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  • Diagonal of polygon is inside or outside?

    - by Himadri
    I have three consecutive points of polygon, say p1,p2,p3. Now I wanted to know whether the orthogonal between p1 and p3 is inside the polygon or outside the polygon. I am doing it by taking three vectors v1,v2 and v3. And the point before the point p1 in polygon say p0. v1 = (p0 - p1) v2 = (p2 - p1) v3 = (p3 - p1) With reference to this question, I am using the method shown in the accepted answer of that question. It is only for counterclockwise. What if my points are clockwise. I am also knowing my whole polygon is clockwise or counterclockwise. And accordingly I select the vectors v1 and v2. But still I am getting some problem. I am showing one case where I am getting problem. This polygon is counterclockwise. and It is starting from the origin of v1 and v2.

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  • CODE1 at SPOJ - cannot solve it

    - by VaioIsBorn
    I am trying to solve the problem Secret Code on SPOJ, and it's obviously a math problem. The full problem For those who are lazy to go and read, it's like this: a0, a1, a2, ..., an - sequence of N numbers B - a Complex Number (has both real and imaginary components) X = a0 + a1*B + a2*(B^2) + a3*(B^3) + ... + an*(B^n) So if you are given B and X, you should find a0, a1, ..an. I don't know how or where to start, because not even N is known, just X and B. The problem is not as easy as expressing a number in a base B, because B is a complex number. How can it be solved?

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  • Find three numbers appeared only once

    - by shilk
    In a sequence of length n, where n=2k+3, that is there are k unique numbers appeared twice and three numbers appeared only once. The question is: how to find the three unique numbers that appeared only once? for example, in sequence 1 1 2 6 3 6 5 7 7 the three unique numbers are 2 3 5. Note: 3<=n<1e6 and the number will range from 1 to 2e9 Memory limits: 1000KB , this implies that we can't store the whole sequence. Method I have tried(Memory limit exceed): I initialize a tree, and when read in one number I try to remove it from the tree, if the remove returns false(not found), I add it to the tree. Finally, the tree has the three numbers. It works, but is Memory limit exceed. I know how to find one or two such number(s) using bit manipulation. So I wonder if we can find three using the same method(or some method similar)? Method to find one/two number(s) appeared only once: If there is one number appeared only once, we can apply XOR to the sequence to find it. If there are two, we can first apply XOR to the sequence, then separate the sequence into 2 parts by one bit of the result that is 1, and again apply XOR to the 2 parts, and we will find the answer.

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  • CODE1 Spoj - cannot solve it

    - by VaioIsBorn
    I am trying to solve the problem Secret Code and it's obviously math problem. The full problem For those who are lazy to go and read, it's like this: a0,a1,a2,...,an - sequence of N numbers B - some number known to us X = a0 + a1*B + a2*(B^2) + a3*(B^3) + ... + an*(B^n) So if you are given B and X, you should find a0,a1,..an. I don't know how or where to start, because not even N is known, just X and B. Can you help me ?

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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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  • red black tree balancing?

    - by Anirudh Kaki
    i am working to generate tango tree, where i need to check whether every sub tree in tango is balanced or not. if its not balanced i need to make it balance? I trying so hard to make entire RB-tree balance but i not getting any proper logic so can any one help me out?? here i am adding code to check how to find my tree is balanced are not but when its not balanced how can i make it balance. static boolean verifyProperty5(rbnode n) { int left = 0, right = 0; if (n != null) { bh++; left = blackHeight(n.left, 0); right = blackHeight(n.right, 0); } if (left == right) { System.out.println("black height is :: " + bh); return true; } else { System.out.println("in balance"); return false; } } public static int blackHeight(rbnode root, int len) { bh = 0; blackHeight(root, path1, len); return bh; } private static void blackHeight(rbnode root, int path1[], int len) { if (root == null) return; if (root.color == "black"){ root.black_count = root.parent.black_count+1; } else{ root.black_count = root.parent.black_count; } if ((root.left == null) && (root.right == null)) { bh = root.black_count; } blackHeight(root.left, path1, len); blackHeight(root.right, path1, len); }

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  • How Can I Improve This Algorithm (LCS)

