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  • Calculate coordinates between startpoint and endpoint

    - by MikeB123
    Given.. 1 - The start-point GPS coordinates, 2 - The end-point GPS coordinates, 3 - The speed at which the object is travelling, 4 - Knowing that the trip trajectory will be a straight line... How can I calculate what my GPS coordinated will be in n minutes' time? That is to say, how can I calculate my position at a given time after the trip has started before the trip has ended?

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  • Sorting 1 million 8-digit numbers in 1MB of RAM

    - by Favourite Chigozie Onwuemene
    I have a computer with 1M of RAM and no other local storage. I must use it to accept 1 million 8-digit decimal numbers over a TCP connection, sort them, and then send the sorted list out over another TCP connection. The list of numbers may contain duplicates, which I must not discard. The code will be placed in ROM, so I need not subtract the size of my code from the 1M. I already have code to drive the ethernet port and handle TCP/IP connections, and it requires 2k for its state data, including a 1k buffer via which the code will read and write data. Is there a solution to this problem?

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  • Enumerating combinations in a distributed manner

    - by Reyzooti
    I have a problem where I must analyse 500C5 combinations (255244687600) of something. Distributing it over a 10 node cluster where each cluster processes roughly 10^6 combinations per second means the job will be complete in about 7hours. The problem I have is distributing the 255244687600 combinations over the 10 nodes. I'd like to present each node with 25524468760, however the algorithms I'm using can only produce the combinations sequentially, I'd like to be able to pass the set of elements and a range of combination indicies eg: [0-10^7) or [10^7,2.0 10^7) etc and have the nodes themselves figure out the combinations. The algorithms I'm using at the moment are from the following: http://home.roadrunner.com/~hinnant/combinations.html A logical question I've considered using a master node, that enumerates each of the combinations and sends work to each of the nodes, however the overhead incurred in iterating the combinations from a single node and communicating back and forth work is enormous, and will subsequently lead to the master node becoming the bottleneck. Are there any good combination iterating algorithms geared up for efficient/optimal distributed enumeration?

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  • Fast ceiling of an integer division in C / C++

    - by andand
    Given integer values x and y, C and C++ returns as the quotient q = x/y the floor of the floating point valued equivalent. I'm interestd in a method of returning the ceiling instead? For example, ceil(10/5) = 2 and ceil(11/5) = 3. The obvious approach involves something like: q = x / y; if (q * y < x) ++q; This requires an extra comparison and multiplication; and other methods I've seen (used in fact) involve casting as a float or double. Is there a more direct method that avoids the additional multiplication (or a second division) and branch, and that also avoids casting as a floating point number?

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  • How can I represent a line of music notes in a way that allows fast insertion at any index?

    - by chairbender
    For "fun", and to learn functional programming, I'm developing a program in Clojure that does algorithmic composition using ideas from this theory of music called "Westergaardian Theory". It generates lines of music (where a line is just a single staff consisting of a sequence of notes, each with pitches and durations). It basically works like this: Start with a line consisting of three notes (the specifics of how these are chosen are not important). Randomly perform one of several "operations" on this line. The operation picks randomly from all pairs of adjacent notes that meet a certain criteria (for each pair, the criteria only depends on the pair and is independent of the other notes in the line). It inserts 1 or several notes (depending on the operation) between the chosen pair. Each operation has its own unique criteria. Continue randomly performing these operations on the line until the line is the desired length. The issue I've run into is that my implementation of this is quite slow, and I suspect it could be made faster. I'm new to Clojure and functional programming in general (though I'm experienced with OO), so I'm hoping someone with more experience can point out if I'm not thinking in a functional paradigm or missing out on some FP technique. My current implementation is that each line is a vector containing maps. Each map has a :note and a :dur. :note's value is a keyword representing a musical note like :A4 or :C#3. :dur's value is a fraction, representing the duration of the note (1 is a whole note, 1/4 is a quarter note, etc...). So, for example, a line representing the C major scale starting on C3 would look like this: [ {:note :C3 :dur 1} {:note :D3 :dur 1} {:note :E3 :dur 1} {:note :F3 :dur 1} {:note :G3 :dur 1} {:note :A4 :dur 1} {:note :B4 :dur 1} ] This is a problematic representation because there's not really a quick way to insert into an arbitrary index of a vector. But insertion is the most frequently performed operation on these lines. My current terrible function for inserting notes into a line basically splits the vector using subvec at the point of insertion, uses conj to join the first part + notes + last part, then uses flatten and vec to make them all be in a one-dimensional vector. For example if I want to insert C3 and D3 into the the C major scale at index 3 (where the F3 is), it would do this (I'll use the note name in place of the :note and :dur maps): (conj [C3 D3 E3] [C3 D3] [F3 G3 A4 B4]), which creates [C3 D3 E3 [C3 D3] [F3 G3 A4 B4]] (vec (flatten previous-vector)) which gives [C3 D3 E3 C3 D3 F3 G3 A4 B4] The run time of that is O(n), AFAIK. I'm looking for a way to make this insertion faster. I've searched for information on Clojure data structures that have fast insertion but haven't found anything that would work. I found "finger trees" but they only allow fast insertion at the start or end of the list. Edit: I split this into two questions. The other part is here.

