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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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• total number of magic square from 9 numbers

  - by Peeyush

  9 numbers need to be arranged in a magic number square. A magic number square is a square of numbers that is arranged such that every row and column has the same sum.(condition for diagonal has been relaxed) For example: 1 2 3 3 2 1 2 2 2 How do we calculate total number of distinct magic square from 9 numbers. Two magic number squares are distinct if they differ in value at one or more positions. For example, there is only one magic number square that can be made of 9 instances of the same number. e.g. for these 9 numbers { 4, 4, 4, 4, 4, 4, 4, 4, 4 }, answer should be 1. Also the complexity should be optimal. Do we need to iterate through all the permutations , discarding if a[0]+a[1]+a[2] %3!=0 such combinations ? moreover how do we remove duplicate magic square?

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• Given 4 objects, how to figure out whether exactly 2 have a certain property

  - by Cocorico

  Hi guys! I have another question on how to make most elegant solution to this problem, since I cannot afford to go to computer school right so my actual "pure programming" CS knowledge is not perfect or great. This is basically an algorhythm problem (someone please correct me if I am using that wrong, since I don't want to keep saying them and embarass myself) I have 4 objects. Each of them has an species property that can either be a dog, cat, pig or monkey. So a sample situation could be: object1.species=pig object2.species=cat object3.species=pig object4.species=dog Now, if I want to figure out if all 4 are the same species, I know I could just say: if ( (object1.species==object2.species) && (object2.species==object3.species) && (object3.species==object4.species) ) { // They are all the same animal (don't care WHICH animal they are) } But that isn't so elegant right? And if I suddenly want to know if EXACTLY 3 or 2 of them are the same species (don't care WHICH species it is though), suddenly I'm in spaghetti code. I am using Objective C although I don't know if that matters really, since the most elegant solution to this is I assume the same in all languages conceptually? Anyone got good idea? Thanks!!

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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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• Chain call in clojure?

  - by Konrad Garus

  I'm trying to implement sieve of Eratosthenes in Clojure. One approach I would like to test is this: Get range (2 3 4 5 6 ... N) For 2 <= i <= N Pass my range through filter that removes multiplies of i For i+1th iteration, use result of the previous filtering I know I could do it with loop/recur, but this is causing stack overflow errors (for some reason tail call optimization is not applied). How can I do it iteratively? I mean invoking N calls to the same routine, passing result of ith iteration to i+1th.

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• Recommend an algorithms exercise book?

  - by Parappa

  I have a little book called Problems on Algorithms by Ian Parberry which is chock full of exercises related to the study of algorithms. Can anybody recommend similar books? What I am not looking for are recommendations of good books related to algorithms or the theory of computation. Introduction to Algorithms is a good one, and of course there's the Knuth stuff. Ideally I want to know of any books that are light on instructional material and heavy on sample problems. In a nutshell, exercise books. Preferably dedicated to algorithms rather than general logic or other math problems. By the way, the Parberry book does not seem to be in print, but it is available as a PDF dowload.

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• Fastest primality test

  - by Grigory Javadyan

  Hi. Could you suggest a fast, deterministic method that is usable in practice, for testing if a large number is prime or not? Also, I would like to know how to use non-deterministic primality tests correctly. For example, if I'm using such a method, I can be sure that a number is not prime if the output is "no", but what about the other case, when the output is "probably"? Do I have to test for primality manually in this case? Thanks in advance.

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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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• 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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• nth smallest number among two databases of size n each using divide and conquer

  - by urfriend

  we have two databases of size n containing numbers without repeats. So, in total we have 2n elements. They can be accessed through a query to one database at a time. The query is such that you give it a k and it returns kth smallest entry in that database. we need to find nth smallest entry among all the 2n elements in O(logn) queries. the idea is to use divide and conquer but i need some help thinking through this. thanks!

