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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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  • Determining the order of a list of numbers (possibly without sorting)

    - by Victor Liu
    I have an array of unique integers (e.g. val[i]), in arbitrary order, and I would like to populate another array (ord[i]) with the the sorted indexes of the integers. In other words, val[ord[i]] is in sorted order for increasing i. Right now, I just fill in ord with 0, ..., N, then sort it based on the value array, but I am wondering if we can be more efficient about it since ord is not populated to begin with. This is more of a question out of curiousity; I don't really care about the extra overhead from having to prepopulate a list and then sort it (it's small, I use insertion sort). This may be a silly question with an obvious answer, but I couldn't find anything online.

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  • A quick way to map unordered list of longs to buffer location ?

    - by alhazen
    I have a large number of points (indexed by long) that are processed by multiple threads and I'm using a buffer to hold the output results in order. As the number of points processed is huge, what would be an efficient way to map the indexes of the points to the corresponding ordered position in the buffer ? Example: long bufferIndex bufferIndex index (if BufferSize = 2) (if BufferSize = 4) ---------------------------------------------- 2938 0 0 2939 1 1 2941 1 3 2940 0 2 Thanks.

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  • Need help with basic optimization problem

    - by ??iu
    I know little of optimization problems, so hopefully this will be didactic for me: rotors = [1, 2, 3, 4...] widgets = ['a', 'b', 'c', 'd' ...] assert len(rotors) == len(widgets) part_values = [ (1, 'a', 34), (1, 'b', 26), (1, 'c', 11), (1, 'd', 8), (2, 'a', 5), (2, 'b', 17), .... ] Given a fixed number of widgets and a fixed number of rotors, how can you get a series of widget-rotor pairs that maximizes the total value where each widget and rotor can only be used once?

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  • Garbage Collection in Java

    - by simion
    On the slides I am revising from it says the following: Live objects can be identified either by maintaining a count of the number of references to each object, or by tracing chains of references from the roots. Reference counting is expensive – it needs action every time a reference changes and it doesn’t spot cyclical structures, but it can reclaim space incrementally. Tracing involves identifying live objects only when you need to reclaim space – moving the cost from general access to the time at which the GC runs, typically only when you are out of memory. I understand the principles of why reference counting is expensive but do not understand what "doesn’t spot cyclical structures, but it can reclaim space incrementally." means. Could anyone help me out a little bit please? Thanks

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  • Generate sample XML from composite hierarchical structure

    - by Jevgenij Nekrasov
    Let's say I have composite hierarchical structure. Each object in the structure has child collection of the same objects. Each object has XPath property, which stores the exact xpath to the element inside XML file. Right now I am trying to create an extension, which can generate XML string from that hierarchical structure, but first I want to make some sort of research what is the most efficient way to do that? ant what is the easiest way?

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  • help implementing algorithm

    - by davit-datuashvili
    http://en.wikipedia.org/wiki/All_nearest_smaller_values this is site of the problem and here is my code but i have some trouble to implement it import java.util.*; public class stack{ public static void main(String[]args){ int x[]=new int[]{ 0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15 }; Stack<Integer> st=new Stack<Integer>(); for (int a:x){ while (!st.empty() && st.pop()>=a){ System.out.println( st.pop()); if (st.empty()){ break; } else{ st.push(a); } } } } } and here is pseudo code from site S = new empty stack data structure for x in the input sequence: while S is nonempty and the top element of S is greater than or equal to x: pop S if S is empty: x has no preceding smaller value else: the nearest smaller value to x is the top element of S push x onto S

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  • Determine coordinates of rotated rectangle

    - by MathieuK
    I'm creating an utility application that should detect and report the coordinates of the corners of a transparent rectangle (alpha=0) within an image. So far, I've set up a system with Javascript + Canvas that displays the image and starts a floodfill-like operation when I click inside the transparent rectangle in the image. It correctly determines the bounding box of the floodfill operation and as such can provide me the correct coordinates. Here's my implementation so-far: http://www.scriptorama.nl/image/ (works in recent Firefox / Safari ). However, the bounding box approach breaks down then the transparent rectangle is rotated (CW or CCW) as the resulting bounding box no longer properly represents the proper width and height. I've tried to come up with a few alternatives to detect to corners, but have not been able to think up a proper solution. So, does anyone have any suggestions on how I might approach this so I can properly detect the coordinates of 4 corners of the rotated rectangle?

