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• Algorithm for finding symmetries of a tree

  - by Paxinum

  I have n sectors, enumerated 0 to n-1 counterclockwise. The boundaries between these sectors are infinite branches (n of them). The sectors live in the complex plane, and for n even, sector 0 and n/2 are bisected by the real axis, and the sectors are evenly spaced. These branches meet at certain points, called junctions. Each junction is adjacent to a subset of the sectors (at least 3 of them). Specifying the junctions, (in pre-fix order, lets say, starting from junction adjacent to sector 0 and 1), and the distance between the junctions, uniquely describes the tree. Now, given such a representation, how can I see if it is symmetric wrt the real axis? For example, n=6, the tree (0,1,5)(1,2,4,5)(2,3,4) have three junctions on the real line, so it is symmetric wrt the real axis. If the distances between (015) and (1245) is equal to distance from (1245) to (234), this is also symmetric wrt the imaginary axis. The tree (0,1,5)(1,2,5)(2,4,5)(2,3,4) have 4 junctions, and this is never symmetric wrt either imaginary or real axis, but it has 180 degrees rotation symmetry if the distance between the first two and the last two junctions in the representation are equal. Edit: This is actually for my research. I have posted the question at mathoverflow as well, but my days in competition programming tells me that this is more like an IOI task. Code in mathematica would be excellent, but java, python, or any other language readable by a human suffices. Here are some examples (pretend the double edges are single and we have a tree) http://www2.math.su.se/~per/files.php?file=contr_ex_1.pdf http://www2.math.su.se/~per/files.php?file=contr_ex_2.pdf http://www2.math.su.se/~per/files.php?file=contr_ex_5.pdf Example 1 is described as (0,1,4)(1,2,4)(2,3,4)(0,4,5) with distances (2,1,3). Example 2 is described as (0,1,4)(1,2,4)(2,3,4)(0,4,5) with distances (2,1,1). Example 5 is described as (0,1,4,5)(1,2,3,4) with distances (2). So, given the description/representation, I want to find some algorithm to decide if it is symmetric wrt real, imaginary, and rotation 180 degrees. The last example have 180 degree symmetry. (These symmetries corresponds to special kinds of potential in the Schroedinger equation, which has nice properties in quantum mechanics.)

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• Php algorithm - How to achieve that without eval

  - by Marcelo

  I have a class that keeps data stores/access data by using words.separated.by.dots keys and it behaves like the following: $object = new MyArray() $object->setParam('user.name','marcelo'); $object->setParam('user.email','[email protected]'); $object->getParams(); /* array( 'user' => array( 'name' => 'marcelo', 'email' => '[email protected]' ) ); */ It is working, but the method unsetParam() was horribly implemented. That happened because i didn't know how to achieve that without eval() function. Although it is working, I found that it was a really challenging algorithm and that you might find fun trying to achieve that without eval(). class MyArray { /** * @param string $key * @return Mura_Session_Abstract */ public function unsetParam($key) { $params = $this->getParams(); $tmp = $params; $keys = explode('.', $key); foreach ($keys as $key) { if (!isset($tmp[$key])) { return $this; } $tmp = $tmp[$key]; } // bad code! $eval = "unset(\$params['" . implode("']['", $keys) . "']);"; eval($eval); $this->setParams($params); return $this; } } The test method: public function testCanUnsetNestedParam() { $params = array( '1' => array( '1' => array( '1' => array( '1' => 'one', '2' => 'two', '3' => 'three', ), '2' => array( '1' => 'one', '2' => 'two', '3' => 'three', ), ) ), '2' => 'something' ); $session = $this->newSession(); $session->setParams($params); unset($params['1']['1']['1']); $session->unsetParam('1.1.1'); $this->assertEquals($params, $session->getParams()); $this->assertEquals($params['1']['1']['2'], $session->getParam('1.1.2')); }

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• Special scheduling Algorithm (pattern expansion)

  - by tovare

  Question Do you think genetic algorithms worth trying out for the problem below, or will I hit local-minima issues? I think maybe aspects of the problem is great for a generator / fitness-function style setup. (If you've botched a similar project I would love hear from you, and not do something similar) Thank you for any tips on how to structure things and nail this right. The problem I'm searching a good scheduling algorithm to use for the following real-world problem. I have a sequence with 15 slots like this (The digits may vary from 0 to 20) : 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 (And there are in total 10 different sequences of this type) Each sequence needs to expand into an array, where each slot can take 1 position. 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 1 0 0 0 1 1 1 0 0 0 1 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1 1 The constraints on the matrix is that: [row-wise, i.e. horizontally] The number of ones placed, must either be 11 or 111 [row-wise] The distance between two sequences of 1 needs to be a minimum of 00 The sum of each column should match the original array. The number of rows in the matrix should be optimized. The array then needs to allocate one of 4 different matrixes, which may have different number of rows: A, B, C, D A, B, C and D are real-world departments. The load needs to be placed reasonably fair during the course of a 10-day period, not to interfere with other department goals. Each of the matrix is compared with expansion of 10 different original sequences so you have: A1, A2, A3, A4, A5, A6, A7, A8, A9, A10 B1, B2, B3, B4, B5, B6, B7, B8, B9, B10 C1, C2, C3, C4, C5, C6, C7, C8, C9, C10 D1, D2, D3, D4, D5, D6, D7, D8, D9, D10 Certain spots on these may be reserved (Not sure if I should make it just reserved/not reserved or function-based). The reserved spots might be meetings and other events The sum of each row (for instance all the A's) should be approximately the same within 2%. i.e. sum(A1 through A10) should be approximately the same as (B1 through B10) etc. The number of rows can vary, so you have for instance: A1: 5 rows A2: 5 rows A3: 1 row, where that single row could for instance be: 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 etc.. Sub problem* I'de be very happy to solve only part of the problem. For instance being able to input: 1 1 2 3 4 2 2 3 4 2 2 3 3 2 3 And get an appropriate array of sequences with 1's and 0's minimized on the number of rows following th constraints above.

