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  • What are the most known arbitrary precision arithmetic implementation approaches?

    - by keykeeper
    I'm going to write a class library for .NET which provide an implementation of arbitrary precision arithmetic for integer, rational and maybe complex numbers. What best known approaches should I become familiar with? I tried to start with Knuth's TAOCP Vol.2 (Seminumerical Algorithms, Chapter 4 – Arithmetic) but it's too complicated. At least I couldn't get the ideas in a relatively short period of time.

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  • Companion Book for Cormen

    - by Robert S. Barnes
    I asked this question on Stackoverflow and they suggested it was more appropriate here. I"m taking a course soon based on the first fourteen chapters of Cormen's Introduction to Algorithms. The course is based on a translation of the 2003 edition. I have two questions: Is it recommended to get the newer 2009 edition and what are the differences? Can anyone recommend a good companion text which has more worked problems and less, "this clearly works" type explanations?

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  • What does path finding in internet routing do and how is it different from A*?

    - by alan2here
    Note: If you don't understand this question then feel free to ask clarification in the comments instead of voting down, it might be that this question needs some more work at the moment. I've been directed here from the Stack Excange chat room Root Access because my question didn't fit on Super User. In many aspects path finding algorithms like A star are very similar to internet routing. For example: A node in an A* path finding system can search for a path though edges between other nodes. A router that's part of the internet can search for a route though cables between other routers. In the case of A*, open and closed lists are kept by the system as a whole, sepratly from any individual node as well as each node being able to temporarily store a state involving several numbers. Routers on the internet seem to have remarkable properties, as I understand it: They are very performant. New nodes can be added at any time that use a free address from a finite (not tree like) address space. It's real routing, like A*, there's never any doubling back for example. Similar IP addresses don't have to be geographically nearby. The network reacts quickly to changes to the networks shape, for example if a line is down. Routers share information and it takes time for new IP's to be registered everywhere, but presumably every router doesn't have to store a list of all the addresses each of it's directions leads most directly to. I'm looking for a basic, general, high level description of the algorithms workings from the point of view of an individual router. Does anyone have one? I presume public internet routers don't use A* as the overheads would be to large, and scale to poorly. I also presume there is a single method worldwide because it seems as if must involve a lot of transferring data to update and communicate a reasonable amount of state between neighboring routers. For example, perhaps the amount of data that needs to be stored in each router scales logarithmically with the number of routers that exist worldwide, the detail and reliability of the routing is reduced over increasing distances, there is increasing backtracking involved in parts of the network that are less geographically uniform or maybe each router really does perform an A* style search, temporarily maintaining open and closed lists when a packet arrives.

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  • Is there a known algorithm for scheduling tournament matchups?

    - by barfoon
    Just wondering if there is a tournament scheduling algorithm already out there that I could use or even adapt slightly. Here are my requirements: A variable number of opponents belonging to a variable number of teams/clubs each must be paired with an opponent Two opponents cannot be from the same club If there are an odd number of players, 1 of them randomly is selected to get a bye Any algorithms related to this sort of requirement set would be appreciated. EDIT: I only need to run this a maximum of one time, creating matchups for the first 'round' of the tournament.

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  • Is it possible (and practical) to search a string for arbitrary-length repeating patterns?

    - by blz
    I've recently developed a huge interest in cryptography, and I'm exploring some of the weaknesses of ECB-mode block ciphers. A common attack scenario involves encrypted cookies, whose fields can be represented as (relatively) short hex strings. Up until now, I've relied on my eyes to pick out repeating blocks, but this is rather tedious. I'm wondering what kind of algorithms (if any) could help me automate my search for repeating patterns within a string. Can anybody point me in the right direction?

