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• Finding the shortest path through a digraph that visits all nodes

  - by Boluc Papuccuoglu

  I am trying to find the shortest possible path that visits every node through a graph (a node may be visited more than once, the solution may pick any node as the starting node.). The graph is directed, meaning that being able to travel from node A to node B does not mean one can travel from node B to node A. All distances between nodes are equal. I was able to code a brute force search that found a path of only 27 nodes when I had 27 nodes and each node had a connection to 2 or 1 other node. However, the actual problem that I am trying to solve consists of 256 nodes, with each node connecting to either 4 or 3 other nodes. The brute force algorithm that solved the 27 node graph can produce a 415 node solution (not optimal) within a few seconds, but using the processing power I have at my disposal takes about 6 hours to arrive at a 402 node solution. What approach should I use to arrive at a solution that I can be certain is the optimal one? For example, use an optimizer algorithm to shorten a non-optimal solution? Or somehow adopt a brute force search that discards paths that are not optimal? EDIT: (Copying a comment to an answer here to better clarify the question) To clarify, I am not saying that there is a Hamiltonian path and I need to find it, I am trying to find the shortest path in the 256 node graph that visits each node AT LEAST once. With the 27 node run, I was able to find a Hamiltonian path, which assured me that it was an optimal solution. I want to find a solution for the 256 node graph which is the shortest.

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• How can I permute pairs across a set?

  - by sila

  I am writing a bet settling app in C# and WinForms. I have 6 selections, 4 of them have won. I know that using the following formula from Excel: =FACT(selections)/(FACT(selections-doubles))/FACT(doubles) This is coded into my app and working well: I can work out how many possible doubles (e.g., AB, AC, AD, AE, BC, BD, BE, etc.) need to be resolved. But what I can't figure out is how to do the actual calculation. How can I efficiently code it so that every combination of A, B, C, and D has been calculated? All my efforts thus far on paper have proved to be ugly and verbose: is there an elegant solution to this problem?

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• What is the Big-O time complexity of this algorithm

  - by grebwerd

  I was wondering what the run time of this small program would be? #include <stdio.h> int main(int argc, char* argv[]) { int i; int j; int inputSize; int sum = 0; if(argc == 1) inputSize = 16; else inputSize = atoi(argv[i]); for(i = 1; i <= inputSize; i++){ for(j = i; j < inputSize; j *=2 ){ printf("The value of sum is %d\n",++sum); } } } n S floor(log n - log (n-i)) = ? i =1 and that each summation would be the floor value between log(n) - log(n-i). Would the run time be n log n?

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• How to get better at solving Dynamic programming problems

  - by newbie

  I recently came across this question: "You are given a boolean expression consisting of a string of the symbols 'true', 'false', 'and', 'or', and 'xor'. Count the number of ways to parenthesize the expression such that it will evaluate to true. For example, there is only 1 way to parenthesize 'true and false xor true' such that it evaluates to true." I knew it is a dynamic programming problem so i tried to come up with a solution on my own which is as follows. Suppose we have a expression as A.B.C.....D where '.' represents any of the operations and, or, xor and the capital letters represent true or false. Lets say the number of ways for this expression of size K to produce a true is N. when a new boolean value E is added to this expression there are 2 ways to parenthesize this new expression 1. ((A.B.C.....D).E) ie. with all possible parenthesizations of A.B.C.....D we add E at the end. 2. (A.B.C.(D.E)) ie. evaluate D.E first and then find the number of ways this expression of size K can produce true. suppose T[K] is the number of ways the expression with size K produces true then T[k]=val1+val2+val3 where val1,val2,val3 are calculated as follows. 1)when E is grouped with D. i)It does not change the value of D ii)it inverses the value of D in the first case val1=T[K]=N.( As this reduces to the initial A.B.C....D expression ). In the second case re-evaluate dp[K] with value of D reversed and that is val1. 2)when E is grouped with the whole expression. //val2 contains the number of 'true' E will produce with expressions which gave 'true' among all parenthesized instances of A.B.C.......D i) if true.E = true then val2 = N ii) if true.E = false then val2 = 0 //val3 contains the number of 'true' E will produce with expressions which gave 'false' among all parenthesized instances of A.B.C.......D iii) if false.E=true then val3=( 2^(K-2) - N ) = M ie. number of ways the expression with size K produces a false [ 2^(K-2) is the number of ways to parenthesize an expression of size K ]. iv) if false.E=false then val3 = 0 This is the basic idea i had in mind but when i checked for its solution http://people.csail.mit.edu/bdean/6.046/dp/dp_9.swf the approach there was completely different. Can someone tell me what am I doing wrong and how can i get better at solving DP so that I can come up with solutions like the one given above myself. Thanks in advance.