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• Making an efficient algorithm

  - by James P.

  Here's my recent submission for the FB programming contest (qualifying round only requires to upload program output so source code doesn't matter). The objective is to find two squares that add up to a given value. I've left it as it is as an example. It does the job but is too slow for my liking. Here's the points that are obviously eating up time: List of squares is being recalculated for each call of getNumOfDoubleSquares(). This could be precalculated or extended when needed. Both squares are being checked for when it is only necessary to check for one (complements). There might be a more efficient way than a double-nested loop to find pairs. Other suggestions? Besides this particular problem, what do you look for when optimizing an algorithm? public static int getNumOfDoubleSquares( Integer target ){ int num = 0; ArrayList<Integer> squares = new ArrayList<Integer>(); ArrayList<Integer> found = new ArrayList<Integer>(); int squareValue = 0; for( int j=0; squareValue<=target; j++ ){ squares.add(j, squareValue); squareValue = (int)Math.pow(j+1,2); } int squareSum = 0; System.out.println( "Target=" + target ); for( int i = 0; i < squares.size(); i++ ){ int square1 = squares.get(i); for( int j = 0; j < squares.size(); j++ ){ int square2 = squares.get(j); squareSum = square1 + square2; if( squareSum == target && !found.contains( square1 ) && !found.contains( square2 ) ){ found.add(square1); found.add(square2); System.out.println( "Found !" + square1 +"+"+ square2 +"="+ squareSum); num++; } } } return num; }

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• C++ Performance/memory optimization guidelines

  - by ML

  Hi All, Does anyone have a resource for C++ memory optimization guidelines? Best practices, tuning, etc? As an example: Class xxx { public: xxx(); virtual ~xxx(); protected: private: }; Would there be ANY benefit on the compiler or memory allocation to get rid of protected and private since there there are no items that are protected and private in this class?

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• Any Javascript optimization benchmarks?

  - by int3

  I watched Nicholas Zakas' talk, Speed up your Javascript, with some interest. I liked how he benchmarked the various performance improvements created by various optimization techniques, e.g. reducing calls to deeply nested objects, changing loops to count down instead of up, etc. I would like to run these benchmarks myself though, to see exactly how our current browsers are faring. I guess it wouldn't be too difficult to cook up some timed loops, but I'd like to know if there are any existing implementations out there.

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• Algorithm to select groups of similar items in 2d array

  - by mafutrct

  There is a 2d array of items (in my case they are called Intersections). A certain item is given as a start. The task is to find all items directly or indirectly connected to this item that satisfy a certain function. So the basic algorithm is like this: Add the start to the result list. Repeat until no modification: Add each item in the array that satisfies the function and touches any item in the result list to the result list. My current implementation looks like this: private IList<Intersection> SelectGroup ( Intersection start, Func<Intersection, Intersection, bool> select) { List<Intersection> result = new List<Intersection> (); Queue<Intersection> source = new Queue<Intersection> (); source.Enqueue (start); while (source.Any ()) { var s = source.Dequeue (); result.Add (s); foreach (var neighbour in Neighbours (s)) { if (select (start, neighbour) && !result.Contains (neighbour) && !source.Contains (neighbour)) { source.Enqueue (neighbour); } } } Debug.Assert (result.Distinct ().Count () == result.Count ()); Debug.Assert (result.All (x => select (x, result.First ()))); return result; } private List<Intersection> Neighbours (IIntersection intersection) { int x = intersection.X; int y = intersection.Y; List<Intersection> list = new List<Intersection> (); if (x > 1) { list.Add (GetIntersection (x - 1, y)); } if (y > 1) { list.Add (GetIntersection (x, y - 1)); } if (x < Size) { list.Add (GetIntersection (x + 1, y)); } if (y < Size) { list.Add (GetIntersection (x, y + 1)); } return list; } (The select function takes a start item and returns true iff the second item satisfies.) This does its job and turned out to be reasonable fast for the usual array sizes (about 20*20). However, I'm interested in further improvements. Any ideas? Example (X satisfies in relation to other Xs, . does never satisfy): .... XX.. .XX. X... In this case, there are 2 groups: a central group of 4 items and a group of a single item in the lower left. Selecting the group (for instance by starting item [2, 2]) returns the former, while the latter can be selected using the starting item and sole return value [0, 3]. Example 2: .A.. ..BB A.AA This time there are 4 groups. The 3 A groups are not connected, so they are returned as separate groups. The bigger A and B groups are connected, but A does not related to B so they are returned as separate groups.

