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• Applying the Knuth-Plass algorithm (or something better?) to read two books with different length and amount of chapters in parallel

  - by user147133

  I have a Bible reading plan that covers the whole Bible in 180 days. For the most of the time, I read 5 chapters in the Old Testament and 1 or 2 (1.5) chapters in the New Testament each day. The problem is that some chapters are longer than others (for example Psalm 119 which is 7 times longer than a average chapter in the Bible), and the plan I'm following doesn't take that in count. I end up with some days having a lot more to read than others. I thought I could use programming to make myself a better plan. I have a datastructure with a list of all chapters in the bible and their length in number of lines. (I found that the number of lines is the best criteria, but it could have been number of verses or number of words as well) I then started to think about this problem as a line wrap problem. Think of a chapter like a word, a day like a line and the whole plan as a paragraph. The "length" of a word (a chapter) is the number of lines in that chapter. I could then generate the best possible reading plan by applying a simplified Knuth-Plass algorithm to find the best breakpoints. This works well if I want to read the Bible from beginning to end. But I want to read a little from the new testament each day in parallel with the old testament. Of course I can run the Knuth-Plass algorithm on the Old Testament first, then on the New Testament and get two separate plans. But those plans merged is not a optimal plan. Worst-case days (days with extra much reading) in the New Testament plan will randomly occur on the same days as the worst-case days in the Old Testament. Since the New Testament have about 180*1.5 chapters, the plan is generally to read one chapter the first day, two the second, one the third etc... And I would like the plan for the Old Testament to compensate for this alternating length. So I will need a new and better algorithm, or I will have to use the Knuth-Plass algorithm in a way that I've not figured out. I think this could be a interesting and challenging nut for people interested in algorithms, so therefore I wanted to see if any of you have a good solution in mind.

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• faster implementation of sum ( for Codility test )

  - by Oscar Reyes

  How can the following simple implementation of sum be faster? private long sum( int [] a, int begin, int end ) { if( a == null ) { return 0; } long r = 0; for( int i = begin ; i < end ; i++ ) { r+= a[i]; } return r; } EDIT Background is in order. Reading latest entry on coding horror, I came to this site: http://codility.com which has this interesting programming test. Anyway, I got 60 out of 100 in my submission, and basically ( I think ) is because this implementation of sum, because those parts where I failed are the performance parts. I'm getting TIME_OUT_ERROR's So, I was wondering if an optimization in the algorithm is possible. So, no built in functions or assembly would be allowed. This my be done in C, C++, C#, Java or pretty much in any other. EDIT As usual, mmyers was right. I did profile the code and I saw most of the time was spent on that function, but I didn't understand why. So what I did was to throw away my implementation and start with a new one. This time I've got an optimal solution [ according to San Jacinto O(n) -see comments to MSN below - ] This time I've got 81% on Codility which I think is good enough. The problem is that I didn't take the 30 mins. but around 2 hrs. but I guess that leaves me still as a good programmer, for I could work on the problem until I found an optimal solution: Here's my result. I never understood what is those "combinations of..." nor how to test "extreme_first"

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• Getting the submatrix with maximum sum?

  - by guirgis

  With the help of the Algorithmist and Larry and a modification of Kadane's Algorithm, here is my solution: int dim = matrix.length; //computing the vertical prefix sum for columns int[][] ps = new int[dim][dim]; for (int i = 0; i < dim; i++) { for (int j = 0; j < dim; j++) { if (j == 0) { ps[j][i] = matrix[j][i]; } else { ps[j][i] = matrix[j][i] + ps[j - 1][i]; } } } int maxSoFar = 0; int min , subMatrix; //iterate over the possible combinations applying Kadane's Alg. //int toplefti =0, topleftj=0, bottomrighti=0, bottomrightj=0; for (int i = 0; i < dim; i++) { for (int j = i; j < dim; j++) { min = 0; subMatrix = 0; for (int k = 0; k < dim; k++) { if (i == 0) { subMatrix += ps[j][k]; } else { subMatrix += ps[j][k] - ps[i-1][k]; } if(subMatrix < min){ min = subMatrix; } if((subMatrix - min) > maxSoFar){ maxSoFar = subMatrix - min; } } } } The only problem left is to determine the submatrix elements, i mean the top left and the bottom right corners. I managed to do this in one dimensional case. Any suggestions?