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• Automated tests for differencing algorithm

  - by Matthew Rodatus

  We are designing a differencing algorithm (based on Longest Common Subsequence) that compares a source text and a modified copy to extract the new content (i.e. content that is only in the modified copy). I'm currently compiling a library of test case data. We need to be able to run automated tests that verify the test cases, but we don't want to verify strict accuracy. Given the heuristic nature of our algorithm, we need our test pass/failures to be fuzzy. We want to specify a threshold of overlap between the desired result and the actual result (i.e. the content that is extracted). I have a few sketches in my mind as to how to solve this, but has anyone done this before? Does anyone have guidance or ideas about how to do this effectively?

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• Name of the Countdown Numbers round problem - and algorithmic solutions?

  - by Dai

  For the non-Brits in the audience, there's a segment of a daytime game-show where contestants have a set of 6 numbers and a randomly generated target number. They have to reach the target number using any (but not necessarily all) of the 6 numbers using only arithmetic operators. All calculations must result in positive integers. An example: Youtube: Countdown - The Most Extraordinary Numbers Game Ever? A detailed description is given on Wikipedia: Countdown (Game Show) For example: The contentant selects 6 numbers - two large (possibilities include 25, 50, 75, 100) and four small (numbers 1 .. 10, each included twice in the pool). The numbers picked are 75, 50, 2, 3, 8, 7 are given with a target number of 812. One attempt is (75 + 50 - 8) * 7 - (3 * 2) = 813 (This scores 7 points for a solution within 5 of the target) An exact answer would be (50 + 8) * 7 * 2 = 812 (This would have scored 10 points exactly matching the target). Obviously this problem has existed before the advent of TV, but the Wikipedia article doesn't give it a name. I've also saw this game at a primary school I attended where the game was called "Crypto" as an inter-class competition - but searching for it now reveals nothing. I took part in it a few times and my dad wrote an Excel spreadsheet that attempted to brute-force the problem, I don't remember how it worked (only that it didn't work, what with Excel's 65535 row limit), but surely there must be an algorithmic solution for the problem. Maybe there's a solution that works the way human cognition does (e.g. in-parallel to find numbers 'close enough', then taking candidates and performing 'smaller' operations).

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• Algorithm to match timestamped events from two sources

  - by urza.cc

  I have two different physical devices (one is camera, one is other device) that observe the same scene and mark when a specified event occures. (record timestamp) So they each produce a serie of timestamps "when the event was observed". Theoretically the recorded timestamps should be very well aligned: Visualized ideal situation on two time lines "s" and "r" as recorded from the two devices: but more likely they will not be so nicely aligned and there might be missing events from timeline s or r: I am looking for algorithm to match events from "s" and "r" like this: So that the result will be something like: (s1,null); (s2,r1); (s3,null); (s4,r2); (s5,r3); (null,r4); (s6,r5); Or something similar. Maybe with some "confidence" rating. I have some ideas, but I feel that this might be probably a well known problem, that has some good known solutions, but I don't know the right terminology. I am a little bit out of my element here, this is not my primary area of programming.. Any helps, suggestions etc will be appreciated.

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• Looking for a non-cryptographic hash function that returns a single character

  - by makerofthings7

  Suppose I have a dictionary of ASCII words stored in uppercase. I also want to save those words into separate files so that the total word count of each file is approximately the same. By simply looking at the word I need to know which file it should be in (if it's there at all). Duplicate words should go into the same file and overwrite the last one. My first attempt at solving this problem is to use .NET's object.GetHashCode() function and .Trim() to get one of the "random" characters that pop up. I asked a similar question here If I only use one character of object.GetHashCode() I would get a hash code character of A..Z or 0..9. However saving the result of GetHashCode to disk is a no-no so I need a substitute. Question: What algorithm (or subset of an algorithm) is appropriate for pigeonholing strings into a single character or range of characters (Like hex 0..F offers 16 chars)? Real world usage: I'll use this answer to modify the Partition key used in Azure Table storage as described here

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• Performing a Depth First Search iteratively using async/parallel processing?