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• Software to Tune/Calibrate Properties for Heuristic Algorithms

  - by Karussell

  Today I read that there is a software called WinCalibra (scroll a bit down) which can take a text file with properties as input. This program can then optimize the input properties based on the output values of your algorithm. See this paper or the user documentation for more information (see link above; sadly doc is a zipped exe). Do you know other software which can do the same which runs under Linux? (preferable Open Source)

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• Optimizing spacing of mesh containing a given set of points

  - by Feynman

  I tried to summarize the this as best as possible in the title. I am writing an initial value problem solver in the most general way possible. I start with an arbitrary number of initial values at arbitrary locations (inside a boundary.) The first part of my program creates a mesh/grid (I am not sure which is the correct nuance), with N points total, that contains all the initial values. My goal is to optimize the mesh such that the spacing is as uniform as possible. My solver seems to work half decently (it needs some more obscure debugging that is not relevant here.) I am starting with one dimension. I intend to generalize the algorithm to an arbitrary number of dimensions once I get it working consistently. I am writing my code in fortran, but feel free to reply with pseudocode or the language of your choice. Allow me to elaborate with an example: Say I am working on a closed interval [1,10] xmin=1 xmax=10 Say I have 3 initial points: xmin, 5 and xmax num_ivc=3 known(num_ivc)=[xmin,5,xmax] //my arrays start at 1. Assume "known" starts sorted I store my mesh/grid points in an array called coord. Say I want 10 points total in my mesh/grid. N=10 coord(10) Remember, all this is arbitrary--except the variable names of course. The algorithm should set coord to {1,2,3,4,5,6,7,8,9,10} Now for a less trivial example: num_ivc=3 known(num_ivc)=[xmin,5.5,xmax or just num_ivc=1 known(num_ivc)=[5.5] Now, would you have 5 evenly spaced points on the interval [1, 5.5] and 5 evenly spaced points on the interval (5.5, 10]? But there is more space between 1 and 5.5 than between 5.5 and 10. So would you have 6 points on [1, 5.5] followed by 4 on (5.5 to 10]. The key is to minimize the difference in spacing. I have been working on this for 2 days straight and I can assure you it is a lot trickier than it sounds. I have written code that only works if N is large only works if N is small only works if it the known points are close together only works if it the known points are far apart only works if at least one of the known points is near a boundary only works if none of the known points are near a boundary So as you can see, I have coded the gamut of almost-solutions. I cannot figure out a way to get it to perform equally well in all possible scenarios (that is, create the optimum spacing.)

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• Problem Solving: Algorithm Required Urgently, Plz Help