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  • How do I recursively define a Hash in Ruby from supplied arguments?

    - by Sarah Beckham
    This snippet of code populates an @options hash. values is an Array which contains zero or more heterogeneous items. If you invoke populate with arguments that are Hash entries, it uses the value you specify for each entry to assume a default value. def populate(*args) args.each do |a| values = nil if (a.kind_of? Hash) # Converts {:k => "v"} to `a = :k, values = "v"` a, values = a.to_a.first end @options[:"#{a}"] ||= values ||= {} end end What I'd like to do is change populate such that it recursively populates @options. There is a special case: if the values it's about to populate a key with are an Array consisting entirely of (1) Symbols or (2) Hashes whose keys are Symbols (or some combination of the two), then they should be treated as subkeys rather than the values associated with that key, and the same logic used to evaluate the original populate arguments should be recursively re-applied. That was a little hard to put into words, so I've written some test cases. Here are some test cases and the expected value of @options afterwards: populate :a => @options is {:a => {}} populate :a => 42 => @options is {:a => 42} populate :a, :b, :c => @options is {:a => {}, :b => {}, :c => {}} populate :a, :b => "apples", :c => @options is {:a => {}, :b => "apples", :c => {}} populate :a => :b => @options is {:a => :b} # Because [:b] is an Array consisting entirely of Symbols or # Hashes whose keys are Symbols, we assume that :b is a subkey # of @options[:a], rather than the value for @options[:a]. populate :a => [:b] => @options is {:a => {:b => {}}} populate :a => [:b, :c => :d] => @options is {:a => {:b => {}, :c => :d}} populate :a => [:a, :b, :c] => @options is {:a => {:a => {}, :b => {}, :c => {}}} populate :a => [:a, :b, "c"] => @options is {:a => [:a, :b, "c"]} populate :a => [:one], :b => [:two, :three => "four"] => @options is {:a => :one, :b => {:two => {}, :three => "four"}} populate :a => [:one], :b => [:two => {:four => :five}, :three => "four"] => @options is {:a => :one, :b => { :two => { :four => :five } }, :three => "four" } } It is acceptable if the signature of populate needs to change to accommodate some kind of recursive version. There is no limit to the amount of nesting that could theoretically happen. Any thoughts on how I might pull this off?

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  • How to generate a LONG guid?

    - by Ron
    I would like to generate a long UUID - something like the session key used by gmail. It should be at least 256 chars and no more than 512. It can contain all alpha-numeric chars and a few special chars (the ones below the function keys on the keyboard). Has this been done already or is there a sample out there? C++ or C#

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  • How to Implement AutoSize

    - by TheCloudlessSky
    I'm trying to figure out a good way to auto-size a Rectangle that has text drawn inside of it. I basically want the size to have a ratio of width/height and then "grow" according to that ratio to fit the text. I've looked at Graphics.MeasureString but I don't think it does what I'm looking for (maybe it does and I'm just using it wrong). I don't want to specify a specific width of the rectangle to be drawn, instead I want to say find the smallest width/height to fit this text but the found rectangle must have some specific ratio of width and height. This doesn't have to be specific to C#, any idea for solving this problem I'm sure can be mapped to C#. Thanks!

