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• Finding recurrence relations of an algorithm

  - by Roarke

  I'm reading my algorithms text book, and I'm reading about recurrence relations and finding the algorithms big O complexity. I run across this line "In the case of the merge-sort algorithm, we get the recurrence equation: t(n) = b if n < 2 = 2t(n/2) +bn if n >= 2 for b > 0 my response was "how the heck did we know that?!?!" So i'm wondering if there is a systematic approach, or just a logical way of getting these recurrence relations from the algorithms can some one explain where the b and the two 2's come from?

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• Counting problem: possible sudoko tables?

  - by Sorush Rabiee

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

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• Algorithm for Source Control System?

  - by Michael Stum

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

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• Factorial Algorithms in different languages

  - by Brad Gilbert

  I want to see all the different ways you can come up with, for a factorial subroutine, or program. The hope is that anyone can come here and see if they might want to learn a new language. Ideas: Procedural Functional Object Oriented One liners Obfuscated Oddball Bad Code Polyglot Basically I want to see an example, of different ways of writing an algorithm, and what they would look like in different languages. Please limit it to one example per entry. I will allow you to have more than one example per answer, if you are trying to highlight a specific style, language, or just a well thought out idea that lends itself to being in one post. The only real requirement is it must find the factorial of a given argument, in all languages represented. Be Creative! Recommended Guideline: # Language Name: Optional Style type - Optional bullet points Code Goes Here Other informational text goes here I will ocasionally go along and edit any answer that does not have decent formatting.

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• I need to stop execution during recursive algorithm

  - by Shaza

  Hey, I have a problem in choosing the right method to accomplish my goal. I'm working on Algorithms teaching system, I'm using C#. I need to divide my algorithm into steps, each step will contain a recursion. I have to stop execution after each step, user can then move to the next step(next recursion) using a button in my GUI. After searching, threads was the right choice, but I found several methods: (Thread.sleep/interrupt): didn't work, my GUI freezed !! (Suspend/Resume): I've read that it's a bad idea to use. (Waithandles): still reading about them. (Monitor wait/resume). I don't have much time to try and read all previous methods, please help me in choosing the best method that fits my system.Any suggestions are extremal welcomed.

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• Task management algorithm in C#

  - by silverwizz

  Hi guys, i am looking for efficient task management fo C# what i mean by task management is executing pre-defined interval time of task. Example: task a needs to be run every 1 mins task b needs to be run every 3 mins task c needs to be run every 5 mins these tasks can be added and removed in arbitary time... And the task that i mentioned can be 100000 or more... The task will bw executed forever until it is removed... Do u guys familiar with this kind of algorithm? I am thinking to implement in either c# or php.... Thanks

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• How to improve performance

  - by Ram

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

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• VB.net Network Graph code/algorithm

  - by Jens

  For a school project we need to visualise a computer network graph. The number of computers with specific properties are read from an XML file, and then a graph should be created. Ad random computers are added and removed. Is there any open source project or algorithm that could help us visualising this in VB.net? Or would you suggest us to switch to java. Update: We eventually switched java and used the Jung libraries because this was easier for us to understand and implement.

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• Determine if a day of week and time fall in a custom weekend period

  - by Y Low

  I've been trying to come up with a method, that given a day of week and time of day, it will return if it falls under a custom weekend period. The weekend period is saved in 4 variables as follows: The day of week when it starts (0-6) The time of day when it starts (0-23) The day of week when it ends (0-6) The time of day when it ends (0-23) Based on these fields, the weekend period can be anything the user selected (even if it is well beyond a regular weekend) I've been banging this one for awhile but to no avail. I'm trying this in delphi but any language will do, as I'm looking for the algorithm and not the implementation.

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• Distance from a point to a polygon

  - by clwen

  I am trying to determine the distance from a point to a polygon in 2D space. The point can be inside or outside the polygon; The polygon can be convex or concave. If the point is within the polygon or outside the polygon with a distance smaller than a user-defined constant d, the procedure should return True; False otherwise. I have found a similar question: Distance from a point to a polyhedron or to a polygon. However, the space is 2D in my case and the polygon can be concave, so it's somehow different from that one. I suppose there should be a method simpler than offsetting the polygon by d and determining it's inside or outside the polygon. Any algorithm, code, or hints for me to google around would be appreciated.

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• How to find all clusters of forest on map?