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  • help implementing All Nearest Smaller Values algorithm

    - by davit-datuashvili
    http://en.wikipedia.org/wiki/All_nearest_smaller_values this is site of the problem and here is my code but i have some trouble to implement it import java.util.*; public class stack{ public static void main(String[]args){ int x[]=new int[]{ 0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15 }; Stack<Integer> st=new Stack<Integer>(); for (int a:x){ while (!st.empty() && st.pop()>=a){ System.out.println( st.pop()); if (st.empty()){ break; } else{ st.push(a); } } } } } and here is pseudo code from site S = new empty stack data structure for x in the input sequence: while S is nonempty and the top element of S is greater than or equal to x: pop S if S is empty: x has no preceding smaller value else: the nearest smaller value to x is the top element of S push x onto S

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  • Open mail-links with gmail in Chrome 9

    - by moose
    it happens quite often, that I click a link over a persons name, just to see that it launches the default mail client of my system. I thought it would be a normal link, but it was a "mailto:"-link. I would like Chrome to start gmail, not my default email client. For Firefox, I had only to paste this in the URL-Bar: javascript:window.navigator.registerProtocolHandler("mailto","https://mail.google.com/mail/?extsrc=mailto&url=%s","GMail") Unfortunately, it doesn't work in Chrome 9. I have found this tutorial for Ubuntu, but I would like a solution in Chome. If it is only in Chrome, I can sync the settings. (So How do I make mailto: links open gmail in Ubuntu? doesn't fit) http://www.google.com/support/forum/p/Chrome/thread?tid=2aad08042607a4eb&hl=en could be related to my problem, but there is no answer. Gnome: $ gnome-default-applications-properties set Email-Client to gnome-open https://mail.google.com/mail/?extsrc=mailto&url=%s

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  • Linked list Recursion ...

    - by epsilon_G
    hey , I'd like to make a recursive function using C++ I make this class class linklist { private: struct node { int data; node *link; }*p; void linklist::print_num(node* p) { if (p != NULL) { cout << p->data << " "; print_num (p->link); } } in the main program what should I write ...

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  • [C++] std::string manipulation: whitespace, "newline escapes '\'" and comments #

    - by rubenvb
    Kind of looking for affirmation here. I have some hand-written code, which I'm not shy to say I'm proud of, which reads a file, removes leading whitespace, processes newline escapes '\' and removes comments starting with #. It also removes all empty lines (also whitespace-only ones). Any thoughts/recommendations? I could probably replace some std::cout's with std::runtime_errors... but that's not a priority here :) const int RecipeReader::readRecipe() { ifstream is_recipe(s_buffer.c_str()); if (!is_recipe) cout << "unable to open file" << endl; while (getline(is_recipe, s_buffer)) { // whitespace+comment removeLeadingWhitespace(s_buffer); processComment(s_buffer); // newline escapes + append all subsequent lines with '\' processNewlineEscapes(s_buffer, is_recipe); // store the real text line if (!s_buffer.empty()) v_s_recipe.push_back(s_buffer); s_buffer.clear(); } is_recipe.close(); return 0; } void RecipeReader::processNewlineEscapes(string &s_string, ifstream &is_stream) { string s_temp; size_t sz_index = s_string.find_first_of("\\"); while (sz_index <= s_string.length()) { if (getline(is_stream,s_temp)) { removeLeadingWhitespace(s_temp); processComment(s_temp); s_string = s_string.substr(0,sz_index-1) + " " + s_temp; } else cout << "Error: newline escape '\' found at EOF" << endl; sz_index = s_string.find_first_of("\\"); } } void RecipeReader::processComment(string &s_string) { size_t sz_index = s_string.find_first_of("#"); s_string = s_string.substr(0,sz_index); } void RecipeReader::removeLeadingWhitespace(string &s_string) { const size_t sz_length = s_string.size(); size_t sz_index = s_string.find_first_not_of(" \t"); if (sz_index <= sz_length) s_string = s_string.substr(sz_index); else if ((sz_index > sz_length) && (sz_length != 0)) // "empty" lines with only whitespace s_string.clear(); } Some extra info: the first s_buffer passed to the ifstream contains the filename, std::string s_buffer is a class data member, so is std::vector v_s_recipe. Any comment is welcome :)

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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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  • C++ priority queue structure userd ?

    - by John Retallack
    While searching for some functions in C++ STL documentation I read that push and pop for priority queues needs constant time. "Constant (in the priority_queue). Although notice that push_heap operates in logarithmic time." My question is what kind of data structure is used to mantain a priority queue with O(1) for push and pop ?

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  • What is the best way to find the digit at n position in a decimal number?

    - by Elijah
    Background I'm working on a symmetric rounding class and I find that I'm stuck with regards to how to best find the number at position x that I will be rounding. I'm sure there is an efficient mathematical way to find the single digit and return it without having to resort to string parsing. Problem Suppose, I have the following (C#) psuedo-code: var position = 3; var value = 102.43587m; // I want this no ? (that is 5) protected static int FindNDigit(decimal value, int position) { // This snippet is what I am searching for } Also, it is worth noting that if my value is a whole number, I will need to return a zero for the result of FindNDigit. Does anyone have any hints on how I should approach this problem? Is this something that is blaringly obvious that I'm missing?