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• Ray-box Intersection Theory

  - by Myx

  Hello: I wish to determine the intersection point between a ray and a box. The box is defined by its min 3D coordinate and max 3D coordinate and the ray is defined by its origin and the direction to which it points. Currently, I am forming a plane for each face of the box and I'm intersecting the ray with the plane. If the ray intersects the plane, then I check whether or not the intersection point is actually on the surface of the box. If so, I check whether it is the closest intersection for this ray and I return the closest intersection. The way I check whether the plane-intersection point is on the box surface itself is through a function bool PointOnBoxFace(R3Point point, R3Point corner1, R3Point corner2) { double min_x = min(corner1.X(), corner2.X()); double max_x = max(corner1.X(), corner2.X()); double min_y = min(corner1.Y(), corner2.Y()); double max_y = max(corner1.Y(), corner2.Y()); double min_z = min(corner1.Z(), corner2.Z()); double max_z = max(corner1.Z(), corner2.Z()); if(point.X() >= min_x && point.X() <= max_x && point.Y() >= min_y && point.Y() <= max_y && point.Z() >= min_z && point.Z() <= max_z) return true; return false; } where corner1 is one corner of the rectangle for that box face and corner2 is the opposite corner. My implementation works most of the time but sometimes it gives me the wrong intersection. I was wondering if the way I'm checking whether the intersection point is on the box is correct or if I should use some other algorithm. Thanks.

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• How should I Test a Genetic Algorithm

  - by James Brooks

  I have made a quite few genetic algorithms; they work (they find a reasonable solution quickly). But I have now discovered TDD. Is there a way to write a genetic algorithm (which relies heavily on random numbers) in a TDD way? To pose the question more generally, How do you test a non-deterministic method/function. Here is what I have thought of: Use a specific seed. Which wont help if I make a mistake in the code in the first place but will help finding bugs when refactoring. Use a known list of numbers. Similar to the above but I could follow the code through by hand (which would be very tedious). Use a constant number. At least I know what to expect. It would be good to ensure that a dice always reads 6 when RandomFloat(0,1) always returns 1. Try to move as much of the non-deterministic code out of the GA as possible. which seems silly as that is the core of it's purpose. Links to very good books on testing would be appreciated too.

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• How do you construct an array suitable for numpy sorting?

  - by Alex

  I need to sort two arrays simultaneously, or rather I need to sort one of the arrays and bring the corresponding element of its associated array with it as I sort. That is if the array is [(5, 33), (4, 44), (3, 55)] and I sort by the first axis (labeled below dtype='alpha') then I want: [(3.0, 55.0) (4.0, 44.0) (5.0, 33.0)]. These are really big data sets and I need to sort first ( for nlog(n) speed ) before I do some other operations. I don't know how to merge my two separate arrays though in the proper manner to get the sort algorithm working. I think my problem is rather simple. I tried three different methods: import numpy x=numpy.asarray([5,4,3]) y=numpy.asarray([33,44,55]) dtype=[('alpha',float), ('beta',float)] values=numpy.array([(x),(y)]) values=numpy.rollaxis(values,1) #values = numpy.array(values, dtype=dtype) #a=numpy.array(values,dtype=dtype) #q=numpy.sort(a,order='alpha') print "Try 1:\n", values values=numpy.empty((len(x),2)) for n in range (len(x)): values[n][0]=y[n] values[n][1]=x[n] print "Try 2:\n", values #values = numpy.array(values, dtype=dtype) #a=numpy.array(values,dtype=dtype) #q=numpy.sort(a,order='alpha') ### values = [(x[0], y[0]), (x[1],y[1]) , (x[2],y[2])] print "Try 3:\n", values values = numpy.array(values, dtype=dtype) a=numpy.array(values,dtype=dtype) q=numpy.sort(a,order='alpha') print "Result:\n",q I commented out the first and second trys because they create errors, I knew the third one would work because that was mirroring what I saw when I was RTFM. Given the arrays x and y (which are very large, just examples shown) how do I construct the array (called values) that can be called by numpy.sort properly? *** Zip works great, thanks. Bonus question: How can I later unzip the sorted data into two arrays again?

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• How does one convert 16-bit RGB565 to 24-bit RGB888?

