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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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• 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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• 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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• 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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• What's a good way to add a large number of small floats together?

  - by splicer

  Say you have 100000000 32-bit floating point values in an array, and each of these floats has a value between 0.0 and 1.0. If you tried to sum them all up like this result = 0.0; for (i = 0; i < 100000000; i++) { result += array[i]; } you'd run into problems as result gets much larger than 1.0. So what are some of the ways to more accurately perform the summation?

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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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• Automatic images translation to 3d model

  - by farrakhov-bulat

  I'm quite interested in automatic images translation to 3d models. Not really for commercial product, but from the point of possible academic research and implementation. What I'd like to achieve is almost transparent for user process of transformation series of images (fewer is better) to 3d model which might be shown in flash/silverlight/javafx or similar. Consider online furniture store with 3d models of all items in stock. Kinda cool to have ability to see the product in 3d before purchasing it. I managed to find a few pieces of software, like insight3d, but it couldn't be used in my case I guess. So, are there any similar projects or tips for me? If it would require to write that piece of software - I'd really love to dig into research on this field.

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• How to find patterns (lines, circles,...) from a list of points?

  - by Burkhard

  I have a list of points. Each point being an x and y coordinate (both of which are integers). Now I'm trying to find known patterns, such as lines, arcs or circles, knowing that the points are not perfectly on the pattern. What's the best way to do it? I don't have many clues to get started. Edit: the points are ordered. The user is drawing something and the program should detect the best patterns. For instance, if a triangle is drawn, it should detect three lines.

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• Why is Dictionary.First() so slow?

  - by Rotsor

  Not a real question because I already found out the answer, but still interesting thing. I always thought that hash table is the fastest associative container if you hash properly. However, the following code is terribly slow. It executes only about 1 million iterations and takes more than 2 minutes of time on a Core 2 CPU. The code does the following: it maintains the collection todo of items it needs to process. At each iteration it takes an item from this collection (doesn't matter which item), deletes it, processes it if it wasn't processed (possibly adding more items to process), and repeats this until there are no items to process. The culprit seems to be the Dictionary.Keys.First() operation. The question is why is it slow? Stopwatch watch = new Stopwatch(); watch.Start(); HashSet<int> processed = new HashSet<int>(); Dictionary<int, int> todo = new Dictionary<int, int>(); todo.Add(1, 1); int iterations = 0; int limit = 500000; while (todo.Count > 0) { iterations++; var key = todo.Keys.First(); var value = todo[key]; todo.Remove(key); if (!processed.Contains(key)) { processed.Add(key); // process item here if (key < limit) { todo[key + 13] = value + 1; todo[key + 7] = value + 1; } // doesn't matter much how } } Console.WriteLine("Iterations: {0}; Time: {1}.", iterations, watch.Elapsed); This results in: Iterations: 923007; Time: 00:02:09.8414388. Simply changing Dictionary to SortedDictionary yields: Iterations: 499976; Time: 00:00:00.4451514. 300 times faster while having only 2 times less iterations. The same happens in java. Used HashMap instead of Dictionary and keySet().iterator().next() instead of Keys.First().

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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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• Problems with dynamic programming

  - by xan

  I've got difficulties with understanding dynamic programming, so I decided to solve some problems. I know basic dynamic algorithms like longest common subsequence, knapsack problem, but I know them because I read them, but I can't come up with something on my own :-( For example we have subsequence of natural numbers. Every number we can take with plus or minus. At the end we take absolute value of this sum. For every subsequence find the lowest possible result. in1: 10 3 5 4; out1: 2 in2: 4 11 5 5 5; out2: 0 in3: 10 50 60 65 90 100; out3: 5 explanation for 3rd: 5 = |10+50+60+65-90-100| what it worse my friend told me that it is simple knapsack problem, but I can't see any knapsack here. Is dynamic programming something difficult or only I have big problems with it?

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• Comparing the "array" with "single direction linked list", what are the pros and cons?

  - by user297850

  Comparing the "array" with "single direction linked list", what are the pros and cons?

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• User submitted content filtering

  - by Jim

  Hey all, Does anyone have any ideas on what could be used as a way to filter untrustworthy user submitted content? Take Yelp for instance, they would need to prevent competitors writing business reviews on their competitors. They would need to prevent business owners favourably reviewing their own business, or forcing friends/family to do so. They would need to prevent poor quality reviews from affecting a businesses rating and so on. I can't think what they might use to do this: Prevent multiple users from the same IP reviewing certain things Prevent business owners reviewing their own business (maybe even other businesses in the same categories as their own?) Somehow determine what a review is about and what the actual intentions behind it are Other than the first and second points, I can't think of any clever/easy way to filter potentially harmful reviews from being made available, other than a human doing it. Obviously for a site the size of Yelp this wouldn't be feasible, so what parameters could they take into consideration? Even with human intervention, how would anyone know it was the owners best buddy writing a fake review without knowing the people? I'm using this as an example in a larger study on the subject of filtering user content automatically. Does anyone have any ideas how these systems may work and what they take into consideration? Thanks!