  - by Prabhu

  Here is a method that does a DFS search and returns a list of all items given a top level item id. How could I modify this to take advantage of parallel processing? Currently, the call to get the sub items is made one by one for each item in the stack. It would be nice if I could get the sub items for multiple items in the stack at the same time, and populate my return list faster. How could I do this (either using async/await or TPL, or anything else) in a thread safe manner? private async Task<IList<Item>> GetItemsAsync(string topItemId) { var items = new List<Item>(); var topItem = await GetItemAsync(topItemId); Stack<Item> stack = new Stack<Item>(); stack.Push(topItem); while (stack.Count > 0) { var item = stack.Pop(); items.Add(item); var subItems = await GetSubItemsAsync(item.SubId); foreach (var subItem in subItems) { stack.Push(subItem); } } return items; } I was thinking of something along these lines, but it's not coming together: var tasks = stack.Select(async item => { items.Add(item); var subItems = await GetSubItemsAsync(item.SubId); foreach (var subItem in subItems) { stack.Push(subItem); } }).ToList(); if (tasks.Any()) await Task.WhenAll(tasks); The language I'm using is C#.

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• Algorithm for rating books: Relative perception

  - by suneet

  So I am developing this application for rating books (think like IMDB for books) using relational database. Problem statement : Let's say book "A" deserves 8.5 in absolute sense. In case if A is the best book I have ever seen, I'll most probably rate it 9.5 whereas for someone else, it might be just an average book, so he/they will rate it less (say around 8). Let's assume 4 such guys rate it 8. If there are 10 guys who are like me (who haven't ever read great literature) and they all rate it 9.5-10. This will effectively make it's cumulative rating greater than 9 (9.5*10 + 8*4) / 14 = 9.1 whereas we needed the result to be 8.5 ... How can I take care of(normalize) this bias due to incorrect perception of individuals. MyProposedSolution : Here's one of the ways how I think it could be solved. We can have a variable Lit_coefficient which tells us how much knowledge a user has about literature. If I rate "A"(the book) 9.5 and person "X" rates it 8, then he must have read books much better than "A" and thus his Lit_coefficient should be higher. And then we can normalize the ratings according to the Lit_coefficient of user. Could there be a better algorithm/solution for the same?

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• Algorithm for flattening overlapping ranges

  - by Joseph

  I am looking for a nice way of flattening (splitting) a list of potentially-overlapping numeric ranges. The problem is very similar to that of this question: Fastest way to split overlapping date ranges, and many others. However, the ranges are not only integers, and I am looking for a decent algorithm that can be easily implemented in Javascript or Python, etc. Example Data: Example Solution: Apologies if this is a duplicate, but I am yet to find a solution.

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• How to manually detect deadlocks

  - by Dawson

  I understand the concepts of deadlock well enough, but when I'm given a problem like the one below I'm not sure how to go about solving it. I can draw a resource allocation graph, but I'm not sure how to solve it from there. Is there a better more formal way of solving this? Consider a system with five processes, P1 through P5, and five resources, R1 through R5. Resource ownership is as follows. • P1 holds R1 and wants R3 • P2 holds R2 and wants R1 • P3 holds R3 and wants R5 • P4 holds R5 and wants R2 • P5 holds R4 and wants R2 Is this system deadlocked? Justify your answer. If the system is deadlocked, list the involved processes.

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• Technique to Solve Hard Programming logic

  - by Paresh Mayani

  I have heard about many techniques which are used by developer/software manager to solve hard programming logic or to create flow of an application and this flow will be implemented by developers to create an actual application. Some of the technique which i know, are: Flowchart Screen-Layout Data Flow Diagram E-R Diagram Algorithm of every programs I'd like to know about two facts: (1) Are there any techniques other than this ? (2) Which one is the most suitable to solve hard programming logic and process of application creation?

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• Amazon Kindle - Whispersync implementation?

  - by Bala

  For those who are not aware of Kindle's whispersync, here is how it works (from amazon.com): "...Whispersync synchronizes the bookmarks and furthest page read among devices registered to the same account. Whispersync is on by default to ensure a seamless reading experience for a book read across multiple Kindles." Can anyone give some details on how the Whispersync feature is implemented in Kindle and in the Backend of Amazon? I am guessing this implementation involves a very simple hashmap for each user account. Each hashmap maps Books with satellite information about the book. Satellite information contains bookmarks, furthest page read, device on which it was read, etc.. Thanks!

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• If your algorithm is correct, does it matter how long it took you to write it?