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  • Finding the index of a given value in a pre-sorted array

    - by bobo
    Today, I went for an interview and the interviewer asked me how I would find the index of a given value (number) in a pre-sorted array like this: $preSortedArr=array(23,32,36,41,45,54); He also said that using recursion is not allowed. I think the function should look like this: function findIndexByValue($preSortedArray,$value){ //some codes here } What solution do you think he was expecting from me? EDIT: sorry, I forgot to add that, he originally asked me to write psuedo codes but I said I don't know. I tried to write in PHP, but I think he's expecting a language-independent solution.

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  • views count calculation

    - by Alexey Poimtsev
    Hi, could you give me idea how to calculate unique views of page? If i will increase counter on each page load it will be no good, otherside storing information of viewed pages in session looks like not ideal solution.

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  • How does the Ableton warp algorithm work exactly?

    - by pepperdreamteam
    I'm looking for any documentation or definitive information on Ableton's warp feature. I understand that it has something to do with finding transients, aligning them with an even rhythm and shifting audio samples accordingly. I'm hoping to find ways to approximate warping with more basic audio editing tools. I understand that this is ableton's unique device, really any information about how it works would be helpful. So...does anyone have any 411?

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  • Are there any well-known algorithms or computer models that computer scientists use to predict FIFA

    - by Khnle
    Occasionally I read news articles that mention about some computer models that computer scientists use to predict winners of some sporting events or the odds for betting which I think there must be a mathematical model behind it. I never bothered to think twice even though I am a "pseudo computer scientist" myself. With the 2010 FIFA World Cup just underway, and since I am also a "pseudo football/soccer player" myself, I just started to wonder about these calculations algorithms. For example, I know one factor is determining the strength of opponents, so that a win against a strong opponent can count more than a win against a weak opponent. But it now kind of gets in a circular loop, or at least how does one determine the strength of a team in the first place, before that team can be considered strong or weak? If it's based on a historical data then there's no way that could be accurate, because those players of the past are no longer on the fields so their impact is none (except maybe if they become coaches like Maradona) Anyway, long question short, if you're happen to be working in this field or have some knowledge, please shed some lights.

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  • Show me some cool python list comprehensions

    - by christangrant
    One of the major strengths of python and a few other (functional) programming languages are the list comprehension. They allow programmers to write complex expressions in 1 line. They may be confusing at first but if one gets used to the syntax, it is much better than nested complicated for loops. With that said, please share with me some of the coolest uses of list comprehensions. (By cool, I just mean useful) It could be for some programming contest, or a production system. For example: To do the transpose of a matrix mat >>> mat = [ ... [1, 2, 3], ... [4, 5, 6], ... [7, 8, 9], ... ] >>> [[row[i] for row in mat] for i in [0, 1, 2]] [[1, 4, 7], [2, 5, 8], [3, 6, 9]] Please include a description of the expression and where it was used (if possible).

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  • Stuck on solving the Minimal Spanning Tree problem.

    - by kunjaan
    I have reduced my problem to finding the minimal spanning tree in the graph. But I want to have one more constraint which is that the total degree for each vertex shouldnt exceed a certain constant factor. How do I model my problem? Is MST the wrong path? Do you know any algorithms that will help me? One more problem: My graph has duplicate edge weights so is there a way to count the number of unique MSTs? Are there algorithms that do this? Thank You. Edit: By degree, I mean the total number of edges connecting the vertex. By duplicate edge weight I mean that two edges have the same weight.

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  • 3-clique counting in a graph

    - by Legend
    I am operating on a (not so) large graph having about 380K edges. I wrote a program to count the number of 3-cliques in the graph. A quick example: List of edges: A - B B - C C - A C - D List of cliques: A - B - C A 3-clique is nothing but a triangle in a graph. Currently, I am doing this using PHP+MySQL. As expected, it is not fast enough. Is there a way to do this in pure MySQL? (perhaps a way to insert all 3-cliques into a table?)

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  • Finding number of different paths

    - by peiska
    I have a game that one player X wants to pass a ball to player Y, but he can be playing with more than one player and the others players can pass the ball to Y. I want to know how many different paths can the ball take from X to Y? for example if he is playing with 3 players there are 5 different paths, 4 players 16 paths, if he is playing with 20 players there are 330665665962404000 paths, and 40 players 55447192200369381342665835466328897344361743780 that the ball can take. the number max. of players that he can play with is 500. I was thinking in using Catalan Numbers? do you think is a correct approach to solve this? Can you give me some tips.