    - by superguay
    (define (lcs lst1 lst2) (define (except-last-pair list) (if (pair? (cdr list)) (cons (car list) (except-last-pair (cdr list))) '())) (define (car-last-pair list) (if (pair? (cdr list)) (car-last-pair (cdr list)) (car list))) (if (or (null? lst1) (null? lst2)) null (if (= (car-last-pair lst1) (car-last-pair lst2)) (append (lcs (except-last-pair lst1) (except-last-pair lst2)) (cons (car-last-pair lst1) '())) **(if (> (length (lcs lst1 (except-last-pair lst2))) (length (lcs lst2 (except-last-pair lst1)))) (lcs lst1 (except-last-pair lst2)) (lcs lst2 (except-last-pair lst1)))))) I dont want it to run over and over.. Regards, Superguay

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  • Zoom image to pixel level

    - by zaf
    For an art project, one of the things I'll be doing is zooming in on an image to a particular pixel. I've been rubbing my chin and would love some advice on how to proceed. Here are the input parameters: Screen: sw - screen width sh - screen height Image: iw - image width ih - image height Pixel: px - x position of pixel in image py - y position of pixel in image Zoom: zf - zoom factor (0.0 to 1.0) Background colour: bc - background colour to use when screen and image aspect ratios are different Outputs: The zoomed image (no anti-aliasing) The screen position/dimensions of the pixel we are zooming to. When zf is 0 the image must fit the screen with correct aspect ratio. When zf is 1 the selected pixel fits the screen with correct aspect ratio. One idea I had was to use something like povray and move the camera towards a big image texture or some library (e.g. pygame) to do the zooming. Anyone think of something more clever with simple pseudo code? To keep it more simple you can make the image and screen have the same aspect ratio. I can live with that. I'll update with more info as its required.

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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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  • 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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  • Easiest way of checking if a string consists of unique characters?

    - by serg555
    I need to check in Java if a word consists of unique letters (case insensitive). As straight solution is boring, I came up with: For every char in a string check if indexOf(char) == lastIndexOf(char). Add all chars to HashSet and check if set size == string length. Convert a string to a char array, sort it alphabetically, loop through array elements and check if c[i] == c[i+1]. Currently I like #2 the most, seems like the easiest way. Any other interesting solutions?

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  • What is the most efficient/elegant way to parse a flat table into a tree?

    - by Tomalak
    Assume you have a flat table that stores an ordered tree hierarchy: Id Name ParentId Order 1 'Node 1' 0 10 2 'Node 1.1' 1 10 3 'Node 2' 0 20 4 'Node 1.1.1' 2 10 5 'Node 2.1' 3 10 6 'Node 1.2' 1 20 What minimalistic approach would you use to output that to HTML (or text, for that matter) as a correctly ordered, correctly intended tree? Assume further you only have basic data structures (arrays and hashmaps), no fancy objects with parent/children references, no ORM, no framework, just your two hands. The table is represented as a result set, which can be accessed randomly. Pseudo code or plain English is okay, this is purely a conceptional question. Bonus question: Is there a fundamentally better way to store a tree structure like this in a RDBMS? EDITS AND ADDITIONS To answer one commenter's (Mark Bessey's) question: A root node is not necessary, because it is never going to be displayed anyway. ParentId = 0 is the convention to express "these are top level". The Order column defines how nodes with the same parent are going to be sorted. The "result set" I spoke of can be pictured as an array of hashmaps (to stay in that terminology). For my example was meant to be already there. Some answers go the extra mile and construct it first, but thats okay. The tree can be arbitrarily deep. Each node can have N children. I did not exactly have a "millions of entries" tree in mind, though. Don't mistake my choice of node naming ('Node 1.1.1') for something to rely on. The nodes could equally well be called 'Frank' or 'Bob', no naming structure is implied, this was merely to make it readable. I have posted my own solution so you guys can pull it to pieces.