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• Efficient data structure design

  - by Sway

  Hi there, I need to match a series of user inputed words against a large dictionary of words (to ensure the entered value exists). So if the user entered: "orange" it should match an entry "orange' in the dictionary. Now the catch is that the user can also enter a wildcard or series of wildcard characters like say "or__ge" which would also match "orange" The key requirements are: * this should be as fast as possible. * use the smallest amount of memory to achieve it. If the size of the word list was small I could use a string containing all the words and use regular expressions. however given that the word list could contain potentially hundreds of thousands of enteries I'm assuming this wouldn't work. So is some sort of 'tree' be the way to go for this...? Any thoughts or suggestions on this would be totally appreciated! Thanks in advance, Matt

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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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• 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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• Is it possible to create thread-safe collections without locks?

  - by Andrey

  This is pure just for interest question, any sort of questions are welcome. So is it possible to create thread-safe collections without any locks? By locks I mean any thread synchronization mechanisms, including Mutex, Semaphore, and even Interlocked, all of them. Is it possible at user level, without calling system functions? Ok, may be implementation is not effective, i am interested in theoretical possibility. If not what is the minimum means to do it? EDIT: Why immutable collections don't work. This of class Stack with methods Add that returns another Stack. Now here is program: Stack stack = new ...; ThreadedMethod() { loop { //Do the loop stack = stack.Add(element); } } this expression stack = stack.Add(element) is not atomic, and you can overwrite new stack from other thread. Thanks, Andrey

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• Mapping Hilbert values to 3D points

  - by Alexander Gladysh

  I have a set of Hilbert values (length from the start of the Hilbert curve to the given point). What is the best way to convert these values to 3D points? Original Hilbert curve was not in 3D, so I guess I have to pick by myself the Hilbert curve rank I need. I do have total curve length though (that is, the maximum value in the set). Perhaps there is an existing implementation? Some library that would allow me to work with Hilbert curve / values? Language does not matter much.

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• Could a truly random number be generated using pings to psuedo-randomly selected IP addresses?

  - by _ande_turner_

  The question posed came about during a 2nd Year Comp Science lecture while discussing the impossibility of generating numbers in a deterministic computational device. This was the only suggestion which didn't depend on non-commodity-class hardware. Subsequently nobody would put their reputation on the line to argue definitively for or against it. Anyone care to make a stand for or against. If so, how about a mention as to a possible implementation?

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• Project euler problem 45

  - by Peter

  Hi, I'm not yet a skilled programmer but I thought this was an interesting problem and I thought I'd give it a go. Triangle, pentagonal, and hexagonal numbers are generated by the following formulae: Triangle T_(n)=n(n+1)/2 1, 3, 6, 10, 15, ... Pentagonal P_(n)=n(3n-1)/2 1, 5, 12, 22, 35, ... Hexagonal H_(n)=n(2n-1) 1, 6, 15, 28, 45, ... It can be verified that T_(285) = P_(165) = H_(143) = 40755. Find the next triangle number that is also pentagonal and hexagonal. Is the task description. I know that Hexagonal numbers are a subset of triangle numbers which means that you only have to find a number where Hn=Pn. But I can't seem to get my code to work. I only know java language which is why I'm having trouble finding a solution on the net womewhere. Anyway hope someone can help. Here's my code public class NextNumber { public NextNumber() { next(); } public void next() { int n = 144; int i = 165; int p = i * (3 * i - 1) / 2; int h = n * (2 * n - 1); while(p!=h) { n++; h = n * (2 * n - 1); if (h == p) { System.out.println("the next triangular number is" + h); } else { while (h > p) { i++; p = i * (3 * i - 1) / 2; } if (h == p) { System.out.println("the next triangular number is" + h); break; } else if (p > h) { System.out.println("bummer"); } } } } } I realize it's probably a very slow and ineffecient code but that doesn't concern me much at this point I only care about finding the next number even if it would take my computer years :) . Peter

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• mod,prime -> inverse possible

  - by Piet

  Hi all. I was wondering if one can do the following: We have: X is a product of N-primes, thus I assume unique. C is a constant. We can assure that C is a number that is part of the N-primes or not. Whichever will work best. Thus: X mod C = Z We have Z and C and we know that X was a product of N-primes, where N is restricted lets say first 100 primes. Is there anyway we can get back 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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• UVA Online Judge 3n+1 : Right answer is Wrong answer