  - by user616417

  Problem Solving: I've been working on something since last week. I am stuck at a point, where I want to find the minimum number of airplanes required to carry out a flight schedule given below. Plz, try out the brainstorming, i need the algorithm really badly, i'm also short of time. Thank u in advance. The Schedule---- Flight #,From,To,Departure,Arrival,Days,Via 6E 204,Agartala,Delhi,10:15:00,13:55:00,Daily,Kolkata 6E 360,Agartala,Imphal,13:50:00,14:35:00,Mo Th Sa, 6E 204,Agartala,Kolkata,10:15:00,11:00:00,Daily, 6E 360,Agartala,Kolkata,13:50:00,16:15:00,Mo Th Sa,Imphal 6E 362,Agartala,Kolkata,15:25:00,16:15:00,Tu We Fr Su, 6E 153,Ahmedabad,Bangalore,17:00:00,19:00:00,Daily, 6E 212,Ahmedabad,Chennai,9:00:00,12:55:00,Daily,Mumbai 6E 154,Ahmedabad,Delhi,12:30:00,14:00:00,Daily, 6E 211,Ahmedabad,Jaipur,19:10:00,20:20:00,Daily, 6E 410,Ahmedabad,Kolkata,15:00:00,17:30:00,Daily, 6E 212,Ahmedabad,Mumbai,9:00:00,10:10:00,Daily, 6E 409,Ahmedabad,Pune,14:25:00,15:40:00,Ex Sat, 6E 154,Bangalore,Ahmedabad,10:00:00,12:00:00,Daily, 6E 277,Bangalore,Chennai,15:35:00,16:25:00,Daily, 6E 132,Bangalore,Delhi,6:00:00,8:25:00,Daily, 6E 102,Bangalore,Delhi,9:50:00,13:45:00,Ex Sat,Pune 6E 154,Bangalore,Delhi,10:00:00,14:00:00,Daily,Ahmedabad 6E 104,Bangalore,Delhi,11:30:00,14:10:00,Sat, 6E 122,Bangalore,Delhi,17:20:00,20:00:00,Daily, 6E 108,Bangalore,Delhi,19:20:00,23:10:00,Sat,Pune 6E 106,Bangalore,Delhi,19:30:00,22:00:00,Ex Sat, 6E 275,Bangalore,Goa,12:15:00,13:15:00,Daily, 6E 351,Bangalore,Hyderabad,8:25:00,9:25:00,Daily, 6E 152,Bangalore,Hyderabad,19:10:00,20:10:00,Ex Sat, 6E 152,Bangalore,Hyderabad,19:30:00,20:35:00,Sat, 6E 152,Bangalore,Jaipur,19:10:00,22:30:00,Ex Sat,Hyderabad 6E 152,Bangalore,Jaipur,19:30:00,22:30:00,Sat,Hyderabad 6E 351,Bangalore,Kolkata,8:25:00,11:55:00,Daily,Hyderabad 6E 277,Bangalore,Kolkata,15:35:00,19:15:00,Daily,Chennai 6E 402,Bangalore,Mumbai,6:05:00,7:45:00,Daily, 6E 275,Bangalore,Mumbai,12:15:00,14:45:00,Daily,Goa 6E 414,Bangalore,Mumbai,12:45:00,14:20:00,Daily, 6E 412,Bangalore,Mumbai,21:20:00,23:20:00,Daily, 6E 102,Bangalore,Pune,9:50:00,11:10:00,Ex Sat, 6E 108,Bangalore,Pune,19:20:00,20:40:00,Sat, 6E 258,Bhubaneshwar,Delhi,18:55:00,20:55:00,Daily, 6E 257,Bhubaneshwar,Hyderabad,10:40:00,12:05:00,Daily, 6E 257,Bhubaneshwar,Mumbai,10:40:00,13:50:00,Daily,Hyderabad 6E 211,Chennai,Ahmedabad,15:10:00,18:40:00,Daily,Mumbai 6E 275,Chennai,Bangalore,10:50:00,11:40:00,Daily, 6E 302,Chennai,Delhi,11:35:00,15:20:00,Daily,Hyderabad 6E 282,Chennai,Delhi,19:45:00,22:30:00,Daily, 6E 275,Chennai,Goa,10:50:00,13:15:00,Daily,Bangalore 6E 302,Chennai,Hyderabad,11:35:00,12:40:00,Daily, 6E 211,Chennai,Jaipur,15:10:00,20:20:00,Daily,Mumbai/Ahmedabad 6E 523,Chennai,Kolkata,8:20:00,10:30:00,Daily, 6E 277,Chennai,Kolkata,16:55:00,19:15:00,Daily, 6E 211,Chennai,Mumbai,15:10:00,16:50:00,Daily, 6E 524,Chennai,Pune,21:15:00,23:00:00,Daily, 6E 273,Delhi,Agartala,6:15:00,9:45:00,Daily,Kolkata 6E 153,Delhi,Ahmedabad,14:45:00,16:30:00,Daily, 6E 101,Delhi,Bangalore,6:30:00,9:10:00,Ex Sat, 6E 103,Delhi,Bangalore,6:45:00,10:40:00,Sat,Pune 6E 121,Delhi,Bangalore,9:30:00,12:10:00,Daily, 6E 105,Delhi,Bangalore,14:20:00,18:30:00,Ex Sat,Pune 6E 153,Delhi,Bangalore,14:45:00,19:00:00,Daily,Ahmedabad 6E 107,Delhi,Bangalore,15:55:00,18:40:00,Sat, 6E 131,Delhi,Bangalore,20:45:00,23:15:00,Daily, 6E 257,Delhi,Bhubaneshwar,8:10:00,10:10:00,Daily, 6E 301,Delhi,Chennai,7:00:00,11:05:00,Daily,Hyderabad 6E 283,Delhi,Chennai,16:30:00,19:05:00,Daily, 6E 181,Delhi,Goa,9:15:00,13:35:00,Daily,Mumbai 6E 333,Delhi,Goa,11:45:00,14:15:00,Daily, 6E 201,Delhi,Guwahati,5:30:00,7:50:00,Daily, 6E 301,Delhi,Hyderabad,7:00:00,9:00:00,Daily, 6E 257,Delhi,Hyderabad,8:10:00,12:05:00,Daily,Bhubaneshwar 6E 305,Delhi,Hyderabad,14:00:00,15:55:00,Daily, 6E 307,Delhi,Hyderabad,21:00:00,22:55:00,Daily, 6E 201,Delhi,Imphal,5:30:00,9:10:00,Daily,Guwahati 6E 305,Delhi,Kochi,14:00:00,18:25:00,Daily,Hyderabad 6E 273,Delhi,Kolkata,6:15:00,8:20:00,Daily, 6E 203,Delhi,Kolkata,15:00:00,17:05:00,Daily, 6E 209,Delhi,Kolkata,18:30:00,20:45:00,Daily, 6E 183,Delhi,Mumbai,6:45:00,8:35:00,Daily, 6E 181,Delhi,Mumbai,9:15:00,11:35:00,Daily, 6E 481,Delhi,Mumbai,10:50:00,13:50:00,Daily,Vadodara 6E 189,Delhi,Mumbai,14:45:00,16:50:00,Daily, 6E 187,Delhi,Mumbai,17:50:00,19:50:00,Daily, 6E 185,Delhi,Mumbai,20:15:00,22:20:00,Daily, 6E 135,Delhi,Nagpur,8:55:00,10:40:00,Ex Sat, 6E 103,Delhi,Pune,6:45:00,8:45:00,Sat, 6E 135,Delhi,Pune,8:55:00,12:30:00,Ex Sat,Nagpur 6E 105,Delhi,Pune,14:20:00,16:30:00,Ex Sat, 6E 481,Delhi,Vadodara,10:50:00,12:20:00,Daily, 6E 277,Goa,Bangalore,14:05:00,15:00:00,Daily, 6E 277,Goa,Chennai,14:05:00,16:25:00,Daily,Bangalore 6E 334,Goa,Delhi,14:45:00,17:10:00,Daily, 6E 277,Goa,Kolkata,14:05:00,19:15:00,Daily,Bangalore/Chennai 6E 275,Goa,Mumbai,13:45:00,14:45:00,Daily, 6E 