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• One-way flight trip problem.

  - by psihodelia

  You are going on a one-way indirect flight trip that includes billions transfers. You are not stopping twice in the same airport. You have 1 ticket for each part of your trip. Each ticket contains src and dst airport. All the tickets you have are randomly sorted. You forgot the original departure airport (very first src) and your destination (last dst). Design an algorithm to reconstruct your trip with minimum big-O complexity.

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• find a duplicate entry in an array in constant space and O(n) time [closed]

  - by Anubhav Agarwal

  Possible Duplicate: Algorithm to find a duplicate entry in constant space and O(n) time Given an array of N integer such that only one integer is repeated. Find the repeated integer in O(n) time and constant space. There is no range for the value of integers or the value of N For example given an array of 6 integers as 23 45 67 87 23 47. The answer is 23 (I hope this covers ambiguous and vague part) I searched on the net but was unable to find any such question in which range of integers was not fixed. Also here is an example that answers a similar question to mine but here he created a hash table with the highest integer value in C++.But the cpp does not allow such to create an array with 2^64 element(on a 64-bit computer).

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• Efficiently remove points with same slope

  - 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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• Algorithm for calculating indefinite integrals

  - by mbac32768

  Suppose I have an integral that's bounded on one (or both) ends by (-)infinity. AFAICT, I can't analytically solve this problem, it takes brute force (e.g. using a Left Riemann Sum). I'm having trouble generalizing the algorithm so that it sets the proper subdivisions; I'll either do far too much work to calculate something trivial, or not do nearly enough and have huge aliasing errors. Answering in any language is cool, but maybe someone with better google-fu can end this quickly. :) Is what I'm looking for as impossible as trying to measure the British coastline?

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• Visit neighbor of a position in a 2d-array

  - by Martin

  I have the following two dimensional array: static int[,] arr = new int[5, 5] { { 00, 00, 00, 01, 00 }, { 00, 00, 01, 01, 00 }, { 00, 00, 01, 01, 00 }, { 00, 00, 01, 01, 00 }, { 00, 00, 00, 01, 00 }, }; I have to a implement a method called Hit(int x, int y). When we hit a 0 in the array (i.e. Hit(0, 0), Hit(1, 1), but not Hit(3, 0)) I would like all the adjacent zeros to the zero we hit to be incremented by 10. So if I call Hit(1, 1), the array should become the following. static int[,] arr = new int[5, 5] { { 10, 10, 10, 01, 00 }, { 10, 10, 01, 01, 00 }, { 10, 10, 01, 01, 00 }, { 10, 10, 01, 01, 00 }, { 10, 10, 10, 01, 00 }, }; Any idea how I could implement that? It sounds to me like a Depth First Search/Recursive sort-of algorithm should do the job, but I haven't been able to implement it for an 2d array. Thanks for the help!

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• Fitting 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 subject?

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• Programming cookbook? [closed]

  - by user73669

  Possible Duplicate: What is the single most influential book every programmer should read? Hello With sites like The Daily WTF and recurring threads on Slashdot and elsewhere about bad programming, I figured that, to avoid people reinventing the wheel (badly or not), there should be a good, fat book on programming that would go through typical programming problems and show good, known algorithms, either in pseudo-code or some language with an easy syntax so that the language is not an issue. Here's the list of books on the subject I saw at my local computer bookstore. Can you recommend a couple, or add to this list if it's missing better options? The art of computer programming Code complete Masterminds of programming 97 things every programmer should know The passionate programmer Pragmatic thinking & learning Coders at work The algorithm design manual Algorithms and programming How to think about algorithms How to think like a programmer Why programs fail Beautiful data Beautiful code The productive programmer Solid code Write great code Clean code Programming language pragmatics Hello world Learning Processing Learn to program Thank you.

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• How to implement square root and exponentiation on arbitrary length numbers?

  - by tomp

  I'm working on new data type for arbitrary length numbers (only non-negative integers) and I got stuck at implementing square root and exponentiation functions (only for natural exponents). Please help. I store the arbitrary length number as a string, so all operations are made char by char. Please don't include advices to use different (existing) library or other way to store the number than string. It's meant to be a programming exercise, not a real-world application, so optimization and performance are not so necessary. If you include code in your answer, I would prefer it to be in either pseudo-code or in C++. The important thing is the algorithm, not the implementation itself. Thanks for the help.

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• Compute column widths in a HTML-like manner (based on cell contents)

  - by cipak

  Hi, I have a grid of data that I want to export to RTF, PDF etc. using various (and not perfect) PHP converters/generators. What I am missing most is the HTML table automatic adjustment of column widths based on the lengths of strings in the cells (strings contain line breaks which complicate things a bit, as they should be preserved). I need an algorithm that, given the contents of the cells (plain text), a total width of the table and an average width of a character, would return a width for each column. I wouldn't want to reinvent the wheel if something is already available. Of course it can't be perfect if the font is variable width, but an approximation would do just fine. Or maybe it could have a configurable table with widths for each character. Any hint would be appreciated. Thank you.

