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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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  • generic binary Search in c#

    - by Pro_Zeck
    Below is my Generic Binary Search it works ok with the intgers type array it finds all the elements in it . But the Problem Arises when i use a string array to find any string data. It runs ok for the first index and last index elements but i cant find the middle elements. Stringarray = new string[] { "b", "a", "ab", "abc", "c" }; public static void BinarySearch<T>(T[] array, T searchFor, Comparer<T> comparer) { int high, low, mid; high = array.Length - 1; low = 0; if (array[0].Equals(searchFor)) Console.WriteLine("Value {0} Found At Index {1}",array[0],0); else if (array[high].Equals(searchFor)) Console.WriteLine("Value {0} Found At Index {1}", array[high], high); else { while (low <= high) { mid = (high + low) / 2; if (comparer.Compare(array[mid], searchFor) == 0) { Console.WriteLine("Value {0} Found At Index {1}", array[mid], mid); break; } else { if (comparer.Compare(searchFor, array[mid]) > 0) high = mid + 1; else low = mid + 1; } } if (low > high) { Console.WriteLine("Value Not Found In the Collection"); } } }

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  • Just for fun (C# and C++)...time yourself [closed]

    - by Ted
    Possible Duplicate: What is your solution to the FizzBuzz problem? OK guys this is just for fun, no flamming allowed ! I was reading the following http://www.codinghorror.com/blog/2007/02/why-cant-programmers-program.html and couldn't believe the following sentence... " I've also seen self-proclaimed senior programmers take more than 10-15 minutes to write a solution." For those that can't be bothered to read the article, the background is this: ....I set out to develop questions that can identify this kind of developer and came up with a class of questions I call "FizzBuzz Questions" named after a game children often play (or are made to play) in schools in the UK. An example of a Fizz-Buzz question is the following: Write a program that prints the numbers from 1 to 100. But for multiples of three print "Fizz" instead of the number and for the multiples of five print "Buzz". For numbers which are multiples of both three and five print "FizzBuzz". SO I decided to test myself. I took 5 minutes in C++ and 3mins in c#! So just for fun try it and post your timings + language used! P.S NO UNIT TESTS REQUIRED, NO OUTSOURCING ALLOWED, SWITCH OFF RESHARPER! :-) P.S. If you'd like to post your source then feel free

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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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  • Setting last N bits in an array

    - by Martin
    I'm sure this is fairly simple, however I have a major mental block on it, so I need a little help here! I have an array of 5 integers, the array is already filled with some data. I want to set the last N bits of the array to be random noise. [int][int][int][int][int] set last 40 bits [unchanged][unchanged][unchanged][24 bits of old data followed 8 bits of randomness][all random] This is largely language agnostic, but I'm working in C# so bonus points for answers in C#

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  • DFS Backtracking with java

    - by Cláudio Ribeiro
    I'm having problems with DFS backtracking in an adjacency matrix. Here's my code: (i added the test to the main in case someone wants to test it) public class Graph { private int numVertex; private int numEdges; private boolean[][] adj; public Graph(int numVertex, int numEdges) { this.numVertex = numVertex; this.numEdges = numEdges; this.adj = new boolean[numVertex][numVertex]; } public void addEdge(int start, int end){ adj[start-1][end-1] = true; adj[end-1][start-1] = true; } List<Integer> visited = new ArrayList<Integer>(); public Integer DFS(Graph G, int startVertex){ int i=0; if(pilha.isEmpty()) pilha.push(startVertex); for(i=1; i<G.numVertex; i++){ pilha.push(i); if(G.adj[i-1][startVertex-1] != false){ G.adj[i-1][startVertex-1] = false; G.adj[startVertex-1][i-1] = false; DFS(G,i); break; }else{ visited.add(pilha.pop()); } System.out.println("Stack: " + pilha); } return -1; } Stack<Integer> pilha = new Stack(); public static void main(String[] args) { Graph g = new Graph(6, 9); g.addEdge(1, 2); g.addEdge(1, 5); g.addEdge(2, 4); g.addEdge(2, 5); g.addEdge(2, 6); g.addEdge(3, 4); g.addEdge(3, 5); g.addEdge(4, 5); g.addEdge(6, 4); g.DFS(g, 1); } } I'm trying to solve the euler path problem. the program solves basic graphs but when it needs to backtrack, it just does not do it. I think the problem might be in the stack manipulations or in the recursive dfs call. I've tried a lot of things, but still can't seem to figure out why it does not backtrack. Can somebody help me ?