202,Guwahati,Delhi,11:00:00,13:25:00,Daily, 6E 201,Guwahati,Imphal,8:25:00,9:10:00,Daily, 6E 208,Guwahati,Jaipur,12:40:00,16:55:00,Daily,Kolkata 6E 208,Guwahati,Kolkata,12:40:00,14:00:00,Daily, 6E 322,Guwahati,Kolkata,15:30:00,16:50:00,Daily, 6E 322,Guwahati,Mumbai,15:30:00,20:20:00,Daily,Kolkata 6E 151,Hyderabad,Bangalore,8:20:00,9:20:00,Daily, 6E 352,Hyderabad,Bangalore,19:40:00,20:40:00,Daily, 6E 258,Hyderabad,Bhubaneshwar,16:40:00,18:20:00,Daily, 6E 301,Hyderabad,Chennai,9:50:00,11:05:00,Daily, 6E 308,Hyderabad,Delhi,6:10:00,8:00:00,Daily, 6E 302,Hyderabad,Delhi,13:10:00,15:20:00,Daily, 6E 258,Hyderabad,Delhi,16:40:00,20:55:00,Daily,Bhubaneshwar 6E 306,Hyderabad,Delhi,21:00:00,23:05:00,Daily, 6E 152,Hyderabad,Jaipur,20:50:00,22:30:00,Ex Sat, 6E 152,Hyderabad,Jaipur,21:10:00,22:30:00,Sat, 6E 305,Hyderabad,Kochi,16:45:00,18:25:00,Daily, 6E 351,Hyderabad,Kolkata,9:55:00,11:55:00,Daily, 6E 257,Hyderabad,Mumbai,12:35:00,13:50:00,Daily, 6E 362,Imphal,Agartala,14:15:00,14:55:00,Tu We Fr Su, 6E 202,Imphal,Delhi,9:40:00,13:25:00,Daily,Guwahati 6E 202,Imphal,Guwahati,9:40:00,10:25:00,Daily, 6E 362,Imphal,Kolkata,14:15:00,16:15:00,Tu We Fr Su,Agartala 6E 360,Imphal,Kolkata,15:05:00,16:15:00,Mo Th Sa, 6E 212,Jaipur,Ahmedabad,7:30:00,8:35:00,Daily, 6E 151,Jaipur,Bangalore,6:00:00,9:20:00,Daily,Hyderabad 6E 212,Jaipur,Chennai,7:30:00,12:55:00,Daily,Mumbai/Ahmedabad 6E 207,Jaipur,Guwahati,8:20:00,12:10:00,Daily,Kolkata 6E 151,Jaipur,Hyderabad,6:00:00,7:40:00,Daily, 6E 207,Jaipur,Kolkata,8:20:00,10:10:00,Daily, 6E 323,Jaipur,Kolkata,17:35:00,23:00:00,Daily,Mumbai 6E 212,Jaipur,Mumbai,7:30:00,10:10:00,Daily,Ahmedabad 6E 323,Jaipur,Mumbai,17:35:00,19:15:00,Daily, 6E 306,Kochi,Delhi,19:00:00,23:05:00,Daily,Hyderabad 6E 306,Kochi,Hyderabad,19:00:00,20:30:00,Daily, 6E 273,Kolkata,Agartala,8:50:00,9:45:00,Daily, 6E 360,Kolkata,Agartala,12:30:00,13:20:00,Mo Th Sa, 6E 362,Kolkata,Agartala,12:30:00,14:55:00,TuWeFrSu,Imphal 6E 409,Kolkata,Ahmedabad,11:10:00,13:50:00,Daily, 6E 275,Kolkata,Bangalore,7:30:00,11:40:00,Daily,Chennai 6E 352,Kolkata,Bangalore,16:50:00,20:40:00,Daily,Hyderabad 6E 275,Kolkata,Chennai,7:30:00,9:50:00,Daily, 6E 524,Kolkata,Chennai,18:15:00,20:25:00,Daily, 6E 210,Kolkata,Delhi,7:45:00,10:05:00,Daily, 6E 204,Kolkata,Delhi,11:40:00,13:55:00,Daily, 6E 274,Kolkata,Delhi,19:45:00,22:10:00,Daily, 6E 275,Kolkata,Goa,7:30:00,13:15:00,Daily,Chennai/Bangalore 6E 207,Kolkata,Guwahati,10:50:00,12:10:00,Daily, 6E 321,Kolkata,Guwahati,13:00:00,14:20:00,Daily, 6E 352,Kolkata,Hyderabad,16:50:00,19:00:00,Daily, 6E 362,Kolkata,Imphal,12:30:00,13:45:00,Tu We Fr Su, 6E 360,Kolkata,Imphal,12:30:00,14:35:00,MoThSa,Agartala 6E 208,Kolkata,Jaipur,14:35:00,16:55:00,Daily, 6E 320,Kolkata,Mumbai,6:00:00,8:30:00,Daily, 6E 322,Kolkata,Mumbai,17:35:00,20:20:00,Daily, 6E 404,Kolkata,Mumbai,18:35:00,21:55:00,Daily,Nagpur 6E 404,Kolkata,Nagpur,18:35:00,20:05:00,Daily, 6E 409,Kolkata,Pune,11:10:00,15:40:00,Ex Sat,Ahmedabad 6E 524,Kolkata,Pune,18:15:00,23:00:00,Daily,Chennai 6E 211,Mumbai,Ahmedabad,17:40:00,18:40:00,Daily, 6E 411,Mumbai,Bangalore,6:20:00,7:50:00,Daily, 6E 413,Mumbai,Bangalore,15:00:00,16:40:00,Daily, 6E 415,Mumbai,Bangalore,21:05:00,22:40:00,Daily, 6E 258,Mumbai,Bhubaneshwar,14:30:00,18:20:00,Daily,Hyderabad 6E 212,Mumbai,Chennai,11:00:00,12:55:00,Daily, 6E 184,Mumbai,Delhi,6:15:00,8:15:00,Daily, 6E 180,Mumbai,Delhi,8:25:00,10:35:00,Daily, 6E 482,Mumbai,Delhi,9:25:00,12:35:00,Daily,Vadodara 6E 188,Mumbai,Delhi,14:25:00,16:35:00,Daily, 6E 186,Mumbai,Delhi,17:50:00,19:55:00,Daily, 6E 182,Mumbai,Delhi,21:15:00,23:20:00,Daily, 6E 181,Mumbai,Goa,12:35:00,13:35:00,Daily, 6E 321,Mumbai,Guwahati,9:20:00,14:20:00,Daily,Kolkata 6E 258,Mumbai,Hyderabad,14:30:00,16:00:00,Daily, 6E 207,Mumbai,Jaipur,5:55:00,7:40:00,Daily, 6E 211,Mumbai,Jaipur,17:40:00,20:20:00,Daily,Ahmedabad 6E 207,Mumbai,Kolkata,5:55:00,10:10:00,Daily,Jaipur 6E 321,Mumbai,Kolkata,9:20:00,12:00:00,Daily, 6E 403,Mumbai,Kolkata,15:35:00,18:50:00,Daily,Nagpur 6E 323,Mumbai,Kolkata,20:05:00,23:00:00,Daily, 6E 403,Mumbai,Nagpur,15:35:00,16:50:00,Daily, 6E 482,Mumbai,Vadodara,9:25:00,10:25:00,Daily, 6E 136,Nagpur,Delhi,18:10:00,19:40:00,Ex Sat, 6E 403,Nagpur,Kolkata,17:20:00,18:50:00,Daily, 6E 404,Nagpur,Mumbai,20:35:00,21:55:00,Daily, 6E 135,Nagpur,Pune,11:20:00,12:30:00,Ex Sat, 6E 410,Pune,Ahmedabad,13:10:00,14:30:00,Ex Sat, 6E 103,Pune,Bangalore,9:15:00,10:40:00,Sat, 6E 105,Pune,Bangalore,17:00:00,18:30:00,Ex Sat, 6E 523,Pune,Chennai,5:55:00,7:40:00,Daily, 6E 102,Pune,Delhi,11:45:00,13:45:00,Ex Sat, 6E 136,Pune,Delhi,16:15:00,19:40:00,Ex Sat,Nagpur 6E 108,Pune,Delhi,21:10:00,23:10:00,Sat, 6E 523,Pune,Kolkata,5:55:00,10:30:00,Daily,Chennai 6E 410,Pune,Kolkata,13:10:00,17:30:00,Ex Sat,Ahmedabad 6E 136,Pune,Nagpur,16:15:00,17:40:00,Ex Sat, 6E 482,Vadodara,Delhi,10:55:00,12:35:00,Daily, 6E 481,Vadodara,Mumbai,12:50:00,13:50:00,Daily,