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• Anyone Know a Great Sparse One Dimensional Array Library in Python?

  - by TheJacobTaylor

  I am working on an algorithm in Python that uses arrays heavily. The arrays are typically sparse and are read from and written to constantly. I am currently using relatively large native arrays and the performance is good but the memory usage is high (as expected). I would like to be able to have the array implementation not waste space for values that are not used and allow an index offset other than zero. As an example, if my numbers start at 1,000,000 I would like to be able to index my array starting at 1,000,000 and not be required to waste memory with a million unused values. Array reads and writes needs to be fast. Expanding into new territory can be a small delay but reads and writes should be O(1) if possible. Does anybody know of a library that can do it? Thanks!

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• Getting plane slices from array data

  - by umanga

  Greetings all, I read 3d grid data (from multiple TIF images) into a structure as follows : typedef struct VolumeData{ int nx; int ny; int nz; unsigned char *data; // size is nx*ny*nz } Now I want to get the plane slices from this 1-D grid data: eg: unsigned char* getXYPlaneStack(VolumeData *vol,int z); I could implement above function because the *data array stores image stack. But i am having difficult time implement along the other axes: unsigned char* getYZPlaneStack(VolumeData *vol,int x); and unsigned char* getXZPlaneStack(VolumeData *vol,int y); any easy algorithm for this? thanks in advance.

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• How do I generate a random string of up to a certain length?

  - by slavy13

  I would like to generate a random string (or a series of random strings, repetitions allowed) of length between 1 and n characters from some (finite) alphabet. Each string should be equally likely (in other words, the strings should be uniformly distributed). The uniformity requirement means that an algorithm like this doesn't work: alphabet = "abcdefghijklmnopqrstuvwxyz" len = rand(1, n) s = "" for(i = 0; i < len; ++i) s = s + alphabet[rand(0, 25)] (pseudo code, rand(a, b) returns a integer between a and b, inclusively, each integer equally likely) It doesn't work because shorter lengths are as likely as longer ones, meaning it's more likely to generate a shorter string than a longer one, so the result is not uniform.

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• Extend MySQL implementation of PiP Algorithm?

  - by Mike

  I need to make a point in polygon MySQL query. I already found these two great solutions: http://forums.mysql.com/read.php?23,286574,286574 MySQL implementation of ray-casting Algorithm? But these functions can only check if one point is inside a poly. I have a query where the PiP part should only be one part of the query and check for x points inside a polygon. Something like this: $points = list/array/whatever of points in language of favour SELECT d.name FROM data AS d WHERE d.name LIKE %red% // just bla bla // how to do this ? AND $points INSIDE d.polygon AND myWithin( $points, d.polygo ) // or UPDATE I tried it with MBR functions like this: SET @g1 = GeomFromText('Polygon((13.43971 52.55757,13.41293 52.49825,13.53378 52.49574, 13.43971 52.55757))'); SET @g2 = GeomFromText('Point(13.497834 52.540489)'); SELECT MBRContains(@g1,@g2); G2 should NOT be inside G1 but MBR says it is.

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• Subdividing 3D mesh into arbitrarily sized pieces

  - by Groky

  I have a mesh defined by 4 points in 3D space. I need an algorithm which will subdivide that mesh into subdivisions of an arbitrary horizontal and vertical size. If the subdivision size isn't an exact divisor of the mesh size, the edge pieces will be smaller. All of the subdivision algorithms I've found only subdivide meshes into exact powers of 2. Does anyone know of one that can do what I want? Failing that, my thoughts about a possible implementation is to rotate the mesh so that it is flat on the Z axis, subdivide in 2D and then translate back into 3D. That's because my mind finds 3D hard ;) Any better suggestions? Using C# if that makes any difference.

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• Best way to search for a saturation value in a sorted list

  - by AB Kolan

  A question from Math Battle. This particular question was also asked to me in one of my job interviews. " A monkey has two coconuts. It is fooling around by throwing coconut down from the balconies of M-storey building. The monkey wants to know the lowest floor when coconut is broken. What is the minimal number of attempts needed to establish that fact? " Conditions: if a coconut is broken, you cannot reuse the same. You are left with only with the other coconut Possible approaches/strategies I can think of are Binary break ups & once you find the floor on which the coconut breaks use upcounting from the last found Binary break up lower index. Window/Slices of smaller sets of floors & use binary break up within the Window/Slice (but on the down side this would require a Slicing algorithm of it's own.) Wondering if there are any other way to do this.