  - by Damir

  How to find all clusters of forest on map ? I have simple class cell like (Type is enum {RIVER, FOREST,GRASS,HILL} class Cell{ public: Type type; int x; int y }; and map like vector<Cell> grid. Can anyone suggest me algorithm to create list<list<Cell>> clusters where list contains FOREST cells in same cluster (cluster are set of connected cells - connection can be in eight direction:up,down,left,right,up_right,up_left,down_left,down_right)? I need to find all clusters of forest on map and put every single cluster in list<Cell>.

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• Scale image to completely fill bounding box

  - by Larsenal

  For instance, if I need to fill a bounding box that is 100px wide by 50px tall, the following input images would have the following behavior: 200w x 200h gets scaled down 50% and 25% gets chopped off the top and bottom. 200w x 100h gets scaled down 50% with no cropping. 100w x 200h gets is not scaled, but 75px get chopped off top and bottom. This seems like it'd be a common resizing function, but I haven't been able to track down an example of the algorithm. Will accept answer in any language including pseudo code. A link to a page with the answer is great too!

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• Rerversing AND Bitwise.

  - by Benjamin

  Hey all, Here's the following algorithm: int encryption(int a, int b) { short int c, c2; uint8_t d; c = a ^ b; c2 = c; d = 0; while(c) { c &= c - 1; d++; } return d; } How can I find which variable a and b I should send in that function to decide of the output value of d? In other words, how can I reverse the algoritm to let's say if I want d=11?

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• Given two lines on a plane, how to find integer points closest to their intersection?

  - by Lukasz Lew

  I can't solve it: You are given 8 integers: A, B, C representing a line on a plane with equation A*x + B*y = C a, b, c representing another line x, y representing a point on a plane The two lines are not parallel therefore divide plane into 4 pieces. Point (x, y) lies inside of one these pieces. Problem: Write a fast algorithm that will find a point with integer coordinates in the same piece as (x,y) that is closest to the cross point of the two given lines. Note: This is not a homework, this is old Euler-type task that I have absolutely no idea how to approach. Update: You can assume that the 8 numbers on input are 32-bit signed integers. But you cannot assume that the solution will be 32 bit.

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• Is there a technical way to speed up a general program above current PC speed limit?

  - by Maksee

  Let's imagine I developed a Windows console application implementing some algorithm calculating something. Let's say it doesn't use any threads, just straightforward linear approach with ifs, loops and so on. Is there any technical way to make if run it 100x times faster than on the most advanced current PC? For example one of the way would be to run it on a super computer that emulates i386 faster than any of the existing PCs. But in this case the question what computer and does it really have ability to emulate Windows. In other words, is there real examples of such approach? Although in general it looks useless, but if there is a way, one could develop some program on his general home computer and pay for running it much faster on some other hardware. I suppose that this question could be asked on superuser.com, but since there are possible specific with such things as assembler instructions or threads, I thought that stackoverflow.com is better

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• Find point which sum of distances to set of other points is minimal

  - by Pawel Markowski

  I have one set (X) of points (not very big let's say 1-20 points) and the second (Y), much larger set of points. I need to choose some point from Y which sum of distances to all points from X is minimal. I came up with an idea that I would treat X as a vertices of a polygon and find centroid of this polygon, and then I will choose a point from Y nearest to the centroid. But I'm not sure whether centroid minimizes sum of its distances to the vertices of polygon, so I'm not sure whether this is a good way? Is there any algorithm for solving this problem? Points are defined by geographical coordinates.

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• Algorithm for non-contiguous netmask match

  - by Gianluca

  Hi, I have to write a really really fast algorithm to match an IP address to a list of groups, where each group is defined using a notation like 192.168.0.0/252.255.0.255. As you can see, the bitmask can contain zeros even in the middle, so the traditional "longest prefix match" algorithms won't work. If an IP matches two groups, it will be assigned to the group containing most 1's in the netmask. I'm not working with many entries (let's say < 1000) and I don't want to use a data structure requiring a large memory footprint (let's say 1-2 MB), but it really has to be fast (of course I can't afford a linear search). Do you have any suggestion? Thanks guys. UPDATE: I found something quite interesting at http://www.cse.usf.edu/~ligatti/papers/grouper-conf.pdf, but it's still too memory-hungry for my utopic use case

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• JQuery/JavaScript div tag "containment" approach/algorithm?

  - by Pete Alvin

  Background: I've created an online circuit design application where div tags are containers that contain smaller div containers and so forth. Question: For any particular div tag I need to quickly identify if it contains other div tags (that may in turn contain other div tags). I've searched JQuery and I don't see any built-in routine for this. Does anyone know of an algorithm that's quicker than O(n^2)? Seems like I have to walk the list of div tags in an outer loop (n) and have an inner loop (another n) to compare against all other div tags and do a "containment test" (position, width, height), building a list of contained div tags. That's n-squared. Then I have to build a list of all nested div tags by concatenating contained lists. So the total would be O(n^2)+n. There must be a better way?