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• Java code optimization leads to numerical inaccuracies and errors

  - by rano

  I'm trying to implement a version of the Fuzzy C-Means algorithm in Java and I'm trying to do some optimization by computing just once everything that can be computed just once. This is an iterative algorithm and regarding the updating of a matrix, the clusters x pixels membership matrix U, this is the update rule I want to optimize: where the x are the element of a matrix X (pixels x features) and v belongs to the matrix V (clusters x features). And m is a parameter that ranges from 1.1 to infinity. The distance used is the euclidean norm. If I had to implement this formula in a banal way I'd do: for(int i = 0; i < X.length; i++) { int count = 0; for(int j = 0; j < V.length; j++) { double num = D[i][j]; double sumTerms = 0; for(int k = 0; k < V.length; k++) { double thisDistance = D[i][k]; sumTerms += Math.pow(num / thisDistance, (1.0 / (m - 1.0))); } U[i][j] = (float) (1f / sumTerms); } } In this way some optimization is already done, I precomputed all the possible squared distances between X and V and stored them in a matrix D but that is not enough, since I'm cycling througn the elements of V two times resulting in two nested loops. Looking at the formula the numerator of the fraction is independent of the sum so I can compute numerator and denominator independently and the denominator can be computed just once for each pixel. So I came to a solution like this: int nClusters = V.length; double exp = (1.0 / (m - 1.0)); for(int i = 0; i < X.length; i++) { int count = 0; for(int j = 0; j < nClusters; j++) { double distance = D[i][j]; double denominator = D[i][nClusters]; double numerator = Math.pow(distance, exp); U[i][j] = (float) (1f / (numerator * denominator)); } } Where I precomputed the denominator into an additional column of the matrix D while I was computing the distances: for (int i = 0; i < X.length; i++) { for (int j = 0; j < V.length; j++) { double sum = 0; for (int k = 0; k < nDims; k++) { final double d = X[i][k] - V[j][k]; sum += d * d; } D[i][j] = sum; D[i][B.length] += Math.pow(1 / D[i][j], exp); } } By doing so I encounter numerical differences between the 'banal' computation and the second one that leads to different numerical value in U (not in the first iterates but soon enough). I guess that the problem is that exponentiate very small numbers to high values (the elements of U can range from 0.0 to 1.0 and exp , for m = 1.1, is 10) leads to ver y small values, whereas by dividing the numerator and the denominator and THEN exponentiating the result seems to be better numerically. The problem is it involves much more operations. Am I doing something wrong? Is there a possible solution to get both the code optimized and numerically stable? Any suggestion or criticism will be appreciated.

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• Problems with with A* algorithm