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• A programming language for teaching data structures and algorithms with? [closed]

  - by Andreas Grech

  Possible Duplicate: Choice of programming language for learning data structures and algorithms Teachers have different opinions on what programming language they would choose to teach data structures and algorithms with. Some would prefer a lower level language such as C because it allows the student to learn more about what goes on beyond the abstractions in terms of memory allocation and deallocation and pointers and pointer arithmetic. On the other hand, others would say that they would prefer a higher level language like Java because it allows the student to learn more about the concepts of the structures and the algorithm design rather than 'waste time' and fiddle around with memory segmentation faults and all the blunders that come with languages where memory management is manual. What is your take on this issue? And also, please post any references you may know of that also discuss this argument.

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• 0/1 Knapsack with irrational weights

  - by user356106

  Consider the 0/1 knapsack problem. The standard Dynamic Programming algorithm applies only when the capacity as well as the weights to fill the knapsack with are integers/ rational numbers. What do you do when the capacity/weights are irrational? The issue is that we can't memoize like we do for integer weights because we may need potentially infinite decimal places for irrational weights - leading to an infinitely large number of columns for the Dynamic Programming Table . Is there any standard method for solving this? Any comments on the complexity of this problem? Any heuristics? What about associated recurrences like (for example): f(x)=1, for x< sqrt(2) f(x)=f(x-sqrt(2))+sqrt(3)

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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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• Implementing a "flag as spam/offensive" system

  - by UltraVi01

  I am looking for a community moderated way of managing/eliminating spam and offensive content. Functionality similar to StackOverflow and many other sites seems like a good way to go. Although I'm sure this could greatly vary based on specific needs, I am curious about the backend mechanism/algorithm --that is, has anyone had success using something like "3 strikes and you're out" -- the flagged post is automatically closed/deleted after 3 reports by users with the required credentials. Would something like this likely be effective or would it require a more complex solution to ensure honesty and effectiveness. Any thoughts / experiences would be great

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• I need to do a BASICE For Loop algorithm for a java Pyramid

  - by user1665119

  Question 2. USE THE FOR LOOP. Design and write an algorithm that will read a single positive number from the keyboard and will then print a pyramid out on the screen. The pyramid will need to be of a height equal in lines to the number inputted by the operator. Your program is not to test for negative numbers, nor is it to cater for them. For your test, use the number 7. If you would like to take the problem further, try 18 and watch what happens. Example input: 4 Example output: 1 121 12321 1234321

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• How to search for closest value in a lookup table?

  - by CSharperWithJava

  I have a simple one dimmensional array of integer values that represent a physical set of part values I have to work with. I then calculate and ideal value mathematically. How could I write an efficient search algorithm that will find the smallest abosulte difference from my ideal value in the array? The array is predetermined and constant, so it can be sorted however I need. Example Lookup array: 100, 152, 256, 282, 300 Searching for an ideal value of 125 would find 100 in the array, whereas 127 would find 152. The actual lookup array will be about 250 items long and never change.

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• Nested loop with dependent bounds trip count

  - by aaa

  hello. just out of curiosity I tried to do the following, which turned out to be not so obvious to me; Suppose I have nested loops with runtime bounds, for example: t = 0 // trip count for l in 0:N for k in 0:N for j in max(l,k):N for i in k:j+1 t += 1 t is loop trip count is there a general algorithm/way (better than N^4 obviously) to calculate loop trip count? I am working on the assumption that the iteration bounds depend only on constant or previous loop variables.

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• Horizontally Flip a One Bit Bitmap Line

  - by roygbiv

  I'm looking for an algorithm to flip a 1 Bit Bitmap line horizontally. Remember these lines are DWORD aligned! I'm currently unencoding an RLE stream to an 8 bit-per-pixel buffer, then re-encoding to a 1 bit line, however, I would like to try and keep it all in the 1 bit space in an effort to increase its speed. Profiling indicates this portion of the program to be relatively slow compared to the rest. Example line (Before Flip): FF FF FF FF 77 AE F0 00 Example line (After Flip): F7 5E EF FF FF FF F0 00

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• question about missing element in array

  - by davit-datuashvili

  i have following problem from book introduction algorithm second edition by MIT university problem is following An array A[1 . . n] contains all the integers from 0 to n except one. It would be easy to determine the missing integer in O(n) time by using an auxiliary array B[0 . . n] to record which numbers appear in A. In this problem, however, we cannot access an entire integer in A with a single operation. The elements of A are represented in binary, and the only operation we can use to access them is “fetch the j th bit of A[i],” which takes constant time. Show that if we use only this operation, we can still determine the missing inte- ger in O(n) time please help

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• Color generation based on random number

  - by Mikulas Dite

  I would like to create a color generator based on random numbers, which might differ just slightly, but I need colors to be easily recognizable from each other. I was thinking about generation then in a rgb format which would be probably easiest. I'm afraid simply multiplying given arguments wouldn't do very well. What algorithm do you suggest using? Also, second generated color should not be the same as previous one, but I don't want to store them - nor multiplying with (micro)time would do well since the scripts' parts are usually faster.

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