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  • Porting Python algorithm to C++ - different solution

    - by cb0
    Hello, I have written a little brute string generation script in python to generate all possible combinations of an alphabet within a given length. It works quite nice, but for the reason I wan't it to be faster I try to port it to C++. The problem is that my C++ Code is creating far too much combination for one word. Heres my example in python: ./test.py gives me aaa aab aac aad aa aba .... while ./test (the c++ programm gives me) aaa aaa aaa aaa aa Here I also get all possible combinations, but I get them twice ore more often. Here is the Code for both programms: #!/usr/bin/env python import sys #Brute String Generator #Start it with ./brutestringer.py 4 6 "abcdefghijklmnopqrstuvwxyz1234567890" "" #will produce all strings with length 4 to 6 and chars from a to z and numbers 0 to 9 def rec(w, p, baseString): for c in "abcd": if (p<w - 1): rec(w, p + 1, baseString + "%c" % c) print baseString for b in range(3,4): rec(b, 0, "") And here the C++ Code #include <iostream> using namespace std; string chars="abcd"; void rec(int w,int b,string p){ unsigned int i; for(i=0;i<chars.size();i++){ if(b < (w-1)){ rec(w, (b+1), p+chars[i]); } cout << p << "\n"; } } int main () { int a=3, b=0; rec (a+1,b, ""); return 0; } Does anybody see my fault ? I don't have much experience with C++. Thanks indeed

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  • Simple Big O with lg(n) proof

    - by halohunter
    I'm attempting to guess and prove the Big O for: f(n) = n^3 - 7n^2 + nlg(n) + 10 I guess that big O is n^3 as it is the term with the largest order of growth However, I'm having trouble proving it. My unsuccesful attempt follows: f(n) <= cg(n) f(n) <= n^3 - 7n^2 + nlg(n) + 10 <= cn^3 f(n) <= n^3 + (n^3)*lg(n) + 10n^3 <= cn^3 f(n) <= N^3(11 + lg(n)) <= cn^3 so 11 + lg(n) = c But this can't be right because c must be constant. What am I doing wrong?

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  • Purpose of IF, ELSE, FOR macros ?

    - by psihodelia
    I have a source code of a library which has a lot of strange IF, ELSE, FOR, etc. macros for all common C-keywords instead of using just usual if,else,for,while keywords. These macros are defined like this: #define IF( a) if( increment_if(), a) where increment_if() function is defined so: static __inline void increment_if( void) { // If the "IF" operator comes just after an "ELSE", its counter // must not be incremented. ... //implementation } I don't really understand, what is the purpose of such macros? This library is for a real-time application and I suppose that using such macros must slow-down an application.

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  • skipping certain number of frames on a timeline

    - by clamp
    hi, i have a mathematical problem which is a bit hard to describe, but i'll give it a try anyway. in a timeline, i have a number of frames, of which i want to skip a certain number of frames, which should be evenly distributed along the timeline. for example i have 10 frames and i want to skip 5, then the solution is easy: we skip every second frame. 10/5 = 2 if (frame%2 == 0) skip(); but what if the above division does result in a floating number? for example in 44 frames i want to skip 15 times. how can i determine the 15 frames which should be skipped? thanks!

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  • How can you Merge sort a .Net framework LinkedList (of T)

    - by Andronicus
    There's a few questions discussing Merge sorting a LinkedList, but how can I do it with the C# LinkedList? Since the LinkedListNode Next and Previous properties are read-only most of the in-place algorithms I've come across are not possible. I've resorted to removing all the nodes, sorting them with a .OrderBy(node = node.Value) and then re-inserting them into the Linked list, but it's fairly crude.

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  • Optimality of Binary Search

    - by templatetypedef
    Hello all- This may be a silly question, but does anyone know of a proof that binary search is asymptotically optimal? That is, if we are given a sorted list of elements where the only permitted operation on those objects is a comparison, how do you prove that the search can't be done in o(lg n)? (That's little-o of lg n, by the way.) Note that I'm restricting this to elements where the only operation permitted operation is a comparison, since there are well-known algorithms that can beat O(lg n) on expectation if you're allowed to do more complex operations on the data (see, for example, interpolation search). Thanks so much! This has really been bugging me since it seems like it should be simple but has managed to resist all my best efforts. :-)

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