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• Nesting maximum amount of shapes on a surface

  - by Fuu

  In industry, there is often a problem where you need to calculate the most efficient use of material, be it fabric, wood, metal etc. So the starting point is X amount of shapes of given dimensions, made out of polygons and/or curved lines, and target is another polygon of given dimensions. I assume many of the current CAM suites implement this, but having no experience using them or of their internals, what kind of computational algorithm is used to find the most efficient use of space? Can someone point me to a book or other reference that discusses this topic?

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• Extracting rightmost N bits of an integer

  - by srandpersonia

  In the yester Code Jam Qualification round http://code.google.com/codejam/contest/dashboard?c=433101#s=a&a=0 , there was a problem called Snapper Chain. From the contest analysis I came to know the problem requires bit twiddling stuff like extracting the rightmost N bits of an integer and checking if they all are 1. I saw a contestant's(Eireksten) code which performed the said operation like below: (((K&(1<<N)-1))==(1<<N)-1) I couldn't understand how this works. What is the use of -1 there in the comparison?. If somebody can explain this, it would be very much useful for us rookies. Also, Any tips on identifying this sort of problems would be much appreciated. I used a naive algorithm to solve this problem and ended up solving only the smaller data set.(It took heck of a time to compile the larger data set which is required to be submitted within 8 minutes.). Thanks in advance.

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• Algorithm for Search page

  - by Geetha

  Hi All, I am creating a search page where we can find the product by entering the text. ex: Brings on the night. My query bring the records which contain atleast word from this. Needs: 1. First row should contains the record with the given sentence. 2. Second most matching....etc How to achieve this. Is there any algorithm for this. It will be more helpful if anyone share your idea. Geetha

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• How to return arrays with the biggest elements in C#?

  - by theateist

  I have multiple int arrays: 1) [1 , 202,4 ,55] 2) [40, 7] 3) [2 , 48 ,5] 4) [40, 8 ,90] I need to get the array that has the biggest numbers in all positions. In my case that would be array #4. Explanation: arrays #2, #4 have the biggest number in 1st position, so after the first iteration these 2 arrays will be returned ([40, 7] and [40, 8 ,90]) now after comparing 2nd position of the returned array from previous iteration we will get array #4 because 8 7 and so on... Can you suggest an efficient algorithm for this? Doing with Linq will be preferable. UPDATE There is no limitation for the length, but as soon as some number in any position is greater, so this array is the biggest.

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• What is the typical method to separate connected letters in a word using OCR

  - by Maysam

  I am very new to OCR and almost know nothing about the algorithms used to recognize words. I am just getting familiar to that. Could anybody please advise on the typical method used to recognize and separate individual characters in connected form (I mean in a word where all letters are linked together)? Forget about handwriting, supposing the letters are connected together using a known font, what is the best method to determine each individual character in a word? When characters are written separately there is no problem, but when they are joined together, we should know where every single character starts and ends in order to go to the next step and match them individually with a letter. Is there any known algorithm for that?

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• What is the JVM Scheduling algorithm ?

  - by IHawk

  Hello ! I am really curious about how does the JVM work with threads ! In my searches in internet, I found some material about RTSJ, but I don't know if it's the right directions for my answers. I also found this topic in sun's forums, http://forums.sun.com/thread.jspa?forumID=513&threadID=472453, but that's not satisfatory. Can someone give me some directions, material, articles or suggestion about the JVM scheduling algorithm ? I am also looking for information about the default configurations of Java threads in the scheduler, like 'how long does it take for every thread' in case of time-slicing. And this stuff. I would appreciate any help ! Thank you !

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• Subset generation by rules

  - by Sazug

  Let's say that we have a 5000 users in database. User row has sex column, place where he/she was born column and status (married or not married) column. How to generate a random subset (let's say 100 users) that would satisfy these conditions: 40% should be males and 60% - females 50% should be born in USA, 20% born in UK, 20% born in Canada, 10% in Australia 70% should be married and 30% not. These conditions are independent, that is we cannot do like this: (0.4 * 0.5 * 0.7) * 100 = 14 users that are males, born in USA and married (0.4 * 0.5 * 0.3) * 100 = 6 users that are males, born in USA and not married. Is there an algorithm to this generation?

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