  - by jleedev

  I’ve got my hands on a 16-bit rgb565 image (specifically, an Android framebuffer dump), and I would like to convert it to 24-bit rgb888 for viewing on a normal monitor. The question is, how does one convert a 5- or 6-bit channel to 8 bits? The obvious answer is to shift it. I started out by writing this: uint16_t buf; while (read(0, &buf, sizeof buf)) { unsigned char red = (buf & 0xf800) >> 11; unsigned char green = (buf & 0x07c0) >> 5; unsigned char blue = buf & 0x003f; putchar(red << 3); putchar(green << 2); putchar(blue << 3); } However, this doesn’t have one property I would like, which is for 0xffff to map to 0xffffff, instead of 0xf8fcf8. I need to expand the value in some way, but I’m not sure how that should work. The Android SDK comes with a tool called ddms (Dalvik Debug Monitor) that takes screen captures. As far as I can tell from reading the code, it implements the same logic; yet its screenshots are coming out different, and white is mapping to white. Here’s the raw framebuffer, the smart conversion by ddms, and the dumb conversion by the above algorithm. (By the way, this conversion is implemented in ffmpeg, but it’s just performing the dumb conversion listed above, leaving the LSBs at all zero.) I guess I have two questions: What’s the most sensible way to convert rgb565 to rgb888? How is DDMS converting its screenshots?

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• Big problem with Dijkstra algorithm in a linked list graph implementation

  - by Nazgulled

  Hi, I have my graph implemented with linked lists, for both vertices and edges and that is becoming an issue for the Dijkstra algorithm. As I said on a previous question, I'm converting this code that uses an adjacency matrix to work with my graph implementation. The problem is that when I find the minimum value I get an array index. This index would have match the vertex index if the graph vertexes were stored in an array instead. And the access to the vertex would be constant. I don't have time to change my graph implementation, but I do have an hash table, indexed by a unique number (but one that does not start at 0, it's like 100090000) which is the problem I'm having. Whenever I need, I use the modulo operator to get a number between 0 and the total number of vertices. This works fine for when I need an array index from the number, but when I need the number from the array index (to access the calculated minimum distance vertex in constant time), not so much. I tried to search for how to inverse the modulo operation, like, 100090000 mod 18000 = 10000 and, 10000 invmod 18000 = 100090000 but couldn't find a way to do it. My next alternative is to build some sort of reference array where, in the example above, arr[10000] = 100090000. That would fix the problem, but would require to loop the whole graph one more time. Do I have any better/easier solution with my current graph implementation?

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• Raytracing (LoS) on 3D hex-like tile maps

  - by herenvardo

  Greetings, I'm working on a game project that uses a 3D variant of hexagonal tile maps. Tiles are actually cubes, not hexes, but are laid out just like hexes (because a square can be turned to a cube to extrapolate from 2D to 3D, but there is no 3D version of a hex). Rather than a verbose description, here goes an example of a 4x4x4 map: (I have highlighted an arbitrary tile (green) and its adjacent tiles (yellow) to help describe how the whole thing is supposed to work; but the adjacency functions are not the issue, that's already solved.) I have a struct type to represent tiles, and maps are represented as a 3D array of tiles (wrapped in a Map class to add some utility methods, but that's not very relevant). Each tile is supposed to represent a perfectly cubic space, and they are all exactly the same size. Also, the offset between adjacent "rows" is exactly half the size of a tile. That's enough context; my question is: Given the coordinates of two points A and B, how can I generate a list of the tiles (or, rather, their coordinates) that a straight line between A and B would cross? That would later be used for a variety of purposes, such as determining Line-of-sight, charge path legality, and so on. BTW, this may be useful: my maps use the (0,0,0) as a reference position. The 'jagging' of the map can be defined as offsetting each tile ((y+z) mod 2) * tileSize/2.0 to the right from the position it'd have on a "sane" cartesian system. For the non-jagged rows, that yields 0; for rows where (y+z) mod 2 is 1, it yields 0.5 tiles. I'm working on C#4 targeting the .Net Framework 4.0; but I don't really need specific code, just the algorithm to solve the weird geometric/mathematical problem. I have been trying for several days to solve this at no avail; and trying to draw the whole thing on paper to "visualize" it didn't help either :( . Thanks in advance for any answer

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• Python: speed up removal of every n-th element from list.