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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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  • Unit Testing - Algorithm or Sample based ?

    - by ohadsc
    Say I'm trying to test a simple Set class public IntSet : IEnumerable<int> { Add(int i) {...} //IEnumerable implementation... } And suppose I'm trying to test that no duplicate values can exist in the set. My first option is to insert some sample data into the set, and test for duplicates using my knowledge of the data I used, for example: //OPTION 1 void InsertDuplicateValues_OnlyOneInstancePerValueShouldBeInTheSet() { var set = new IntSet(); //3 will be added 3 times var values = new List<int> {1, 2, 3, 3, 3, 4, 5}; foreach (int i in values) set.Add(i); //I know 3 is the only candidate to appear multiple times int counter = 0; foreach (int i in set) if (i == 3) counter++; Assert.AreEqual(1, counter); } My second option is to test for my condition generically: //OPTION 2 void InsertDuplicateValues_OnlyOneInstancePerValueShouldBeInTheSet() { var set = new IntSet(); //The following could even be a list of random numbers with a duplicate var values = new List<int> { 1, 2, 3, 3, 3, 4, 5}; foreach (int i in values) set.Add(i); //I am not using my prior knowledge of the sample data //the following line would work for any data CollectionAssert.AreEquivalent(new HashSet<int>(values), set); } Of course, in this example, I conveniently have a set implementation to check against, as well as code to compare collections (CollectionAssert). But what if I didn't have either ? This is the situation when you are testing your real life custom business logic. Granted, testing for expected conditions generically covers more cases - but it becomes very similar to implementing the logic again (which is both tedious and useless - you can't use the same code to check itself!). Basically I'm asking whether my tests should look like "insert 1, 2, 3 then check something about 3" or "insert 1, 2, 3 and check for something in general" EDIT - To help me understand, please state in your answer if you prefer OPTION 1 or OPTION 2 (or neither, or that it depends on the case, etc )

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  • Enumerating combinations in a distributed manner

    - by Reyzooti
    I have a problem where I must analyse 500C5 combinations (255244687600) of something. Distributing it over a 10 node cluster where each cluster processes roughly 10^6 combinations per second means the job will be complete in about 7hours. The problem I have is distributing the 255244687600 combinations over the 10 nodes. I'd like to present each node with 25524468760, however the algorithms I'm using can only produce the combinations sequentially, I'd like to be able to pass the set of elements and a range of combination indicies eg: [0-10^7) or [10^7,2.0 10^7) etc and have the nodes themselves figure out the combinations. The algorithms I'm using at the moment are from the following: http://home.roadrunner.com/~hinnant/combinations.html A logical question I've considered using a master node, that enumerates each of the combinations and sends work to each of the nodes, however the overhead incurred in iterating the combinations from a single node and communicating back and forth work is enormous, and will subsequently lead to the master node becoming the bottleneck. Are there any good combination iterating algorithms geared up for efficient/optimal distributed enumeration?

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  • Javascript plugins design pattern like jQuery

    - by Marco Demaio
    Could someone write down a very simple basic example in javascript to conceptualize (and hopefully make me understand) how the jQuery plugin design pattern is done and how it works? I'm not interested in how creating plugin for jQuery (so no jQuery code here at all). I'm interested in a simple explanation (maybe with a bit of Javascript code) to explain how it is done the plugin concept. Plz do not reply me to go and read jQuery code, I tried, but I it's too complex, otherwise I would have not post a question here.

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  • Is it possible to compute the minimum of three numbers by using two comparisons at the same time?

    - by Milo Hou
    I've been trying to think up of some way that I could do two comparisons at the same time to find the greatest/least of three numbers. Arithmetic operations on them are considered "free" in this case. That is to say, the classical way of finding the greater of two, and then comparing it to the third number isn't valid in this case because one comparison depends on the result of the other. Is it possible to use two comparisons where this isn't the case? I was thinking maybe comparing the differences of the numbers somehow or their products or something, but came up with nothing. Just to reemphasize, two comparisons are still done, just that neither comparison relies on the result of the other comparison. EDIT: what about: boolA = A^2 + B^2 < C^2 boolB = A > B if boolA then max=C else if boolB then max=A else max=B

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  • Sorting 1 million 8-digit numbers in 1MB of RAM

    - by Favourite Chigozie Onwuemene
    I have a computer with 1M of RAM and no other local storage. I must use it to accept 1 million 8-digit decimal numbers over a TCP connection, sort them, and then send the sorted list out over another TCP connection. The list of numbers may contain duplicates, which I must not discard. The code will be placed in ROM, so I need not subtract the size of my code from the 1M. I already have code to drive the ethernet port and handle TCP/IP connections, and it requires 2k for its state data, including a 1k buffer via which the code will read and write data. Is there a solution to this problem?