  - by Samuraisoulification

  Ive been toying with this problem for more than a week now, I have optimized it a lot, I seem to be getting the right answer, since it's the same as when I compare it to other's answers that got accepted, but I keep getting wrong answer. Im not sure what's going on! Anyone have any advice? I think it's a problem with the input or the output, cause Im not exactly sure how this judge thing works. So if anyone could pinpoint the problem, and also give me any advice on my code, Id be very appreciative!!! #include <iostream> #include <cstdlib> #include <stdio.h> #include <vector> using namespace std; class Node{ // node for each number that has teh cycles and number private: int number; int cycles; bool cycleset; // so it knows whether to re-set the cycle public: Node(int num){ number = num; cycles = 0; cycleset = false; } int getnumber(){ return number; } int getcycles(){ return cycles; } void setnumber(int num){ number = num; } void setcycles(int num){ cycles = num; cycleset = true; } bool cycled(){ return cycleset; } }; class Cycler{ private: vector<Node> cycleArray; int biggest; int cycleReal(unsigned int number){ // actually cycles through the number int cycles = 1; if (number != 1) { if (number < 1000000) { // makes sure it's in vector bounds if (!cycleArray[number].cycled()) { // sees if it's been cycled if (number % 2 == 0) { cycles += this->cycleReal((number / 2)); } else { cycles += this->cycleReal((3 * number) + 1); } } else { // if cycled get the number of cycles and don't re-calculate, ends recursion cycles = cycleArray[number].getcycles(); } } else { // continues recursing if it's too big for the vector if (number % 2 == 0) { cycles += this->cycleReal((number / 2)); } else { cycles += this->cycleReal((3 * number) + 1); } } } if(number < 1000000){ // sets cycles table for the number in the vector if (!cycleArray[number].cycled()) { cycleArray[number].setcycles(cycles); } } return cycles; } public: Cycler(){ biggest = 0; for(int i = 0; i < 1000000; i++){ // initialize the vector, set the numbers Node temp(i); cycleArray.push_back(temp); } } int cycle(int start, int end){ // cycles thorugh the inputted numbers. int size = 0; for(int i = start; i < end ; i++){ size = this->cycleReal(i); if(size > biggest){ biggest = size; } } int temp = biggest; biggest = 0; return temp; } int getBiggest(){ return biggest; } }; int main() { Cycler testCycler; int i, j; while(cin>>i>>j){ //read in untill \n int biggest = 0; if(i > j){ biggest = testCycler.cycle(j, i); }else{ biggest = testCycler.cycle(i, j); } cout << i << " " << j << " " << biggest << endl; } return 0; }

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• Interpolating in HSV color space

  - by user146780

  I have an HSV color A at 3/10 of a line and HSV color B at 9/10 of a line. I'm making multistep gradients and for example if I wanted to find the color at 6/10ths of a line, how could I interpolate these HSV colors? I'm firmiliar with the technique for rgb but not HSV. I should also add that my HSV's are integers H(0,360) S(0,100) V(0,100). Thanks

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• 3-way quicksort, question

  - by peiska

  I am trying to understand the 3-way radix Quicksort, and i dont understand why the the CUTOFF variable there? and the insertion method? public class Quick3string { private static final int CUTOFF = 15; // cutoff to insertion sort // sort the array a[] of strings public static void sort(String[] a) { // StdRandom.shuffle(a); sort(a, 0, a.length-1, 0); assert isSorted(a); } // return the dth character of s, -1 if d = length of s private static int charAt(String s, int d) { assert d >= 0 && d <= s.length(); if (d == s.length()) return -1; return s.charAt(d); } // 3-way string quicksort a[lo..hi] starting at dth character private static void sort(String[] a, int lo, int hi, int d) { // cutoff to insertion sort for small subarrays if (hi <= lo + CUTOFF) { insertion(a, lo, hi, d); return; } int lt = lo, gt = hi; int v = charAt(a[lo], d); int i = lo + 1; while (i <= gt) { int t = charAt(a[i], d); if (t < v) exch(a, lt++, i++); else if (t > v) exch(a, i, gt--); else i++; } // a[lo..lt-1] < v = a[lt..gt] < a[gt+1..hi]. sort(a, lo, lt-1, d); if (v >= 0) sort(a, lt, gt, d+1); sort(a, gt+1, hi, d); } // sort from a[lo] to a[hi], starting at the dth character private static void insertion(String[] a, int lo, int hi, int d) { for (int i = lo; i <= hi; i++) for (int j = i; j > lo && less(a[j], a[j-1], d); j--) exch(a, j, j-1); } // exchange a[i] and a[j] private static void exch(String[] a, int i, int j) { String temp = a[i]; a[i] = a[j]; a[j] = temp; } // is v less than w, starting at character d private static boolean less(String v, String w, int d) { assert v.substring(0, d).equals(w.substring(0, d)); return v.substring(d).compareTo(w.substring(d)) < 0; } // is the array sorted private static boolean isSorted(String[] a) { for (int i = 1; i < a.length; i++) if (a[i].compareTo(a[i-1]) < 0) return false; return true; } public static void main(String[] args) { // read in the strings from standard input String[] a = StdIn.readAll().split("\\s+"); int N = a.length; // sort the strings sort(a); // print the results for (int i = 0; i < N; i++) StdOut.println(a[i]); } } from http://www.cs.princeton.edu/algs4/51radix/Quick3string.java.html