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  • Finding the width of a directed acyclic graph... with only the ability to find parents

    - by Platinum Azure
    Hi guys, I'm trying to find the width of a directed acyclic graph... as represented by an arbitrarily ordered list of nodes, without even an adjacency list. The graph/list is for a parallel GNU Make-like workflow manager that uses files as its criteria for execution order. Each node has a list of source files and target files. We have a hash table in place so that, given a file name, the node which produces it can be determined. In this way, we can figure out a node's parents by examining the nodes which generate each of its source files using this table. That is the ONLY ability I have at this point, without changing the code severely. The code has been in public use for a while, and the last thing we want to do is to change the structure significantly and have a bad release. And no, we don't have time to test rigorously (I am in an academic environment). Ideally we're hoping we can do this without doing anything more dangerous than adding fields to the node. I'll be posting a community-wiki answer outlining my current approach and its flaws. If anyone wants to edit that, or use it as a starting point, feel free. If there's anything I can do to clarify things, I can answer questions or post code if needed. Thanks! EDIT: For anyone who cares, this will be in C. Yes, I know my pseudocode is in some horribly botched Python look-alike. I'm sort of hoping the language doesn't really matter.

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  • help in the Donalds B. Johnson's algorithm, i cannot understand the pseudo code (PART II)

    - by Pitelk
    Hi all , i cannot understand a certain part of the paper published by Donald Johnson about finding cycles (Circuits) in a graph. More specific i cannot understand what is the matrix Ak which is mentioned in the following line of the pseudo code : Ak:=adjacency structure of strong component K with least vertex in subgraph of G induced by {s,s+1,....n}; to make things worse some lines after is mentins " for i in Vk do " without declaring what the Vk is... As far i have understand we have the following: 1) in general, a strong component is a sub-graph of a graph, in which for every node of this sub-graph there is a path to any node of the sub-graph (in other words you can access any node of the sub-graph from any other node of the sub-graph) 2) a sub-graph induced by a list of nodes is a graph containing all these nodes plus all the edges connecting these nodes. in paper the mathematical definition is " F is a subgraph of G induced by W if W is subset of V and F = (W,{u,y)|u,y in W and (u,y) in E)}) where u,y are edges , E is the set of all the edges in the graph, W is a set of nodes. 3)in the code implementation the nodes are named by integer numbers 1 ... n. 4) I suspect that the Vk is the set of nodes of the strong component K. now to the question. Lets say we have a graph G= (V,E) with V = {1,2,3,4,5,6,7,8,9} which it can be divided into 3 strong components the SC1 = {1,4,7,8} SC2= {2,3,9} SC3 = {5,6} (and their edges) Can anybody give me an example for s =1, s= 2, s= 5 what if going to be the Vk and Ak according to the code? The pseudo code is in my previous question in http://stackoverflow.com/questions/2908575/help-in-the-donalds-b-johnsons-algorithm-i-cannot-understand-the-pseudo-code and the paper can be found at http://stackoverflow.com/questions/2908575/help-in-the-donalds-b-johnsons-algorithm-i-cannot-understand-the-pseudo-code thank you in advance

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  • please help me to choose good books on algorithms [closed]

    - by davit-datuashvili
    Possible Duplicate: What is the best book for learning about Algorithms? i want to help me to choose good books on algorithms many people from this site say me that show me your code and now i ask u to help me to choose good books on algorithms please i have not books on algorithms and in case i decide to buy it of course must buy book which has high quality yes? so please any ideas ?links everything

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  • Looking for algorithms regarding scaling and moving

    - by user1806687
    I've been bashing my head for the past couple of weeks trying to find algorithms that would help me accomplish, on first look very easy task. So, I got this one object currently made out of 5 cuboids (2 sides, 1 top, 1 bottom, 1 back), this is just for an example, later on there will be whole range of different set ups. I have included three pictures of this object(as said this is just for an example). Now, the thing is when the user scales the whole object this is what should happen: X scale: top and bottom cuboids should get scaled by a scale factor, sides should get moved so they are positioned just like they were before(in this case at both ends of top and bottom cuboids), back should get scaled so it fits like before(if I simply scale it by a scale factor it will leave gaps on each side). Y scale: sides should get scaled by a scale factor, top and bottom cuboid should get moved, and back should also get scaled. Z scale: sides, top and bottom cuboids should get scaled, back should get moved. Here is an image of the example object (a thick walled box, with one face missing, where each wall is made by a cuboid): Front of the object: Hope you can help,

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  • Is it possible to efficiently store all possible phone numbers in memory?

    - by Spencer K
    Given the standard North American phone number format: (Area Code) Exchange - Subscriber, the set of possible numbers is about 6 billion. However, efficiently breaking down the nodes into the sections listed above would yield less than 12000 distinct nodes that can be arranged in groupings to get all the possible numbers. This seems like a problem already solved. Would it done via a graph or tree?