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  • What Software Engineering Areas should be stressed upon while Interviewing Candidate for Fulltime So

    - by Rachel
    Hi, This question is somewhat related to other posts which I found on Stackoverflow but not exactly and so am prompted to ask about it. I know we must ask for Data-Structures and Algorithms but what specific data-structures or Algorithms or other CS Concepts should be asked while interviewing Sr. Software Engineering Fulltime Position as compared with Software Engineering Position. Thanks.

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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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  • Big-O for Eight Year Olds?

    - by Jason Baker
    I'm asking more about what this means to my code. I understand the concepts mathematically, I just have a hard time wrapping my head around what they mean conceptually. For example, if one were to perform an O(1) operation on a data structure, I understand that the amount of operations it has to perform won't grow because there are more items. And an O(n) operation would mean that you would perform a set of operations on each element. Could somebody fill in the blanks here? Like what exactly would an O(n^2) operation do? And what the heck does it mean if an operation is O(n log(n))? And does somebody have to smoke crack to write an O(x!)?

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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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  • 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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  • Faster way to compare two sets of points in N-dimensional space?

    - by Amit
    List1 contains a high number (~7^10) of N-dimensional points (N <=10), List2 contains the same or fewer number of N-dimensional points (N <=10). My task is this: I want to check which point in List2 is closest (euclidean distance) to a point in List1 for every point in List1 and subsequently perform some operation on it. I have been doing it the simple- the nested loop way when I didn't have more than 50 points in List1, but with 7^10 points, this obviously takes up a lot of time. What is the fastest way to do this? Any concepts from Computational Geometry might help?

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  • Find a node in a Graph that minimizes the distance between two other nodes

    - by Andrés
    Here is the thing. I have a directed weighted graph G, with V vertices and E edges. Given two nodes in the graph, let's say A, and B, and given the weight of an edge A-B denoted as w(A, B), I need to find a node C so that max(w(A, C), w(B, C)) is minimal among all possibilities. By possibilities I mean all the values C can take. I don't know if it is completely clear, if it's not, I'll try to be more precise. Thanks in advance.

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  • What's the best way to implement one-dimensional collision detection?

    - by cyclotis04
    I'm writing a piece of simulation software, and need an efficient way to test for collisions along a line. The simulation is of a train crossing several switches on a track. When a wheel comes within N inches of the switch, the switch turns on, then turns off when the wheel leaves. Since all wheels are the same size, and all switches are the same size, I can represent them as a single coordinate X along the track. Switch distances and wheel distances don't change in relation to each other, once set. This is a fairly trivial problem when done through brute force by placing the X coordinates in lists, and traversing them, but I need a way to do so efficiently, because it needs to be extremely accurate, even when the train is moving at high speeds. There's a ton of tutorials on 2D collision detection, but I'm not sure the best way to go about this unique 1D scenario.

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  • Number distribution

    - by Carra
    Problem: We have x checkboxes and we want to check y of them evenly. Example 1: select 50 checkboxes of 100 total. [-] [x] [-] [x] ... Example 2: select 33 checkboxes of 100 total. [-] [-] [x] [-] [-] [x] ... Example 3: select 66 checkboxes of 100 total: [-] [x] [x] [-] [x] [x] ... But we're having trouble to come up with a formula to check them in code, especially once you go 11/111 or something similar. Anyone has an idea?

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  • Given a number N, find the number of ways to write it as a sum of two or more consecutive integers

    - by hilal
    Here is the problem (Given a number N, find the number of ways to write it as a sum of two or more consecutive integers) and example 15 = 7+8, 1+2+3+4+5, 4+5+6 I solved with math like that : a + (a + 1) + (a + 2) + (a + 3) + ... + (a + k) = N (k + 1)*a + (1 + 2 + 3 + ... + k) = N (k + 1)a + k(k+1)/2 = N (k + 1)*(2*a + k)/2 = N Then check that if N divisible by (k+1) and (2*a+k) then I can find answer in O(N) time Here is my question how can you solve this by dynamic-programming ? and what is the complexity (O) ? P.S : excuse me, if it is a duplicate question. I searched but I can find

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