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• Python script to calculate aded combinations from a dictionary

  - by dayde

  I am trying to write a script that will take a dictionary of items, each containing properties of values from 0 - 10, and add the various elements to select which combination of items achieve the desired totals. I also need the script to do this, using only items that have the same "slot" in common. For example: item_list = { 'item_1': {'slot': 'top', 'prop_a': 2, 'prop_b': 0, 'prop_c': 2, 'prop_d': 1 }, 'item_2': {'slot': 'top', 'prop_a': 5, 'prop_b': 0, 'prop_c': 1, 'prop_d':-1 }, 'item_3': {'slot': 'top', 'prop_a': 2, 'prop_b': 5, 'prop_c': 2, 'prop_d':-2 }, 'item_4': {'slot': 'mid', 'prop_a': 5, 'prop_b': 5, 'prop_c':-5, 'prop_d': 0 }, 'item_5': {'slot': 'mid', 'prop_a':10, 'prop_b': 0, 'prop_c':-5, 'prop_d': 0 }, 'item_6': {'slot': 'mid', 'prop_a':-5, 'prop_b': 2, 'prop_c': 3, 'prop_d': 5 }, 'item_7': {'slot': 'bot', 'prop_a': 1, 'prop_b': 3, 'prop_c':-4, 'prop_d': 4 }, 'item_8': {'slot': 'bot', 'prop_a': 2, 'prop_b': 2, 'prop_c': 0, 'prop_d': 0 }, 'item_9': {'slot': 'bot', 'prop_a': 3, 'prop_b': 1, 'prop_c': 4, 'prop_d':-4 }, } The script would then need to select which combinations from the "item_list" dict that using 1 item per "slot" that would achieve a desired result when added. For example, if the desired result was: 'prop_a': 3, 'prop_b': 3, 'prop_c': 8, 'prop_d': 0, the script would select 'item_2', 'item_6', and 'item_9', along with any other combination that worked. 'item_2': {'slot': 'top', 'prop_a': 5, 'prop_b': 0, 'prop_c': 1, 'prop_d':-1 } 'item_6': {'slot': 'mid', 'prop_a':-5, 'prop_b': 2, 'prop_c': 3, 'prop_d': 5 } 'item_9': {'slot': 'bot', 'prop_a': 3, 'prop_b': 1, 'prop_c': 4, 'prop_d':-4 } 'total': 'prop_a': 3, 'prop_b': 3, 'prop_c': 8, 'prop_d': 0 Any ideas how to accomplish this? It does not need to be in python, or even a thorough script, but just an explanation on how to do this in theory would be enough for me. I have tried working out looping through every combination, but that seems to very quickly get our of hand and unmanageable. The actual script will need to do this for about 1,000 items using 20 different "slots", each with 8 properties. Thanks for the help!

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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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• comparison of sorting algorithms

  - by hash5

  When do we prefer a) bucket sort, and b) radix sort over comparison sorts like bubble sort insertion sort selection sort merge sort quick sort?

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