  - by V_Programmer

  I'm trying to implement the A* algorithm in Java. I followed this tutorial,in particular, this pseudocode: http://theory.stanford.edu/~amitp/GameProgramming/ImplementationNotes.html The problem is my code doesn't work. It goes into an infinite loop. I really don't know why this happens... I suspect that the problem are in F = G + H function implemented in Graph constructors. I suspect I am not calculate the neighbor F correclty. Here's my code: List<Graph> open; List<Graph> close; private void createRouteAStar(Unit u) { open = new ArrayList<Graph>(); close = new ArrayList<Graph>(); u.ai_route_endX = 11; u.ai_route_endY = 5; List<Graph> neigh; int index; int i; boolean finish = false; Graph current; int cost; Graph start = new Graph(u.xMap, u.yMap, 0, ManhattanDistance(u.xMap, u.yMap, u.ai_route_endX, u.ai_route_endY)); open.add(start); current = start; while(!finish) { index = findLowerF(); current = new Graph(open, index); System.out.println(current.x); System.out.println(current.y); if (current.x == u.ai_route_endX && current.y == u.ai_route_endY) { finish = true; } else { close.add(current); neigh = current.getNeighbors(); for (i = 0; i < neigh.size(); i++) { cost = current.g + ManhattanDistance(current.x, current.y, neigh.get(i).x, neigh.get(i).y); if (open.contains(neigh.get(i)) && cost < neigh.get(i).g) { open.remove(open.indexOf(neigh)); } else if (close.contains(neigh.get(i)) && cost < neigh.get(i).g) { close.remove(close.indexOf(neigh)); } else if (!open.contains(neigh.get(i)) && !close.contains(neigh.get(i))) { neigh.get(i).g = cost; neigh.get(i).f = cost + ManhattanDistance(neigh.get(i).x, neigh.get(i).y, u.ai_route_endX, u.ai_route_endY); neigh.get(i).setParent(current); open.add(neigh.get(i)); } } } } System.out.println("step"); for (i=0; i < close.size(); i++) { if (close.get(i).parent != null) { System.out.println(i); System.out.println(close.get(i).parent.x); System.out.println(close.get(i).parent.y); } } } private int findLowerF() { int i; int min = 10000; int minIndex = -1; for (i=0; i < open.size(); i++) { if (open.get(i).f < min) { min = open.get(i).f; minIndex = i; System.out.println("min"); System.out.println(min); } } return minIndex; } private int ManhattanDistance(int ax, int ay, int bx, int by) { return Math.abs(ax-bx) + Math.abs(ay-by); } And, as I've said. I suspect that the Graph class has the main problem. However I've not been able to detect and fix it. public class Graph { int x, y; int f,g,h; Graph parent; public Graph(int x, int y, int g, int h) { this.x = x; this.y = y; this.g = g; this.h = h; this.f = g + h; } public Graph(List<Graph> list, int index) { this.x = list.get(index).x; this.y = list.get(index).y; this.g = list.get(index).g; this.h = list.get(index).h; this.f = list.get(index).f; this.parent = list.get(index).parent; } public Graph(Graph gp) { this.x = gp.x; this.y = gp.y; this.g = gp.g; this.h = gp.h; this.f = gp.f; } public Graph(Graph gp, Graph parent) { this.x = gp.x; this.y = gp.y; this.g = gp.g; this.h = gp.h; this.f = g + h; this.parent = parent; } public List<Graph> getNeighbors() { List<Graph> aux = new ArrayList<Graph>(); aux.add(new Graph(x+1, y, g,h)); aux.add(new Graph(x-1, y, g,h)); aux.add(new Graph(x, y+1, g,h)); aux.add(new Graph(x, y-1, g,h)); return aux; } public void setParent(Graph g) { parent = g; } } Little Edit: Using the System.out and the Debugger I discovered that the program ALWAYS is check the same "current" graph, (15,8) which is the (u.xMap, u.yMap) position. Looks like it keeps forever in the first step.

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• PHP website Optimization

  - by ana

  I have a high traffic website and I need make sure my site is fast enough to display my pages to everyone rapidly. I searched on Google many articles about speed and optimization and here's what I found: Cache the page Save it to the disk Caching the page in memory: This is very fast but if I need to change the content of my page I have to remove it from cache and then re-save the file on the disk. Save it to disk This is very easy to maintain but every time the page is accessed I have to read on the disk. Which method should I go with? Thanks

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• Performance optimization strategies of last resort?

  - by jerryjvl

  There are plenty of performance questions on this site already, but it occurs to me that almost all are very problem-specific and fairly narrow. And almost all repeat the advice to avoid premature optimization. Let's assume: the code already is working correctly the algorithms chosen are already optimal for the circumstances of the problem the code has been measured, and the offending routines have been isolated all attempts to optimize will also be measured to ensure they do not make matters worse What I am looking for here is strategies and tricks to squeeze out up to the last few percent in a critical algorithm when there is nothing else left to do but whatever it takes. Ideally, try to make answers language agnostic, and indicate any down-sides to the suggested strategies where applicable. I'll add a reply with my own initial suggestions, and look forward to whatever else the SO community can think of.

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• Does MATLAB perform tail call optimization?

  - by Shea Levy

  I've recently learned Haskell, and am trying to carry the pure functional style over to my other code when possible. An important aspect of this is treating all variables as immutable, i.e. constants. In order to do so, many computations that would be implemented using loops in an imperative style have to be performed using recursion, which typically incurs a memory penalty due to the allocation a new stack frame for each function call. In the special case of a tail call (where the return value of a called function is immediately returned to the callee's caller), however, this penalty can be bypassed by a process called tail call optimization (in one method, this can be done by essentially replacing a call with a jmp after setting up the stack properly). Does MATLAB perform TCO by default, or is there a way to tell it to?

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• Including associations optimization in Rails

  - by Vitaly

  Hey, I'm looking for help with Ruby optimization regarding loading of associations on demand. This is simplified example. I have 3 models: Post, Comment, User. References are: Post has many comments and Comment has reference to User (:author). Now when I go to the post page, I expect to see post body + all comments (and their respective authors names). This requires following 2 queries: select * from Post -- to get post data (1 row) select * from Comment inner join User -- to get comment + usernames (N rows) In the code I have: Post.find(params[:id], :include => { :comments => [:author] } But it doesn't work as expected: as I see in the back end, there're still N+1 hits (some of them are cached though). How can I optimize that?

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• why optimization does not happen?