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  • Microsoft Interview Preparation

    - by Manish
    I have 8 years of java background. Need help in identifying topics I need to prepare for Microsoft interview. I need to know how many rounds Microsoft will have and what all things these rounds consist of. I have identified the following topics. Please let me know if I need to prepare anything else as well. Arrays Linked Lists Recursion Stacks Queue Trees Graph -- What all I should prepare here Dynamic Programming -- again what all I need to prepare Sorting, Searching String Algos

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  • Need help on a problemset in a programming contest

    - by topher
    I've attended a local programming contest on my country. The name of the contest is "ACM-ICPC Indonesia National Contest 2013". The contest has ended on 2013-10-13 15:00:00 (GMT +7) and I am still curious about one of the problems. You can find the original version of the problem here. Brief Problem Explanation: There are a set of "jobs" (tasks) that should be performed on several "servers" (computers). Each job should be executed strictly from start time Si to end time Ei Each server can only perform one task at a time. (The complicated thing goes here) It takes some time for a server to switch from one job to another. If a server finishes job Jx, then to start job Jy it will need an intermission time Tx,y after job Jx completes. This is the time required by the server to clean up job Jx and load job Jy. In other word, job Jy can be run after job Jx if and only if Ex + Tx,y = Sy. The problem is to compute the minimum number of servers needed to do all jobs. Example: For example, let there be 3 jobs S(1) = 3 and E(1) = 6 S(2) = 10 and E(2) = 15 S(3) = 16 and E(3) = 20 T(1,2) = 2, T(1,3) = 5 T(2,1) = 0, T(2,3) = 3 T(3,1) = 0, T(3,2) = 0 In this example, we need 2 servers: Server 1: J(1), J(2) Server 2: J(3) Sample Input: Short explanation: The first 3 is the number of test cases, following by number of jobs (the second 3 means that there are 3 jobs for case 1), then followed by Ei and Si, then the T matrix (sized equal with number of jobs). 3 3 3 6 10 15 16 20 0 2 5 0 0 3 0 0 0 4 8 10 4 7 12 15 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 8 10 4 7 12 15 1 4 0 50 50 50 50 0 50 50 50 50 0 50 50 50 50 0 Sample Output: Case #1: 2 Case #2: 1 Case #3: 4 Personal Comments: The time required can be represented as a graph matrix, so I'm supposing this as a directed acyclic graph problem. Methods I tried so far is brute force and greedy, but got Wrong Answer. (Unfortunately I don't have my code anymore) Could probably solved by dynamic programming too, but I'm not sure. I really have no clear idea on how to solve this problem. So a simple hint or insight will be very helpful to me.

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  • Merge sort versus quick sort performance