  - by John Isaacks

  I recently found out that Facebook had a programming challenge that if completed correctly you automatically get a phone interview. There is a sample challenge that asks you to write an algorithm that can solve a Tower of Hanoi type problem. Given a number of pegs and discs, an initial and final configuration; Your algorithm must determine the fewest steps possible to get to the final configuration and output the steps. This sample challenge gives you a 45 minute time limit but allows you to still test your code to see if it passes once your time limit expires. I did not know of any cute math solution that could solve it, and I didn't want to look for one since I think that would be cheating. So I tried to solve the challenge the best I could on my own. I was able to make an algorithm that worked and passed. However, it took me over 4 hours to make, much longer than the 45 minute requirement. Since it took me so much longer than the allotted time, I have not attempted the actual challenge. This got me wondering though, in reality does it really matter that it took me that long? I mean is this a sign that I will not be able to get a job at a place like this (not just Facebook, but Google, Fog Creek, etc.) and need to lower my aspirations, or does the fact that I actually passed on my first attempt even though it took too long be taken as good?

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• Logic or Algorithm to solve this problem [closed]

  - by jade

  I have two lists. List1 {a,b,c,d,e} and List2 {f,g,h,i,j} The relation between the two list is as follows a->g,a->h,h->c,h->d,d->i,d->j Now I have these two lists displayed. Based on the relation above on selecting element a from List1, List2 shows g,h. On selecting h from List2, in List1 c,d are shown in List1. On selecting d from List1 it shows i,j in List2. How to trace back to initial state by deselecting the elements in reverse order in which they have been selected?

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• Sorting Algorithm : output

  - by Aaditya

  I faced this problem on a website and I quite can't understand the output, please help me understand it :- Bogosort, is a dumb algorithm which shuffles the sequence randomly until it is sorted. But here we have tweaked it a little, so that if after the last shuffle several first elements end up in the right places we will fix them and don't shuffle those elements furthermore. We will do the same for the last elements if they are in the right places. For example, if the initial sequence is (3, 5, 1, 6, 4, 2) and after one shuffle we get (1, 2, 5, 4, 3, 6) we will keep 1, 2 and 6 and proceed with sorting (5, 4, 3) using the same algorithm. Calculate the expected amount of shuffles for the improved algorithm to sort the sequence of the first n natural numbers given that no elements are in the right places initially. Input: 2 6 10 Output: 2 1826/189 877318/35343 For each test case output the expected amount of shuffles needed for the improved algorithm to sort the sequence of first n natural numbers in the form of irreducible fractions. I just can't understand the output.

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• Conventions for search result scoring

  - by DeaconDesperado

  I assume this type of question is more on-topic here than on regular SO. I have been working on a search feature for my team's web application and have had a lot of success building a multithreaded, "divide and conquer" processing system to work through a large amount of fulltext. Our problem domain is pretty specific. Users of the app generate posts, and as a general rule, posts that are more recent are considered to be of greater relevance. Some of the data we are trying to extract from search is very specific (user's feelings about specific items or things) and we are using python nltk to do named-entity extraction to find interesting likely query terms. Essentially we look for descriptive adjective-noun pairs and generate a general picture of a user's expressed sentiment as a list of tokens. This search is intended as an internal tool for our team to draw out a local picture of sentiments like "soggy pizza." There's some machine learning in there too to do entity resolution on terms like "soggy" to all manner of adjectives expressing nastiness. My problem is I am at a loss for how to go about scoring these results. The text being searched is split up into tokens in a list, so my initial approach would be to normalize a float score between 0.0-1.0 generated off of how far into the list the terms appear and how often they are repeated (a later mention of the term being worth less, earlier more, greater frequency-greater score, etc.) A certain amount of weight could be given to the timestamp as well, though I am not certain how to calculate this. I am curious if anyone has had to solve a similar problem in a search relevance grading between appreciable metrics (frequency, term location/colocation, recency) and if there are and guidelines for how to weight each. I should mention as well that the final fallback procedure in the search is to pipe the query to Sphinx, which has its own scoring practices. Sphinx operates as the last resort in case our application specific processing can't find any eligible candidates.

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• In Search Data Structure And Algorithm Project Title Based on Topic

  - by Salehin Suhaimi

  As the title says, my lecturer gave me a project that i needed to finish in 3 weeks before final semester exams. So i thought i will start now. The requirement is to "build a simple program that has GUI based on all the chapter that we've learned." But i got stuck on WHAT program should i build. Any idea a program that is related to this chapter i've learned? Any input will help. list, array list, linked list, vectors, stacks, Queues, ADT, Hashing, Binary Search Tree, AVL Tree, That's about all i can remember. Any idea where can i start looking?

