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  • Reverse factorial

    - by dada
    Well, we all know that if N is given it's easy to calculate N!. But what about reversing? N! is given and you are about to find N - Is that possible ? I'm curious.

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  • determine if intersection of a set with conjunction of two other sets is empty

    - by koen
    For any three given sets A, B and C: is there a way to determine (programmatically) whether there is an element of A that is part of the conjunction of B and C? example: A: all numbers greater than 3 B: all numbers lesser than 7 C: all numbers that equal 5 In this case there is an element in set A, being the number 5, that fits. I'm implementing this as specifications, so this numerical range is just an example. A, B, C could be anything.

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  • Complex LINQ paging algorithm

    - by sharepointmonkey
    We have a list of projects that may or may not have a collection of subprojects. Our report needs to contain all the projects except those that are the parent project of a subproject. I need to page this into pages of, say, 25 rows. But if subprojects appear on that page then ALL the subprojects of that project must appear on the same page. So more than 25 items may appear if necessary. I've got as far as var pagedProjects = db.Projects.Where(x => !x.SubProjects.Any()).Skip( (pageNo -1) * pageSize).Take(pageSize); Obviously, this fails the second part of the requirements. As a further pain in the arse, I need to have a pager control on the report. So I'll need to be able to calculate the total number of pages. I could loop through the whole table of projects but the performance will suffer. Can anybody come up with a paged solution? EDIT - I should probably mention that SubProjects joins back onto Projects via a selfreferencing foreign key so the whole lot comes back as an IQueryable<Project>.

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  • Removing elements from heap

    - by user193138
    I made a heap. I am curious if there's something subtley wrong with my remove function: int Heap::remove() { if (n == 0) exit(1); int temp = arr[0]; arr[0] = arr[--n]; heapDown(0); arr[n] = 0; return temp; } void Heap::heapDown(int i) { int l = left(i); int r = right(i); // comparing parent to left/right child // each has an inner if to handle if the first swap causes a second swap // ie 1 -> 3 -> 5 // 3 5 1 5 1 3 if (l < n && arr[i] < arr[l]) { swap(arr[i], arr[l]); heapDown(l); if (r < n && arr[i] < arr[r]) { swap(arr[i], arr[r]); heapDown(r); } } else if (r < n && arr[i] < arr[r]) { swap(arr[i], arr[r]); heapDown(r); if (l < n && arr[i] < arr[l]) { swap(arr[i], arr[l]); heapDown(l); } } } Here's my output i1i2i3i4i5i6i7 p Active heap: 7 4 6 1 3 2 5 r Removed 7 r Removed 6 p Active heap: 5 3 4 1 2 Here's my teacher's sample output: p Active heap : 7 4 6 1 3 2 5 r Removed 7 r Removed 6 p Active heap : 5 4 2 1 3 s Heapsorted : 1 2 3 4 5 While our outputs are completely different, I do seem to hold maxheap principle of having everything left oriented and for all nodes parent child(in every case I tried). I try to do algs like this from scratch, so maybe I'm just doing something really weird and wrong (I would only consider it "wrong" if it's O(lg n), as removes are intended to be for heaps). Is there anything in particular "wrong" about my remove? Thanks, http://ideone.com/PPh4eQ

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  • A shortest path problem with superheroes and intergalactic journeys

    - by Dman
    You are a super-hero in the year 2222 and you are faced with this great challenge: starting from your home planet Ilop you must try to reach Acinhet or else your planet will be destroyed by evil green little monsters. To do this you are given a map of the universe: there are N planets and M inter-planetary connections ( bidirectional ) that bind these planets. Each connection requires a certain time and a certain amount of fuel in order for you to cover the connection from one planet to another. The total time spent going from one planet to another is obtained by multiplying the time past to cover each connection between all the planets you go through. There are some "key planets", that allow you to refuel if you arrive on those certain "key planets". A "key planet" is the planet with the property that if it disappears the road between at least two planets would be lost.(In the example posted below with the input/output files such a "key planet" is 2 because without it the road to 7 would be lost) When you start your mission you are given the possibility of choosing between K ships each with its own maximum fuel capacity. The goal is to find the SHORTEST TIME CONSUMING path but also choose the ship with the minimum fuel capacity that can cover that shortest path(this means that if more ships can cover the shortest path you choose the one with the minimum fuel capacity). Because the minimum time can be a rather large number (over long long int) you are asked to provide only the last 6 digits of the number. For a better understanding of the task, here is an example of input/output files: INPUT: mission.in 7 8 6 1 4 6 5 9 8 7 10 1 2 7 8 1 4 14 9 1 5 3 1 2 3 1 2 2 7 7 1 3 4 2 2 4 6 4 1 5 6 3 7 On the first line (in order): N M K On the second line :the number for the starting planet and the finishing planet On the third line :K numbers that represent the capacities of the ships you can choose from Then you have M lines, all of them have the same structure: Xi Yi Ti Fi-which means that there is a connection between Xi and Yi and you can cover the distance from Xi to Yi in Ti time and with a Fi fuel consumption. OUTPUT:mission.out 000014 8 1 2 3 4 On the first line:the minimum time and fuel consumption; On the second line :the path Restrictions: 2 = N = 1 000 1 = M = 30 000 1 = K = 10 000 Any suggestions or ideas of how this problem might be solved would be most welcomed.