    - by Giorgio
    I have implemented merge sort and quick sort using C (GCC 4.4.3 on Ubuntu 10.04 running on a 4 GB RAM laptop with an Intel DUO CPU at 2GHz) and I wanted to compare the performance of the two algorithms. The prototypes of the sorting functions are: void merge_sort(const char **lines, int start, int end); void quick_sort(const char **lines, int start, int end); i.e. both take an array of pointers to strings and sort the elements with index i : start <= i <= end. I have produced some files containing random strings with length on average 4.5 characters. The test files range from 100 lines to 10000000 lines. I was a bit surprised by the results because, even though I know that merge sort has complexity O(n log(n)) while quick sort is O(n^2), I have often read that on average quick sort should be as fast as merge sort. However, my results are the following. Up to 10000 strings, both algorithms perform equally well. For 10000 strings, both require about 0.007 seconds. For 100000 strings, merge sort is slightly faster with 0.095 s against 0.121 s. For 1000000 strings merge sort takes 1.287 s against 5.233 s of quick sort. For 5000000 strings merge sort takes 7.582 s against 118.240 s of quick sort. For 10000000 strings merge sort takes 16.305 s against 1202.918 s of quick sort. So my question is: are my results as expected, meaning that quick sort is comparable in speed to merge sort for small inputs but, as the size of the input data grows, the fact that its complexity is quadratic will become evident? Here is a sketch of what I did. In the merge sort implementation, the partitioning consists in calling merge sort recursively, i.e. merge_sort(lines, start, (start + end) / 2); merge_sort(lines, 1 + (start + end) / 2, end); Merging of the two sorted sub-array is performed by reading the data from the array lines and writing it to a global temporary array of pointers (this global array is allocate only once). After each merge the pointers are copied back to the original array. So the strings are stored once but I need twice as much memory for the pointers. For quick sort, the partition function chooses the last element of the array to sort as the pivot and scans the previous elements in one loop. After it has produced a partition of the type start ... {elements <= pivot} ... pivotIndex ... {elements > pivot} ... end it calls itself recursively: quick_sort(lines, start, pivotIndex - 1); quick_sort(lines, pivotIndex + 1, end); Note that this quick sort implementation sorts the array in-place and does not require additional memory, therefore it is more memory efficient than the merge sort implementation. So my question is: is there a better way to implement quick sort that is worthwhile trying out? If I improve the quick sort implementation and perform more tests on different data sets (computing the average of the running times on different data sets) can I expect a better performance of quick sort wrt merge sort? EDIT Thank you for your answers. My implementation is in-place and is based on the pseudo-code I have found on wikipedia in Section In-place version: function partition(array, 'left', 'right', 'pivotIndex') where I choose the last element in the range to be sorted as a pivot, i.e. pivotIndex := right. I have checked the code over and over again and it seems correct to me. In order to rule out the case that I am using the wrong implementation I have uploaded the source code on github (in case you would like to take a look at it). Your answers seem to suggest that I am using the wrong test data. I will look into it and try out different test data sets. I will report as soon as I have some results.

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  • Approach for packing 2D shapes while minimizing total enclosing area

    - by Dennis
    Not sure on my tags for this question, but in short .... I need to solve a problem of packing industrial parts into crates while minimizing total containing area. These parts are motors, or pumps, or custom-made components, and they have quite unusual shapes. For some, it may be possible to assume that a part === rectangular cuboid, but some are not so simple, i.e. they assume a shape more of that of a hammer or letter T. With those, (assuming 2D shape), by alternating direction of top & bottom, one can pack more objects into the same space, than if all tops were in the same direction. Crude example below with letter "T"-shaped parts: ***** xxxxx ***** x ***** *** ooo * x vs * x vs * x vs * x o * x * xxxxx * x * x o xxxxx xxx Right now we are solving the problem by something like this: using CAD software, make actual models of how things fit in crate boxes make estimates of actual crate dimensions & write them into Excel file (1) is crazy amount of work and as the result we have just a limited amount of possible entries in (2), the Excel file. The good things is that programming this is relatively easy. Given a combination of products to go into crates, we do a lookup, and if entry exists in the Excel (or Database), we bring it out. If it doesn't, we say "sorry, no data!". I don't necessarily want to go full force on making up some crazy algorithm that given geometrical part description can align, rotate, and figure out best part packing into a crate, given its shape, but maybe I do.. Question Well, here is my question: assuming that I can represent my parts as 2D (to be determined how), and that some parts look like letter T, and some parts look like rectangles, which algorithm can I use to give me a good estimate on the dimensions of the encompassing area, while ensuring that the parts are packed in a minimal possible area, to minimize crating/shipping costs? Are there approximation algorithms? Seeing how this can get complex, is there an existing library I could use? My thought / Approach My naive approach would be to define a way to describe position of parts, and place the first part, compute total enclosing area & dimensions. Then place 2nd part in 0 degree orientation, repeat, place it at 180 degree orientation, repeat (for my case I don't think 90 degree rotations will be meaningful due to long lengths of parts). Proceed using brute force "tacking on" other parts to the enclosing area until all parts are processed. I may have to shift some parts a tad (see 3rd pictorial example above with letters T). This adds a layer of 2D complexity rather than 1D. I am not sure how to approach this. One idea I have is genetic algorithms, but I think those will take up too much processing power and time. I will need to look out for shape collisions, as well as adding extra padding space, since we are talking about real parts with irregularities rather than perfect imaginary blocks. I'm afraid this can get geometrically messy fairly fast, and I'd rather keep things simple, if I can. But what if the best (practical) solution is to pack things into different crate boxes rather than just one? This can get a bit more tricky. There is human element involved as well, i.e. like parts can go into same box and are thus a constraint to be considered. Some parts that are not the same are sometimes grouped together for shipping and can be considered as a common grouped item. Sometimes customers want things shipped their way, which adds human element to constraints. so there will have to be some customization.