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• What are startups expecting when they ask you to solve a programming challenge before interviewing? [closed]

  - by Swapnil Tailor

  I have applied to couple of startups and most of them are asking to solve programming challenge before they start on the interviewing candidate. I have submitted couple of the solutions and all the time getting rejected in the initial screening. Now what I think is, they will see my coding style, algorithm and OOD concepts that I have used to solve the problem. Can you guys input more on it as what other details are taken into consideration and how can I improve my coding for getting selected. By the way, I did all my coding in either Java/Perl. EDIT I feel the biggest reason for rejection is code didn't work for couple of use cases.

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• Construct an array from an existing array

  - by Luv

  Given an array of integers A[1...n-1] where 'N' is the length of array A[ ]. Construct an array B such that B[i] = min(A[i], A[i+1], ..., A[i+K-1]), where K will be given. Array B will have N-K+1 elements. We can solve the problem using min-heaps Construct min-heap for k elements - O(k) For every next element delete the first element and insert the new element and heapify Hence Worst Case Time - O( (n-k+1)*k ) + O(k) Space - O(k) Can we do it better?

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• booth multiplication algorithm

  - by grassPro

  Is booth algorithm for multiplication only for multiplying 2 negative numbers (-3 * -4) or one positive and one negative number (-3 * 4) ? Whenever i multiply 2 positive numbers using booth algorithm i get a wrong result. example : 5 * 4 A = 101 000 0 // binary of 5 is 101 S = 011 000 0 // 2's complement of 5 is 011 P = 000 100 0 // binary of 4 is 100 x = 3 y = 3 m = 5 -m = 2's complement of m r = 4 After right shift of P by 1 bit 0 000 100 After right shift of P by 1 bit 0 000 010 P+S = 011 001 0 After right shift by 1 bit 0 011 001 Discarding the LSB 001100 But that comes out to be the binary of 12 . It should have been 20(010100)

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• Refactoring While Programming

  - by Kirby

  When posed with a problem, particularly when it is complicated in nature, I try to take some time to think about the approach I am going to take to solve the problem. Despite this, what often happens is, as I am programming the solution, I start to think of details of the problem that I missed, and I adjust the code accordingly. What results is a mess of code that needs to be refactored. I want to "refactor as I go," but while it sounds easy enough to do, I have a really hard time doing it. When the detail that I missed is small, it is tempting to make a small update to my design, rather than erase what I've already written and write it the way it is supposed to be. It sounds like a question with an obvious answer, but are there any techniques to use to better "refactor as you go"? I know that this is a good principle, but I fail with it time and time again.

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• Possible applications of algorithm devised for differentiating between structured vs random text

  - by rooznom

  I have written a program that can rapidly (within 5 sec on a 2GB RAM desktop, 2.33 Ghz CPU) differentiate between structured text (e.g english text) and random alphanumeric strings. It can also provide a probability score for the prediction. Are there any practical applications/uses of such a program. Note that the program is based on entropy models and does not have any dictionary comparisons in its workflow. Thanks in advance for your responses

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• Tail-recursive implementation of take-while

  - by Giorgio

  I am trying to write a tail-recursive implementation of the function take-while in Scheme (but this exercise can be done in another language as well). My first attempt was (define (take-while p xs) (if (or (null? xs) (not (p (car xs)))) '() (cons (car xs) (take-while p (cdr xs))))) which works correctly but is not tail-recursive. My next attempt was (define (take-while-tr p xs) (let loop ((acc '()) (ys xs)) (if (or (null? ys) (not (p (car ys)))) (reverse acc) (loop (cons (car ys) acc) (cdr ys))))) which is tail recursive but needs a call to reverse as a last step in order to return the result list in the proper order. I cannot come up with a solution that is tail-recursive, does not use reverse, only uses lists as data structure (using a functional data structure like a Haskell's sequence which allows to append elements is not an option), has complexity linear in the size of the prefix, or at least does not have quadratic complexity (thanks to delnan for pointing this out). Is there an alternative solution satisfying all the properties above? My intuition tells me that it is impossible to accumulate the prefix of a list in a tail-recursive fashion while maintaining the original order between the elements (i.e. without the need of using reverse to adjust the result) but I am not able to prove this. Note The solution using reverse satisfies conditions 1, 3, 4.

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