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  • C++ find largest BST in a binary tree

    - by fonjibe
    what is your approach to have the largest BST in a binary tree? I refer to this post where a very good implementation for finding if a tree is BST or not is bool isBinarySearchTree(BinaryTree * n, int min=std::numeric_limits<int>::min(), int max=std::numeric_limits<int>::max()) { return !n || (min < n->value && n->value < max && isBinarySearchTree(n->l, min, n->value) && isBinarySearchTree(n->r, n->value, max)); } It is quite easy to implement a solution to find whether a tree contains a binary search tree. i think that the following method makes it: bool includeSomeBST(BinaryTree* n) { if(!isBinarySearchTree(n)) { if(!isBinarySearchTree(n->left)) return isBinarySearchTree(n->right); } else return true; else return true; } but what if i want the largest BST? this is my first idea, BinaryTree largestBST(BinaryTree* n) { if(isBinarySearchTree(n)) return n; if(!isBinarySearchTree(n->left)) { if(!isBinarySearchTree(n->right)) if(includeSomeBST(n->right)) return largestBST(n->right); else if(includeSomeBST(n->left)) return largestBST(n->left); else return NULL; else return n->right; } else return n->left; } but its not telling the largest actually. i struggle to make the comparison. how should it take place? thanks

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  • substitution cypher with different alphabet length

    - by seanizer
    I would like to implement a simple substitution cypher to mask private ids in URLs I know how my IDs will look like (combination of upperchase ascii, digits and underscore), and they will be rather long, as they are composed keys. I would like to use a longer alphabet to shorten the resulting codes (I'd like to use upper and lower case ascii letters, digits and nothing else). So my incoming alphabet would be [A-Z0-9_] (37 chars) and my outgoing alphabet would be [A-Za-z0-9] (62 chars) so a compression of almost 50% would be available. let's say my URLs look like this: /my/page/GFZHFFFZFZTFZTF_24_F34 and I want them to look like this instead: /my/page/Ft32zfegZFV5 Obviously both arrays would be shuffled to bring some random order in. This does not have to be secure. if someone figures it out: fine, but I don't want the scheme to be obvious. My desired solution would be to convert the string to an integer representation of radix 37, convert the radix to 62 and use the second alphabet to write out that number. is there any sample code available that does something similar? Integer.parseInt ( http://java.sun.com/javase/6/docs/api/java/lang/Integer.html#parseInt%28java.lang.String,%20int%29 ) has some similar logic, but it is hard-coded to use standard digit behavior Any hints? I am using java to implement this but code or pseudo-code in any other language is of course also helpful

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  • Reduce number of points in line

    - by culebrón
    I'm searching for algorithms to reduce the LOD of polylines, lines (looped or not) of nodes. In simple words, I want to take hi-resolution coastline data and be able to reduce its LOD hundred- or thousandfold to render it in small-scale. I found polygon reduction algorithms (but they require triangles) and Laplacian smoothing, but that doesn't seem exactly what I need.

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  • Generating a URL pattern when provided a set of 5 or so URLs

    - by ryan
    Provided with a set of URLs, I need to generate a pattern, For example: http://www.buy.com/prod/disney-s-star-struck/q/loc/109/213724402.html http://www.buy.com/prod/samsung-f2380-23-widescreen-1080p-lcd-monitor-150-000-1-dc-8ms-1920-x/q/loc/101/211249863.html http://www.buy.com/prod/panasonic-nnh765wf-microwave-oven-countertop-1-6-ft-1250w-panasonic/q/loc/66357/202045865.html http://www.buy.com/prod/escape-by-calvin-klein-for-women-3-4-oz-edp-spray/q/loc/66740/211210860.html http://www.buy.com/prod/v-touch-8gb-mp3-mp4-2-8-touch-screen-2mp-camera-expandable-minisd-w/q/loc/111/211402014.html Pattern is http://www.buy.com/prod/[^~]/q/loc/[^~].html

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  • RSA Factorization problem

    - by dada
    At class we found this programming problem, and currently, we have no idea how to solve it. The positive integer n is given. It is known that n = p * q, where p and q are primes, p<=q and |q-k*p|<10^5 for some given positive integer k. You must find p and q. Input: 35 1 121 1 1000730021 9 Output: 5 * 7 11 * 11 10007 * 100003 It's not a homework, we are just trying to solve some interesting problems. If you have some ideas, please post them here so we can try something, thanks.

