work to each of the nodes, however the overhead incurred in iterating the combinations from a single node and communicating back and forth work is enormous, and will subsequently lead to the master node becoming the bottleneck. Are there any good combination iterating algorithms geared up for efficient/optimal distributed enumeration?

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• what are the recent dataStructure and algorithms that one should know?

  - by Shamik

  Recently I came across the SkipList data structure. It really helped me to solve one otherwise critical problem to be solved. I was struggling to solve the same problem with Balanced Binary tree but it became very complex as the tree needs to be always balanced and I wanted to know the existence of not only a particular value but values in certain range. SkipList helped me to solve that problem effectively. I am wondering what else data structures that I need to know? I know - Array, List, Stack, Queue, Linked List, hashtable, tree and its different forms like B-tree, Trie etc. Would like to know if you find some other data structure/concept very interesting to know yet effective enough to be used in a daily development cycle.

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• C++ priority queue structure userd ?

  - by John Retallack

  While searching for some functions in C++ STL documentation I read that push and pop for priority queues needs constant time. "Constant (in the priority_queue). Although notice that push_heap operates in logarithmic time." My question is what kind of data structure is used to mantain a priority queue with O(1) for push and pop ?

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• Determine coordinates of rotated rectangle

  - by MathieuK

  I'm creating an utility application that should detect and report the coordinates of the corners of a transparent rectangle (alpha=0) within an image. So far, I've set up a system with Javascript + Canvas that displays the image and starts a floodfill-like operation when I click inside the transparent rectangle in the image. It correctly determines the bounding box of the floodfill operation and as such can provide me the correct coordinates. Here's my implementation so-far: http://www.scriptorama.nl/image/ (works in recent Firefox / Safari ). However, the bounding box approach breaks down then the transparent rectangle is rotated (CW or CCW) as the resulting bounding box no longer properly represents the proper width and height. I've tried to come up with a few alternatives to detect to corners, but have not been able to think up a proper solution. So, does anyone have any suggestions on how I might approach this so I can properly detect the coordinates of 4 corners of the rotated rectangle?

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• Meshing of Point Clouds from a 3Dlaser scanner

  - by iceman

  Is there any package/software which can do Meshing of Point Clouds in real time? What is the data structure used to represent 3D Point Clouds ?

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• Need help with basic optimization problem

  - by ??iu

  I know little of optimization problems, so hopefully this will be didactic for me: rotors = [1, 2, 3, 4...] widgets = ['a', 'b', 'c', 'd' ...] assert len(rotors) == len(widgets) part_values = [ (1, 'a', 34), (1, 'b', 26), (1, 'c', 11), (1, 'd', 8), (2, 'a', 5), (2, 'b', 17), .... ] Given a fixed number of widgets and a fixed number of rotors, how can you get a series of widget-rotor pairs that maximizes the total value where each widget and rotor can only be used once?

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