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  • Reading graph inputs for a programming puzzle and then solving it

    - by Vrashabh
    I just took a programming competition question and I absolutely bombed it. I had trouble right at the beginning itself from reading the input set. The question was basically a variant of this puzzle http://codercharts.com/puzzle/evacuation-plan but also had an hour component in the first line(say 3 hours after start of evacuation). It reads like this This puzzle is a tribute to all the people who suffered from the earthquake in Japan. The goal of this puzzle is, given a network of road and locations, to determine the maximum number of people that can be evacuated. The people must be evacuated from evacuation points to rescue points. The list of road and the number of people they can carry per hour is provided. Input Specifications Your program must accept one and only one command line argument: the input file. The input file is formatted as follows: the first line contains 4 integers n r s t n is the number of locations (each location is given by a number from 0 to n-1) r is the number of roads s is the number of locations to be evacuated from (evacuation points) t is the number of locations where people must be evacuated to (rescue points) the second line contains s integers giving the locations of the evacuation points the third line contains t integers giving the locations of the rescue points the r following lines contain to the road definitions. Each road is defined by 3 integers l1 l2 width where l1 and l2 are the locations connected by the road (roads are one-way) and width is the number of people per hour that can fit on the road Now look at the sample input set 5 5 1 2 3 0 3 4 0 1 10 0 2 5 1 2 4 1 3 5 2 4 10 The 3 in the first line is the additional component and is defined as the number of hours since the resuce has started which is 3 in this case. Now my solution was to use Dijisktras algorithm to find the shortest path between each of the rescue and evac nodes. Now my problem started with how to read the input set. I read the first line in python and stored the values in variables. But then I did not know how to store the values of the distance between the nodes and what DS to use and how to input it to say a standard implementation of dijikstras algorithm. So my question is two fold 1.) How do I take the input of such problems? - I have faced this problem in quite a few competitions recently and I hope I can get a simple code snippet or an explanation in java or python to read the data input set in such a way that I can input it as a graph to graph algorithms like dijikstra and floyd/warshall. Also a solution to the above problem would also help. 2.) How to solve this puzzle? My algorithm was: Find shortest path between evac points (in the above example it is 14 from 0 to 3) Multiply it by number of hours to get maximal number of saves Also the answer given for the variant for the input set was 24 which I dont understand. Can someone explain that also. UPDATE: I get how the answer is 14 in the given problem link - it seems to be just the shortest path between node 0 and 3. But with the 3 hour component how is the answer 24 UPDATE I get how it is 24 - its a complete graph traversal at every hour and this is how I solve it Hour 1 Node 0 to Node 1 - 10 people Node 0 to Node 2- 5 people TotalRescueCount=0 Node 1=10 Node 2= 5 Hour 2 Node 1 to Node 3 = 5(Rescued) Node 2 to Node 4 = 5(Rescued) Node 0 to Node 1 = 10 Node 0 to Node 2 = 5 Node 1 to Node 2 = 4 TotalRescueCount = 10 Node 1 = 10 Node 2= 5+4 = 9 Hour 3 Node 1 to Node 3 = 5(Rescued) Node 2 to Node 4 = 5+4 = 9(Rescued) TotalRescueCount = 9+5+10 = 24 It hard enough for this case , for multiple evac and rescue points how in the world would I write a pgm for this ?

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  • Problem with OOP Class Definitions

    - by oben
    Hi, this is Oben from Turkey. I work for my homework in C++ and i have some problems with multiply definitions. My graph class ; class Graph{ private: string name; //Graph name fstream* graphFile; //Graph's file protected: string opBuf; //Operations buffer int containsNode(string); //Query if a node is present Node* nodes; //Nodes in the graph int nofNodes; //Number of nodes in the graph public: static int nOfGraphs; //Number of graphs produced Graph(); //Constructors and destructor Graph(int); Graph(string); Graph(const Graph &); ~Graph(); string getGraphName(); //Get graph name bool addNode(string); //add a node to the graph bool deleteNode(string); //delete a node from the graph bool addEdge(string,string); //add an edge to the graph bool deleteEdge(string,string); //delete an edge from the graph void intersect(const Graph&); //intersect the graph with the <par> void unite(const Graph&); //intersect the graph with the <par> string toString(); //get string representation of the graph void acceptTraverse(BreadthFirst*); void acceptTraverse(DepthFirst *); }; and my traversal class; class Traversal { public: string *visitedNodes; virtual string traverse (const Graph & ); }; class BreadthFirst : public Traversal { public : BreadthFirst(); string traverse(); }; class DepthFirst : public Traversal { public : DepthFirst(); string traverse(); }; My problem is in traversal class , i need to declare Graph class at the same time , in graph class i need traversal class to declare. I have big problems with declerations :) Could you please help me ?