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  • STL vector reserve() and copy()

    - by natersoz
    Greetings, I am trying to perform a copy from one vector (vec1) to another vector (vec2) using the following 2 abbreviated lines of code (full test app follows): vec2.reserve( vec1.size() ); copy(vec1.begin(), vec1.end(), vec2.begin()); While the call to vec2 sets the capacity of vector vec2, the copying of data to vec2 seems to not fill in the values from vec1 to vec2. Replacing the copy() function with calls to push_back() works as expected. What am I missing here? Thanks for your help. vectest.cpp test program followed by resulting output follows. Compiler: gcc 3.4.4 on cygwin. Nat /** * vectest.cpp */ #include <iostream> #include <vector> using namespace std; int main() { vector<int> vec1; vector<int> vec2; vec1.push_back(1); vec1.push_back(2); vec1.push_back(3); vec1.push_back(4); vec1.push_back(5); vec1.push_back(6); vec1.push_back(7); vec2.reserve( vec1.size() ); copy(vec1.begin(), vec1.end(), vec2.begin()); cout << "vec1.size() = " << vec1.size() << endl; cout << "vec1.capacity() = " << vec1.capacity() << endl; cout << "vec1: "; for( vector<int>::const_iterator iter = vec1.begin(); iter < vec1.end(); ++iter ) { cout << *iter << " "; } cout << endl; cout << "vec2.size() = " << vec2.size() << endl; cout << "vec2.capacity() = " << vec2.capacity() << endl; cout << "vec2: "; for( vector<int>::const_iterator iter = vec2.begin(); iter < vec2.end(); ++iter ) { cout << *iter << endl; } cout << endl; } output: vec1.size() = 7 vec1.capacity() = 8 vec1: 1 2 3 4 5 6 7 vec2.size() = 0 vec2.capacity() = 7 vec2:

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  • How do I modify an attribute across all rows in a table?

    - by prgmatic
    Hi folks, My apologies for asking such a novice question but, I need help building a script using either PHP or directly in MySQL that can do the following: Take the values of a column in a table (text) Change them into capitalized words (from "this is a title" to "This Is A Title") Replace the old values (uncapitalized) with the new values (capitalized). Thanks for the help and support.

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  • Finding the longest road in a Settlers of Catan game algorithmically

    - by Jay
    I'm writing a Settlers of Catan clone for a class. One of the extra credit features is automatically determining which player has the longest road. I've thought about it, and it seems like some slight variation on depth-first search could work, but I'm having trouble figuring out what to do with cycle detection, how to handle the joining of a player's two initial road networks, and a few other minutiae. How could I do this algorithmically? For those unfamiliar with the game, I'll try to describe the problem concisely and abstractly: I need to find the longest possible path in an undirected cyclic graph.

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  • Brackets matching using BIT

    - by amit.codename13
    edit: I was trying to solve a spoj problem. Here is the link to the problem : http://spoj.pl/problems/BRCKTS I can think of two possible data structures for solving the problem one using segment tree and the other using a BIT. I have already implemented the solution using a segment tree. I have read about BIT but i can't figure out how to do a particular thing with it(which i have mentioned below) I am trying to check if brackets are balanced in a given string containing only ('s or )'s. I am using a BIT(Binary indexed tree) for solving the problem. The procedure i am following is as follows: I am taking an array of size equal to the number of characters in the string. I am assigning -1 for ) and 1 for ( to the corresponding array elements. Brackets are balanced in the string only if the following two conditions are true. The cumulative sum of the whole array is zero. Minimum cumulative sum is non negative. i.e the minimum of cumulative sums of all the prefixes of the array is non-negative. Checking condition 1 using a BIT is trivial. I am facing problem in checking condition 2.

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  • Behavior Tree Implementations

    - by Hamza Yerlikaya
    I am looking for behavior tree implementations in any language, I would like to learn more about how they are implemented and used so can roll my own but I could only find one Owyl, unfortunately, it does not contain examples of how it is used. Any one know any other open source ones that I can browse through the code see some examples of how they are used etc? EDIT: Behavior tree is the name of the data structure.

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  • Re-adjusting a binary heap after removing the minimum element

    - by BeeBand
    After removing the minimum element in a binary heap, i.e. after removing the root, why is the last leaf then assigned to the root and sifted down? Why not take the lesser child of what used to be the root and just keep sifting up all the children? Isn't this the same amount of operations, so why is the "sift down" method preferred?