  - by ChristopheD

  I'm trying to solve this programming riddle and althought the solution (see code below) works correct, it is too slow for succesful submission. Any pointers as how to make this run faster? (removal of every n-th element from a list)? Or suggestions for a better algorithm to calculate the same; seems I can't think of anything else then brute-force for now... Basically the task at hand is: GIVEN: L = [2,3,4,5,6,7,8,9,10,11,........] 1. Take the first remaining item in list L (in the general case 'n'). Move it to the 'lucky number list'. Then drop every 'n-th' item from the list. 2. Repeat 1 TASK: Calculate the n-th number from the 'lucky number list' ( 1 <= n <= 3000) My current code (it calculates the 3000 first lucky numbers in about a second on my machine - but unfortunately too slow): """ SPOJ Problem Set (classical) 1798. Assistance Required URL: http://www.spoj.pl/problems/ASSIST/ """ sieve = range(3, 33900, 2) luckynumbers = [2] while True: wanted_n = input() if wanted_n == 0: break while len(luckynumbers) < wanted_n: item = sieve[0] luckynumbers.append(item) items_to_delete = set(sieve[::item]) sieve = filter(lambda x: x not in items_to_delete, sieve) print luckynumbers[wanted_n-1]

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• Average of two strings in alphabetical/lexicographical order

  - by Bemmu

  Suppose you take the strings 'a' and 'z' and list all the strings that come between them in alphabetical order: ['a','b','c' ... 'x','y','z']. Take the midpoint of this list and you find 'm'. So this is kind of like taking an average of those two strings. You could extend it to strings with more than one character, for example the midpoint between 'aa' and 'zz' would be found in the middle of the list ['aa', 'ab', 'ac' ... 'zx', 'zy', 'zz']. Might there be a Python method somewhere that does this? If not, even knowing the name of the algorithm would help. I began making my own routine that simply goes through both strings and finds midpoint of the first differing letter, which seemed to work great in that 'aa' and 'az' midpoint was 'am', but then it fails on 'cat', 'doggie' midpoint which it thinks is 'c'. I tried Googling for "binary search string midpoint" etc. but without knowing the name of what I am trying to do here I had little luck.

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• sample java code for approximate string matching or boyer-moore extended for approximate string matc

  - by Dolphin

  Hi I need to find 1.mismatch(incorrectly played notes), 2.insertion(additional played), & 3.deletion (missed notes), in a music piece (e.g. note pitches [string values] stored in a table) against a reference music piece. This is either possible through exact string matching algorithms or dynamic programming/ approximate string matching algos. However I realised that approximate string matching is more appropriate for my problem due to identifying mismatch, insertion, deletion of notes. Or an extended version of Boyer-moore to support approx. string matching. Is there any link for sample java code I can try out approximate string matching? I find complex explanations and equations - but I hope I could do well with some sample code and simple explanations. Or can I find any sample java code on boyer-moore extended for approx. string matching? I understand the boyer-moore concept, but having troubles with adjusting it to support approx. string matching (i.e. to support mismatch, insertion, deletion). Also what is the most efficient approx. string matching algorithm (like boyer-moore in exact string matching algo)? Greatly appreciate any insight/ suggestions. Many thanks in advance

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• Average of two strings in alphabetical order

  - by Bemmu

  Suppose you take the strings 'a' and 'z' and list all the strings that come between them in alphabetical order: ['a','b','c' ... 'x','y','z']. Take the midpoint of this list and you find 'm'. So this is kind of like taking an average of those two strings. You could extend it to strings with more than one character, for example the midpoint between 'aa' and 'zz' would be found in the middle of the list ['aa', 'ab', 'ac' ... 'zx', 'zy', 'zz']. Might there be a Python method somewhere that does this? If not, even knowing the name of the algorithm would help. I began making my own routine that simply goes through both strings and finds midpoint of the first differing letter, which seemed to work great in that 'aa' and 'az' midpoint was 'am', but then it fails on 'cat', 'doggie' midpoint which it thinks is 'c'. Rather than invent a method I thought it better to ask. I tried Googling for "binary search string midpoint" etc. but without knowing the name of what I am trying to do here I had little luck.

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• How to code a URL shortener?