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  • Recommend an algorithms exercise book?

    - by Parappa
    I have a little book called Problems on Algorithms by Ian Parberry which is chock full of exercises related to the study of algorithms. Can anybody recommend similar books? What I am not looking for are recommendations of good books related to algorithms or the theory of computation. Introduction to Algorithms is a good one, and of course there's the Knuth stuff. Ideally I want to know of any books that are light on instructional material and heavy on sample problems. In a nutshell, exercise books. Preferably dedicated to algorithms rather than general logic or other math problems. By the way, the Parberry book does not seem to be in print, but it is available as a PDF dowload.

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  • programming practices starting

    - by Tamim Ad Dari
    I have taken my major as computer science and Engineering and I am really confused at this moment. My first course was about learning C and C++ and I learned the basics of those. Now I am really confused what to do next. Some says I should practice algorithms and do contests in ACM-ICPC for now. Others tell me to start software development. But As I started digging its really a vast topic and there are many aspects of these, like web design, web-development, iOS-development, android... etc many things. And I am really confused about what should I do just now. Any advice for me to start with?

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  • Why hill climbing is called anytime algorithm?

    - by crucified soul
    From wikipedia, Anytime algorithm In computer science an anytime algorithm is an algorithm that can return a valid solution to a problem even if it's interrupted at any time before it ends. The algorithm is expected to find better and better solutions the more time it keeps running. Hill climbing Hill climbing can often produce a better result than other algorithms when the amount of time available to perform a search is limited, such as with real-time systems. It is an anytime algorithm: it can return a valid solution even if it's interrupted at any time before it ends. Hill climbing algorithm can stuck into local optima or ridge, after that even if it runs infinite time, the result won't be any better. Then, why hill climbing is called anytime algorithm?

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  • Programmaticaly finding the Landau notation (Big O or Theta notation) of an algorithm?

    - by Julien L
    I'm used to search for the Landau (Big O, Theta...) notation of my algorithms by hand to make sure they are as optimized as they can be, but when the functions are getting really big and complex, it's taking way too much time to do it by hand. it's also prone to human errors. I spent some time on Codility (coding/algo exercises), and noticed they will give you the Landau notation for your submitted solution (both in Time and Memory usage). I was wondering how they do that... How would you do it? Is there another way besides Lexical Analysis or parsing of the code? PS: This question concerns mainly PHP and or JavaScript, but I'm opened to any language and theory.

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  • Reverse horizontal and vertical for a HTML table

    - by porton
    There is a two-dimensional array describing a HTML table. Each element of the array consists of: the cell content rowspan colspan Every row of this two dimensional array corresponds to <td> cells of a <tr> of the table which my software should generate. I need to "reverse" the array (interchange vertical and horizontal direction). Insofar I considered algorithm based on this idea: make a rectangular matrix of the size of the table and store in every element of this matrix the corresponding index of the element of the above mentioned array. (Note that two elements of the matrix may be identical due rowspan/colspan.) Then I could use this matrix to calculate rowspan/colspan for the inverted table. But this idea seems bad for me. Any other algorithms? Note that I program in PHP.

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  • Random number generation algorithm for human brains?

    - by Magnus Wolffelt
    Are you aware of, or have you devised, any practical, simple-to-learn "in-head" algorithms that let humans generate (somewhat "true") random numbers? By "in-head" I mean.. preferrably without any external tools or devices. Also, a high output (many random numbers per minute) is desirable. Asked this on SO but it didn't get much interest. Maybe this is better suited for programmers.. :) I'm genuinely curious about anything that people might have come up with on this problem.

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