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  • Need help iteratating over an array, retrieve two possibilites, no repeats, for Poker AI

    - by elguapo-85
    Can't really think of a good way to word this question, nor a good title, and maybe the answer is so ridiculously simple that I am missing it. I am working on a poker AI, and I want to calculate the number of hands that exist which are better then mine, I understand how to that, but want I can't figure out is the best way to iterate over a group of cards. So I am at the flop, I know what my two cards are and there are 3 cards on the board. So there are 47 unknown cards and I want to iterate over all possible combination of those 47 cards assuming that two are passed out, so you can't have two cards of the same rank and suit, and you if you have previously calculated a set you don't want to do it over again, because I will being wasting time, and this will be called many times. If you don't understand want I am asking please tell me and I will clarify more. So I can set something up like this, if that element equals one, it means it is not in my hand and not on the board, 4 for each suit, and 13 for each rank. setOfCards[4][13] If I do a simple set of for loops like this: (pseudocode) //remove cards I know are in play from setOfCards by setting values to zero for(int i = 0; i < 4; i++) for(int j = 0; j < 13; j++) for(int k = 0; k < 4; k++) for(int l = 0; l < 4; l++) //skip if values equal zero card1 = setOfCards[i][j] card2 = setOfCards[k][l] //now compare card1, card2 and set of board cards So this is actually going to repeat many values, for example: card1 = AceOfHearts, card2 = KingOfHearts is the same as card1 = KingOfHearts, card2 = AceOfHearts. It will also alter my calculations. How should I go about avoiding this? Also is there a name for this technique? Thank you.

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  • recursion tree and binary tree cost calculation

    - by Tony
    Hi all, I've got the following recursion: T(n) = T(n/3) + T(2n/3) + O(n) The height of the tree would be log3/2 of 2. Now the recursion tree for this recurrence is not a complete binary tree. It has missing nodes lower down. This makes sense to me, however I don't understand how the following small omega notation relates to the cost of all leaves in the tree. "... the total cost of all leaves would then be Theta (n^log3/2 of 2) which, since log3/2 of 2 is a constant strictly greater then 1, is small omega(n lg n)." Can someone please help me understand how the Theta(n^log3/2 of 2) becomes small omega(n lg n)?

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  • what is the idea behind scaling an image using lanczos?

    - by banister
    Hi, I'm interested in image scaling algorithms and have implemented the bilinear and bicubic methods. However, I have heard of the lanczos and other more sophisticated methods for even higher quality image scaling and I am very curious how they work. Could someone here explain the basic idea behind scaling an image using lanczos (both upscaling and downscaling) and why it results in higher quality? I do have a background in fourier analysis and have done some signal processing stuff in the past, but not with relation to image processing, so don't be afraid to use terms like "frequency response" and such in your answer :) EDIT: I guess what i really want to know is the concept and theory behind using a convolution filter for interpolation. (Note: i have already read the wikipedia article on lanczos resampling but it didn't have nearly enough detail for me) thanks alot!

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  • Find subset with K elements that are closest to eachother

    - by Nima
    Given an array of integers size N, how can you efficiently find a subset of size K with elements that are closest to each other? Let the closeness for a subset (x1,x2,x3,..xk) be defined as: 2 <= N <= 10^5 2 <= K <= N constraints: Array may contain duplicates and is not guaranteed to be sorted. My brute force solution is very slow for large N, and it doesn't check if there's more than 1 solution: N = input() K = input() assert 2 <= N <= 10**5 assert 2 <= K <= N a = [] for i in xrange(0, N): a.append(input()) a.sort() minimum = sys.maxint startindex = 0 for i in xrange(0,N-K+1): last = i + K tmp = 0 for j in xrange(i, last): for l in xrange(j+1, last): tmp += abs(a[j]-a[l]) if(tmp > minimum): break if(tmp < minimum): minimum = tmp startindex = i #end index = startindex + K? Examples: N = 7 K = 3 array = [10,100,300,200,1000,20,30] result = [10,20,30] N = 10 K = 4 array = [1,2,3,4,10,20,30,40,100,200] result = [1,2,3,4]

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  • PHP script to draw a spiral?

    - by Vacilando
    Does anybody have a PHP (or other language) script for drawing a spiral. A simple (Archimedean spiral) would be just fine. Of course the principle is simple but coding it in SVG or GD would take some time, so I wonder if somebody has one ready :-)

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  • return first non repeating character in a string

    - by Amm Sokun
    I had to solve this question in which given a string, i had to return the first non repeating character present in the string. I solved it using hashtable and wrote a method which takes a constant reference to the string and returns the first non repeating character. However, when there is no non repeating character present in the string, i return -1 and in the main program i check as follows char c = firstNonRepeating( word ); if (static_cast<int> (c) == -1) cout<<"no non repeating character present\n"; else cout<<c<<endl; is that the correct way to return -1 when required character is not present?

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