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  • Generating different randoms valid for a day on different independent devices?

    - by Pentium10
    Let me describe the system. There are several mobile devices, each independent from each other, and they are generating content for the same record id. I want to avoid generating the same content for the same record on different devices, for this I though I would use a random and make it so too cluster the content pool based on these randoms. Suppose you have choices from 1 to 100. Day 1 Device#1 will choose for the record#33 between 1-10 Device#2 will choose for the record#33 between 40-50 Device#3 will choose for the record#33 between 50-60 Device#1 will choose for the record#55 between 40-50 Device#2 will choose for the record#55 between 1-10 Device#3 will choose for the record#55 between 10-20 Device#1 will choose for the record#11 between 1-10 Device#2 will choose for the record#22 between 1-10 Device#3 will choose for the record#99 between 1-10 Day 2 Device#1 will choose for the record#33 between 90-100 Device#2 will choose for the record#33 between 1-10 Device#3 will choose for the record#33 between 50-60 They don't have access to a central server. Data available for each of them: IMEI (unique per mobile) Date of today (same on all devices) Record id (same on all devices) What do you think, how is it possible? ps. tags can be edited

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  • Time complexity of a powerset generating function

    - by Lirik
    I'm trying to figure out the time complexity of a function that I wrote (it generates a power set for a given string): public static HashSet<string> GeneratePowerSet(string input) { HashSet<string> powerSet = new HashSet<string>(); if (string.IsNullOrEmpty(input)) return powerSet; int powSetSize = (int)Math.Pow(2.0, (double)input.Length); // Start at 1 to skip the empty string case for (int i = 1; i < powSetSize; i++) { string str = Convert.ToString(i, 2); string pset = str; for (int k = str.Length; k < input.Length; k++) { pset = "0" + pset; } string set = string.Empty; for (int j = 0; j < pset.Length; j++) { if (pset[j] == '1') { set = string.Concat(set, input[j].ToString()); } } powerSet.Add(set); } return powerSet; } So my attempt is this: let the size of the input string be n in the outer for loop, must iterate 2^n times (because the set size is 2^n). in the inner for loop, we must iterate 2*n times (at worst). 1. So Big-O would be O((2^n)*n) (since we drop the constant 2)... is that correct? And n*(2^n) is worse than n^2. if n = 4 then (4*(2^4)) = 64 (4^2) = 16 if n = 100 then (10*(2^10)) = 10240 (10^2) = 100 2. Is there a faster way to generate a power set, or is this about optimal?

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  • Sort string based upon the count of characters Options

    - by prp
    Sample Data : input : "abcdacdc" Output : "cadb" here we have to sort strings in order of count of characters. If the count is same for characters. maintain the original order of the characters from input string. my approach: i have used array of 26 for maintaining occurrence of all characters and sort it then print it.But while doing so i am not able to maintain order in case if two characters have same count. please suggest any improvement or any other algo.

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  • Find recipes that can be cooked from provided ingridients

    - by skaurus
    Sorry for bad English :( Suppose i can preliminary organize recipes and ingredients data in any way. How can i effectively conduct search of recipes by user-provided ingredients, preferably sorted by max match - so, first going recipes that use maximum of provided ingridients and do not contain any other ingrs, after them recipes that uses less of provided set and still not any other ingrs, after them recipes with minimum additional requirements and so on? All i can think about is represent recipe ingridients like bitmasks, and compare required bitmask with all recipes, but it is obviously a bad way to go. And related things like Levenstein distance i don't see how to use here. I believe it should be quite common task...

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  • Is this linear search implementation actually useful?

    - by Helper Method
    In Matters Computational I found this interesting linear search implementation (it's actually my Java implementation ;-)): public static int linearSearch(int[] a, int key) { int high = a.length - 1; int tmp = a[high]; // put a sentinel at the end of the array a[high] = key; int i = 0; while (a[i] != key) { i++; } // restore original value a[high] = tmp; if (i == high && key != tmp) { return NOT_CONTAINED; } return i; } It basically uses a sentinel, which is the searched for value, so that you always find the value and don't have to check for array boundaries. The last element is stored in a temp variable, and then the sentinel is placed at the last position. When the value is found (remember, it is always found due to the sentinel), the original element is restored and the index is checked if it represents the last index and is unequal to the searched for value. If that's the case, -1 (NOT_CONTAINED) is returned, otherwise the index. While I found this implementation really clever, I wonder if it is actually useful. For small arrays, it seems to be always slower, and for large arrays it only seems to be faster when the value is not found. Any ideas?

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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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