  - by marco92w

  I want to create a URL shortener service where you can write a long URL into an input field and the service shortens the URL to "http://www.example.org/abcdef". Instead of "abcdef" there can be any other string with six characters containing a-z, A-Z and 0-9. That makes 56 trillion possible strings. My approach: I have a database table with three columns: id, integer, auto-increment long, string, the long URL the user entered short, string, the shortened URL (or just the six characters) I would then insert the long URL into the table. Then I would select the auto-increment value for "id" and build a hash of it. This hash should then be inserted as "short". But what sort of hash should I build? Hash algorithms like MD5 create too long strings. I don't use these algorithms, I think. A self-built algorithm will work, too. My idea: For "http://www.google.de/" I get the auto-increment id 239472. Then I do the following steps: short = ''; if divisible by 2, add "a"+the result to short if divisible by 3, add "b"+the result to short ... until I have divisors for a-z and A-Z. That could be repeated until the number isn't divisible any more. Do you think this is a good approach? Do you have a better idea?

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• Autodetect Presence of CSV Headers in a File

  - by banzaimonkey

  Short question: How do I automatically detect whether a CSV file has headers in the first row? Details: I've written a small CSV parsing engine that places the data into an object that I can access as (approximately) an in-memory database. The original code was written to parse third-party CSV with a predictable format, but I'd like to be able to use this code more generally. I'm trying to figure out a reliable way to automatically detect the presence of CSV headers, so the script can decide whether to use the first row of the CSV file as keys / column names or start parsing data immediately. Since all I need is a boolean test, I could easily specify an argument after inspecting the CSV file myself, but I'd rather not have to (go go automation). I imagine I'd have to parse the first 3 to ? rows of the CSV file and look for a pattern of some sort to compare against the headers. I'm having nightmares of three particularly bad cases in which: The headers include numeric data for some reason The first few rows (or large portions of the CSV) are null There headers and data look too similar to tell them apart If I can get a "best guess" and have the parser fail with an error or spit out a warning if it can't decide, that's OK. If this is something that's going to be tremendously expensive in terms of time or computation (and take more time than it's supposed to save me) I'll happily scrap the idea and go back to working on "important things". I'm working with PHP, but this strikes me as more of an algorithmic / computational question than something that's implementation-specific. If there's a simple algorithm I can use, great. If you can point me to some relevant theory / discussion, that'd be great, too. If there's a giant library that does natural language processing or 300 different kinds of parsing, I'm not interested.

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• Algorithms for finding a numerical record in a list of ordered numbers

  - by Ankur

  I have a list of incomplete ordered numbers. I want to find a particular number with as few steps as possible. Are there any improvements on this algorithm, I assume you can count the set size without difficulty - it will be stored and updated every time a new item is added. Your object is to get your cursor over the value x The first number (smallest) is s, and the last number (greatest) is g. Take the midpoint m1 of the set: calculate is x < m1, If yes then s <= x < m1 If no then m1 < x <= g If m1 = x then you're done. Keep repeating till you find x. Basically dividing the set into two parts with each iteration till you hit x. The purpose is to retrieve a numerical id from a very large table to then find the associated other records. I would imagine this is the most trivial kind of indexing available, are there improvements?

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• Please Help Me with my Homework Problem in C++

  - by sil3nt

  Hey there, this is part of a question i got in class, im at the final stretch but this has become a major problem. In it im given a certain value which is called the "gold value" and it is 40.5, this value changes in input. and i have these constants const int RUBIES_PER_DIAMOND = 5; // relative values. * const int EMERALDS_PER_RUBY = 2; const int GOLDS_PER_EMERALDS = 5; const int SILVERS_PER_GOLD = 4; const int COPPERS_PER_SILVER = 5; const int DIAMOND_VALUE = 50; // gold values. * const int RUBY_VALUE = 10; const int EMERALD_VALUE = 5; const float SILVER_VALUE = 0.25; const float COPPER_VALUE = 0.05; which means that basically for every diamond there are 5 rubies, and for every ruby there are 2 emeralds. So on and so forth. and the "gold value" for every diamond for example is 50 (diamond value = 50) this is how much one diamond is worth in golds. my problem is converting 40.5 into these diamonds and ruby values. I know the answer is 4rubies and 2silvers but how do i write the algorithm for this so that it gives the best estimate for every goldvalue that comes along??