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  • compare function for upper_bound / lower_bound

    - by Martin Beckett
    I want to find the first item in a sorted vector that has a field less than some value x. I need to supply a compare function that compares 'x' with the internal value in MyClass but I can't work out the function declaration. Can't I simply overload '<' but how do I do this when the args are '&MyClass' and 'float' ? float x; std::vector< MyClass >::iterator last = std::upper_bound(myClass.begin(),myClass.end(),x);

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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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  • 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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  • Choice of programming language for learning data structures and algorithms

    - by bguiz
    Which programming language would you recommend to learn about data structures and algorithms in? Considering the follwing: Personal experience Language features (pointers, OO, etc) Suitability for learning DS & A concepts I ask because there are some books out there that are programming language-agnostic (written from a Mathematical perspective, and use pseudocode). If I learn from one of these I would like to work out the algorithms in a chosen language. Then, there are other books which introduce DS & A concepts with examples in a particular programming laguage - and I would follow these examples as well. Either way, I have to choose a language, and I would like to stick to one throughout. Which one best fits the bill.

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  • Finding a small image in a bigger one

    - by tur1ng
    Given an image with a large dimension ( 1.000 x 1.000). What is a good approach to find a small image (e.g. 50 x 50) in the big one? The smaller image can be rotated and differ in the size, but only with a 1:1 ratio. It's not related to any programming language - I'm just interested in pattern recognition. Thank you.

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  • How to check if a integer is sum of given integers?

    - by p3trix
    Lets say I have a integer result and an array of integers, lets say [a,b,c] (not a fixed length). I need to detect if result=a*i +b*j + c*k, with i,j,k=0. I prefer a solution in C/C# if it is possible. PS The problem is from a reservation system, a trip can be sold if its durations is a combination of given durations. Thanks!

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  • Texture coordintes for a polygon and a square texture

    - by user146780
    basically I have a texture. I also have a lets say octagon (or any polygon). I find that octagon's bounding box. Let's say my texture is the size of the octagon's bounding box. How could I figure out the texture coordinates so that the texture maps to it. To clarify, lets say you had a square of tin foil and cut the octagon out you'd be left with a tin foil textured polygon.I'm just not sure how to figure it out for an arbitrary polygon. Thanks

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  • Grouping php array items based on user and created time

    - by Jim
    This is an array of objects showing a user uploading photos: Array ( [12] => stdClass Object ( [type] => photo [created] => 2010-05-14 23:36:41 [user] => stdClass Object ( [id] => 760 [username] => mrsmith ) [photo] => stdClass Object ( [id] => 4181 ) ) [44] => stdClass Object ( [type] => photo [created] => 2010-05-14 23:37:15 [user] => stdClass Object ( [id] => 760 [username] => mrsmith ) [photo] => stdClass Object ( [id] => 4180 ) ) ) However instead of showing: mr smith uploaded one photo mr smith uploaded one photo I'd like to display: mr smith uploaded two photos by grouping similar items, grouping by user ID and them having added them within, let's say 15 minutes of each other. So I'd like to get the array in this sort of shape: Array ( [12] => stdClass Object ( [type] => photo [created] => 2010-05-14 23:36:41 [user] => stdClass Object ( [id] => 760 [username] => mrsmith ) [photos] => Array ( [0] => stdClass Object ( [id] => 4181 ) [1] => stdClass Object ( [id] => 4180 ) ) ) ) preserving the first item of the group and it's created time, and supplementing it with any other groupable photos and then unsetting any items that were grouped (so the final array doesn't have key 44 anymore as it was grouped in with 12). The array contains other actions than just photos, hence the original keys of 12 and 44. I just can't figure out a way to do this efficiently. I used to use MySQL and PHP to do this but am trying to just use pure PHP for caching reasons. Can anyone shed any insights? I thought about going through each item and seeing if I can group it with the previous one in the array but the previous one might not necessarily be relevant or even a photo. I've got total brain freeze :(

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  • Test if single linked list is circular by traversing it only once

    - by user1589754
    I am a fresher and I was asked this question in a recent interview I gave. The question was --- By traversing each element of linked list just once find if the single linked list is circular at any point. To this I answered that we will store reference of each node while traversing the list in another linked list and for every node in the list being tested we will find if the reference exists in the list I am storing the references. The interviewer said that he needs a more optimized way to solve this problem. Can anyone please tell me what would be a more optimized method to solve this problem.

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