  - by aaa

  hi. I have C/C++ code, that looks like this: static int function(double *I) { int n = 0; // more instructions, loops, for (int i; ...; ++i) n += fabs(I[i] > tolerance); return n; } function(I); // return value is not used. compiler inlines function, however it does not optimize out n manipulations. I would expect compiler is able to recognize that value is never used as rhs only. Is there some side effect, which prevents optimization? Thanks

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• Static variable for optimization

  - by keithjgrant

  I'm wondering if I can use a static variable for optimization: public function Bar() { static $i = moderatelyExpensiveFunctionCall(); if ($i) { return something(); } else { return somethingElse(); } } I know that once $i is initialized, it won't be changed by by that line of code on successive calls to Bar(). I assume this means that moderatelyExpensiveFunctionCall() won't be evaluated every time I call, but I'd like to know for certain. Once PHP sees a static variable that has been initialized, does it skip over that line of code? In other words, is this going to optimize my execution time if I make a lot of calls to Bar(), or am I wasting my time?

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• Copy method optimization in compilers

  - by Dženan

  Hi All! I have the following code: void Stack::operator =(Stack &rhs) { //do the actual copying } Stack::Stack(Stack &rhs) //copy-constructor { top=NULL; //initialize this as an empty stack (which it is) *this=rhs; //invoke assignment operator } Stack& Stack::CopyStack() { return *this; //this statement will invoke copy contructor } It is being used like this: unsigned Stack::count() { unsigned c=0; Stack copy=CopyStack(); while (!copy.empty()) { copy.pop(); c++; } return c; } Removing reference symbol from declaration of CopyStack (returning a copy instead of reference) makes no difference in visual studio 2008 (with respect to number of times copying is invoked). I guess it gets optimized away - normally it should first make a copy for the return value, then call assignment operator once more to assign it to variable sc. What is your experience with this sort of optimization in different compilers? Regards, Dženan

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• Common optimization rules

  - by mafutrct

  This is a dangerous question, so let me try to phrase it correctly. Premature optimization is the root of all evil, but if you know you need it, there is a basic set of rules that should be considered. This set is what I'm wondering about. For instance, imagine you got a list of a few thousand items. How do you look up an item with a specific, unique ID? Of course, you simply use a Dictionary to map the ID to the item. And if you know that there is a setting stored in a database that is required all the time, you simply cache it instead of issuing a database request hundred times a second. I guess there are a few even more basic ideas. I am specifically not looking for "don't do it, for experts: don't do it yet" or "use a profiler" answers, but for really simple, general hints. If you feel this is an argumentative question, you probably misunderstood my intention.

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• Which isometric angles can be mirrored (and otherwise transformed) for optimization?

  - by Tom

  I am working on a basic isometric game, and am struggling to find the correct mirrors. Mirror can be any form of transform. I have managed to get SE out of SW, by scaling the sprite on X axis by -1. Same applies for NE angle. Something is bugging me, that I should be able to also mirror N to S, but I cannot manage to pull this one off. Am I just too sleepy and trying to do the impossible, or a basic -1 scale on Y axis is not enough? What are the common used mirror table for optimizing 8 angle (N, NE, E, SE, S, SW, W, NW) isometric sprites?

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• When should an API favour optimization over readability and ease-of-use?

  - by jmlane

  I am in the process of designing a small library, where one of my design goals is to use as much of the native domain language as possible in the API. While doing so, I've noticed that there are some cases in the API outline where a more intuitive, readable attribute/method call requires some functionally unnecessary encapsulation. Since the final product will not necessarily require high performance, I am unconcerned about making the decision to favour ease-of-use in my current project over the most efficient implementation of the code in question. I know not to assume readability and ease-of-use are paramount in all expected use-cases, such as when performance is required. I would like to know if there are more general reasons that argue for an API design preferring (marginally) more efficient implementations?

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• When should code favour optimization over readability and ease-of-use?

  - by jmlane

  I am in the process of designing a small library, where one of my design goals is that the API should be as close to the domain language as possible. While working on the design, I've noticed that there are some cases in the code where a more intuitive, readable attribute/method call requires some functionally unnecessary encapsulation. Since the final product will not necessarily require high performance, I am unconcerned about making the decision to favour ease-of-use in my current project over the most efficient implementation of the code in question. I know not to assume readability and ease-of-use are paramount in all expected use-cases, such as when performance is required. I would like to know if there are more general reasons that argue for a design preferring more efficient implementations—even if only marginally so?

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• Software to Tune/Calibrate Properties for Heuristic Algorithms

  - by Karussell

  Today I read that there is a software called WinCalibra (scroll a bit down) which can take a text file with properties as input. This program can then optimize the input properties based on the output values of your algorithm. See this paper or the user documentation for more information (see link above; sadly doc is a zipped exe). Do you know other software which can do the same which runs under Linux? (preferable Open Source) EDIT: Since I need this for a java application I will now invest my research in java libraries like jgap. Other ideas and links would be appreciated!

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• image archive VS image strip

  - by DevA

  Hi, i've noticed that plenty of games / applications (very common on mobile builds) pack numerous images into an image strip. I figured that the advantages in this are making the program more tidy (file system - wise) and reducing (un)installation time. During the runtime of the application, the entire image strip is allocated and copied from FS to RAM. On the contrary, images can be stored in an image archive and unpacked during runtime to a number of image structures in RAM. The way I see it, the image strip approach is less efficient because of worse caching performance and because that even if the optimal rectangle packing algorithm is used, there will be empty spaces between the stored images in the strip, causing a waste of RAM. What are the advantages in using an image strip over using an image archive file?

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