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• Fuzzy Search on Material Descriptions including numerical sizes & general descriptions of material t

  - by Kyle

  We're looking to provide a fuzzy search on an electrical materials database (i.e. conduit, cable, etc.). The problem is that, because of a lack of consistency across all material types, we could not split sizes into separate fields from the text description because some materials are rated by things other than size. I've attempted a combination of a full text search & a SQL CLR implementation of the Levenshtein search algorithm (for assistance in ranking), but my results are a little funky (i.e. they are not sorting correctly due to improper ranking). For example, if the search term is "3/4" ABCD Conduit", I'll might get back several irrelevant results in the following order: 1/2" Conduit 1/4" X 3/4" Cable 1/4" Cable Ties 3/4" DFC Conduit Tees 3/4" ABCD Conduit 3/4" Conduit I believe I've nailed the problem down to the fact that these two search algorithms do not factor in the relevance of punctuation & numeric. That is, in such a search, I'd expect the size to take precedence over any fuzzy match on the rest of the description, but my results don't reflect that. My question is: Can anyone recommend better search algorithms or different approaches that may be better suited for searching a combination of alphanumerics & punctuation characters?

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• Programmer Puzzle: Encoding a chess board state throughout a game

  - by Andrew Rollings

  Not strictly a question, more of a puzzle... Over the years, I've been involved in a few technical interviews of new employees. Other than asking the standard "do you know X technology" questions, I've also tried to get a feel for how they approach problems. Typically, I'd send them the question by email the day before the interview, and expect them to come up with a solution by the following day. Often the results would be quite interesting - wrong, but interesting - and the person would still get my recommendation if they could explain why they took a particular approach. So I thought I'd throw one of my questions out there for the Stack Overflow audience. Question: What is the most space-efficient way you can think of to encode the state of a chess game (or subset thereof)? That is, given a chess board with the pieces arranged legally, encode both this initial state and all subsequent legal moves taken by the players in the game. No code required for the answer, just a description of the algorithm you would use. EDIT: As one of the posters has pointed out, I didn't consider the time interval between moves. Feel free to account for that too as an optional extra :) EDIT2: Just for additional clarification... Remember, the encoder/decoder is rule-aware. The only things that really need to be stored are the player's choices - anything else can be assumed to be known by the encoder/decoder. EDIT3: It's going to be difficult to pick a winner here :) Lots of great answers!

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• Finding subsets that can be completed to tuples without duplicates

  - by Jules

  We have a collection of sets A_1,..,A_n. The goal is to find new sets for each of the old sets. newA_i = {a_i in A_i such that there exist (a_1,..,a_n) in (A1,..,An) with no a_k = a_j for all k and j} So in words this says that we remove all the elements from A_i that can't be used to form a tuple (a_1,..a_n) from the sets (A_1,..,A_n) such that the tuple doesn't contain duplicates. My question is how to compute these new sets quickly. If you just implement this definition by generating all possible v's this will take exponential time. Do you know a better algorithm? Edit: here's an example. Take A_1 = {1,2,3,4} A_2 = {2}. Now the new sets look like this: newA_1 = {1,3,4} newA_2 = {2} The 2 has been removed from A_1 because if you choose it the tuple will always be (2,2) which is invalid because it contains duplicates. On the other hand 1,3,4 are valid because (1,2), (3,2) and (4,2) are valid tuples. Another example: A_1 = {1,2,3} A_2 = {1,4,5} A_3 = {2,4,5} A_4 = {1,2,3} A_5 = {1,2,3} Now the new sets are: newA_1 = {1,2,3} newA_2 = {4,5} newA_3 = {4,5} newA_4 = {1,2,3} newA_5 = {1,2,3} The 1 and 2 are removed from sets 2 and 3 because if you choose the 1 or 2 from these sets you'll only have 2 values left for sets 1, 4 and 5, so you will always have duplicates in tuples that look like (_,1,_,_,_) or like (_,_,2,_,_).

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• A function where small changes in input always result in large changes in output

  - by snowlord

  I would like an algorithm for a function that takes n integers and returns one integer. For small changes in the input, the resulting integer should vary greatly. Even though I've taken a number of courses in math, I have not used that knowledge very much and now I need some help... An important property of this function should be that if it is used with coordinate pairs as input and the result is plotted (as a grayscale value for example) on an image, any repeating patterns should only be visible if the image is very big. I have experimented with various algorithms for pseudo-random numbers with little success and finally it struck me that md5 almost meets my criteria, except that it is not for numbers (at least not from what I know). That resulted in something like this Python prototype (for n = 2, it could easily be changed to take a list of integers of course): import hashlib def uniqnum(x, y): return int(hashlib.md5(str(x) + ',' + str(y)).hexdigest()[-6:], 16) But obviously it feels wrong to go over strings when both input and output are integers. What would be a good replacement for this implementation (in pseudo-code, python, or whatever language)?