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• finding long repeated substrings in a massive string

  - by Will

  I naively imagined that I could build a suffix trie where I keep a visit-count for each node, and then the deepest nodes with counts greater than one are the result set I'm looking for. I have a really really long string (hundreds of megabytes). I have about 1 GB of RAM. This is why building a suffix trie with counting data is too inefficient space-wise to work for me. To quote Wikipedia's Suffix tree: storing a string's suffix tree typically requires significantly more space than storing the string itself. The large amount of information in each edge and node makes the suffix tree very expensive, consuming about ten to twenty times the memory size of the source text in good implementations. The suffix array reduces this requirement to a factor of four, and researchers have continued to find smaller indexing structures. And that was wikipedia's comments on the tree, not trie. How can I find long repeated sequences in such a large amount of data, and in a reasonable amount of time (e.g. less than an hour on a modern desktop machine)? (Some wikipedia links to avoid people posting them as the 'answer': Algorithms on strings and especially Longest repeated substring problem ;-) )

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• How to find the number of inversions in an array ?

  - by Michael

  This is an phone interview question: "Find the number of inversions in an array". I guess they mean O(N*log N) solution since O(N^2) is trivial. I guess it cannot be better than O(N*log N) since sorting is O(N*log N) I have checked a similar question from SO and can summarize the answers as follows: Calculate half the distance the elements should be moved to sort the array : copy the array and sort the copy. For each element of the original array a[i] find it's position j in the sorted copy (binary search) and sum abs(i - j)/2. Modify merge sort : modify merge to count inversions between two sorted arrays (it takes O(N)) and run merge sort with the modified merge. Does it make sense ? Are there other (maybe simpler) solution ? Isn't it too hard for a phone interview ?

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• Using MySQL as a job queue

  - by user237815

  I'd like to use MySQL as a job queue. Multiple machines will be producing and consuming jobs. Jobs need to be scheduled; some may run every hour, some every day, etc. It seems fairly straightforward: for each job, have a "nextFireTime" column, and have worker machines search for the job with the nextFireTime, change the status of the record to "inProcess", and then update the nextFireTime when the job ends. The problem comes in when a worker dies silently. It won't be able to update the nextFireTime or set the status back to "idle". Unfortunately, jobs can be long-running, so a reaper thread that looks for jobs that have been inProcess too long isn't an option. There's no timeout value that would work. Can anyone suggest a design pattern that would properly handle unreliable worker machines?

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• List circular group membership from active directory

  - by KAPes

  We have 40K+ groups in our active directory and we are increasingly facing problem of circular nested groups which are creating problems for some applications. Does anyone know how to list down the full route through which a circular group membership exists ? e.g. G1 --> G2 --> G3 --> G4 --> G1 How do I list it down.

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• Minimize the sequence by putting appropriate operations ' DP'

  - by Vikas

  Given a sequence,say, 222 We have to put a '+' or '* ' between each adjacent pair. '* ' has higher precedence over '+' We have to o/p the string whose evaluation leads to minimum value. O/p must be lexicographically smallest if there are more than one. inp:222 o/p: 2*2+2 Explaination: 2+2+2=6 2+2*2=6 2*2+2=6 of this 3rd is lexicographically smallest. I was wondering how to construct a DP solution for this.

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• How to reduce duplicate web pages when rolling my own search engine?

  - by user198729

  One articles can be posted on many sites the same article on a specific website can be visited by several different urls. How do I reduce duplicated stuff in the above occasions?

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• How do I find the next multiple of 10 of any integer?

  - by Tommy

  Dynamic integer will be any number from 0 to 150. i.e. - number returns 41, need to return 50. If number is 10 need to return 10. Number is 1 need to return 10. Was thinking I could use the ceiling function if I modify the integer as a decimal...? then use ceiling function, and put back to decimal? Only thing is would also have to know if the number is 1, 2 or 3 digits (i.e. - 7 vs 94 vs 136) Is there a better way to achieve this? Thank You,

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• which is time consuming construct in following program?

  - by user388338

  while submitting a solution for practise problem 6(odd) i got TLE error but while using using print and scanf in place cin and cout my sol was submitted successfully with 0.77s time..i want to know how can i make it more efficient link to problem is codechef problem 6 #include<iostream> #include<cstdio> using namespace std; int main() {int n,N; scanf("%d",&n); for(int l=0;l<n;l++) { scanf("%d",&N); int i=0,x; if(N<=0) continue; for(;N>=(x=(2<<i));i++); printf("%d",x/2); cout<<"\n"; } }

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• Efficient way to get highly correlated pairs from large data set in Python or R

  - by Akavall

  I have a large data set (Let's say 10,000 variables with about 1000 elements each), we can think of it as 2D list, something like: [[variable_1], [variable_2], ............ [variable_n] ] I want to extract highly correlated variable pairs from that data. I want "highly correlated" to be a parameter that I can choose. I don't need all pairs to be extracted, and I don't necessarily want the most correlated pairs. As long as there is an efficient method that gets me highly correlated pairs I am happy. Also, it would be nice if a variable does not show up in more than one pair. Although this might not be crucial. Of course, there is a brute force way to finding such pairs, but it is too slow for me. I've googled around for a bit and found some theoretical work on this issue, but I wasn't able for find a package that could do what I am looking for. I mostly work in python, so a package in python would be most helpful, but if there exists a package in R that does what I am looking for it will be great. Does anyone know of a package that does the above in Python or R? Or any other ideas? Thank You in Advance

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