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• Count all lists of adjacent nodes stored in an array.

  - by Ben Brodie

  There are many naive approaches to this problem, but I'm looking for a good solution. Here is the problem (will be implemented in Java): You have a function foo(int a, int b) that returns true if 'a' is "adjacent" to 'b' and false if 'a' is not adjacent to 'b'. You have an array such as this [1,4,5,9,3,2,6,15,89,11,24], but in reality has a very long length, like 120, and will be repeated over and over (its a genetic algorithm fitness function) which is why efficiency is important. I want a function that returns the length of each possible 'list' of adjacencies in the array, but not including the 'lists' which simply subsets of a larger list. For example, if foo(1,4) - true, foo(4,5) - true, foo(5,9)- false, foo(9,3) & foo(3,2) & foo(2,6), foo(6,15) - true, then there are 'lists' (1,4,5) and (9,3,2,6), so length 3 and 4. I don't want it to return (3,2,6), though, because this is simply a subset of 9,3,2,6. Thanks.

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• How to find minimum cut-sets for several subgraphs of a graph of degrees 2 to 4

  - by Tore

  I have a problem, Im trying to make A* searches through a grid based game like pacman or sokoban, but i need to find "enclosures". What do i mean by enclosures? subgraphs with as few cut edges as possible given a maximum size and minimum size for number of vertices that act as soft constraints. Alternatively you could say i am looking to find bridges between subgraphs, but its generally the same problem. Given a game that looks like this, what i want to do is find enclosures so that i can properly find entrances to them and thus get a good heuristic for reaching vertices inside these enclosures. So what i want is to find these colored regions on any given map. The reason for me bothering to do this and not just staying content with the performance of a simple manhattan distance heuristic is that an enclosure heuristic can give more optimal results and i would not have to actually do the A* to get some proper distance calculations and also for later adding competitive blocking of opponents within these enclosures when playing sokoban type games. Also the enclosure heuristic can be used for a minimax approach to finding goal vertices more properly. Do you know of a good algorithm for solving this problem or have any suggestions in things i should explore?

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• Random Pairings that don't Repeat

  - by Andrew Robinson

  This little project / problem came out of left field for me. Hoping someone can help me here. I have some rough ideas but I am sure (or at least I hope) a simple, fairly efficient solution exists. Thanks in advance.... pseudo code is fine. I generally work in .NET / C# if that sheds any light on your solution. Given: A pool of n individuals that will be meeting on a regular basis. I need to form pairs that have not previously meet. The pool of individuals will slowly change over time. For the purposes of pairing, (A & B) and (B & A) constitute the same pair. The history of previous pairings is maintained. For the purpose of the problem, assume an even number of individuals. For each meeting (collection of pairs) and individual will only pair up once. Is there an algorithm that will allow us to form these pairs? Ideally something better than just ordering the pairs in a random order, generating pairings and then checking against the history of previous pairings. In general, randomness within the pairing is ok.

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• Time complexity with bit cost

  - by Keyser

  I think I might have completely misunderstood bit cost analysis. I'm trying to wrap my head around the concept of studying an algorithm's time complexity with respect to bit cost (instead of unit cost) and it seems to be impossible to find anything on the subject. Is this considered to be so trivial that no one ever needs to have it explained to them? Well I do. (Also, there doesn't even seem to be anything on wikipedia which is very unusual). Here's what I have so far: The bit cost of multiplication and division of two numbers with n bits is O(n^2) (in general?) So, for example: int number = 2; for(int i = 0; i < n; i++ ){ number = i*i; } has a time complexity with respect to bit cost of O(n^3), because it does n multiplications (right?) But in a regular scenario we want the time complexity with respect to the input. So, how does that scenario work? The number of bits in i could be considered a constant. Which would make the time complexity the same as with unit cost except with a bigger constant (and both would be linear). Also, I'm guessing addition and subtraction can be done in constant time, O(1). Couldn't find any info on it but it seems reasonable since it's one assembler operation.

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