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• How to calculate Sin function quicker and more precisely?

  - by user1297181

  I want to calculate y(n)=32677Sin(45/1024•n), where y is an integer and n ranges from 0 to 2048. How can I make this process quicker and more precisely? Now I want to show you a reference answer: Since Sin(a+b)=Sin(a)Cos(b)+Cos(a)Sin(b) And Cos(a+b)=Cos(a)Cos(b)-Sin(a)Cos(b). So I can store Sin(45/1024•1) andCos(45/1024•1) ` only.Then use this formula: Sin(45/1024•2)=Sin(45/1024•1+45/1024•1), Cos(45/1024•2)=Cos(45/1024•1+45/1024•1), .... `Sin(45/1024•n)=Sin(45/1024•(n-1)+45/1024•1) `, `Cos(45/1024•n)=Cos(45/1024•(n-1)+45/1024•1) `, This way maybe quicker without storing large array.

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• Inexpensive generation of hierarchical unique IDs

  - by romaninsh

  My application is building a hierarchical structure like this: root = { 'id': 'root', 'children': [ { 'name': 'root_foo', 'children': [] }, { 'id': 'root_foo2', 'children': [ { 'id': 'root_foo2_bar', 'children': [] } ] } ] } in other words, it's a tree of nodes, where each node might have child elements and unique identifier I call "id". When a new child is added, I need to generate a unique identifier for it, however I have two problems: identifiers are getting too long adding many children takes slower, as I need to find first available id My requirement is: naming of a child X must be determined only from the state in their ancestors When I re-generate tree with same contents, the IDs must be same or in other words, when we have nodes A and B, creating child in A, must not affect the name given to children of B. I know that one way to optimize would be to introduce counter in each node and append it to the names which will solve my performance issue, but will not address the issue with the "long identifiers". Could you suggest me the algorithm for quickly coming up with new IDs?

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• Searching for entity awareness in 3D space algorithm and data structure

  - by Khanser

  I'm trying to do some huge AI system just for the fun and I've come to this problem. How can I let the AI entities know about each other without getting the CPU to perform redundant and costly work? Every entity has a spatial awareness zone and it has to know what's inside when it has to decide what to do. First thoughts, for every entity test if the other entities are inside the first's reach. Ok, so it was the first try and yep, that is redundant and costly. We are working with real time AI over 10000+ entities so this is not a solution. Second try, calculate some grid over the awareness zone of every entity and test whether in this zones are entities (we are working with 3D entities with float x,y,z location coordinates) testing every point in the grid with the indexed-by-coordinate entities. Well, I don't like this because is also costly, but not as the first one. Third, create some multi linked lists over the x's and y's indexed positions of the entities so when we search for an interval between x,y and z,w positions (this interval defines the square over the spatial awareness zone) over the multi linked list, we won't have 'voids'. This has the problem of finding the nearest proximity value if there isn't one at the position where we start the search. I'm not convinced with any of the ideas so I'm searching for some enlightening. Do you people have any better ideas?

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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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• Does LINQ require significantly more processing cycles and memory than lower-level data iteration techniques?

  - by Matthew Patrick Cashatt

  Background I am recently in the process of enduring grueling tech interviews for positions that use the .NET stack, some of which include silly questions like this one, and some questions that are more valid. I recently came across an issue that may be valid but I want to check with the community here to be sure. When asked by an interviewer how I would count the frequency of words in a text document and rank the results, I answered that I would Use a stream object put the text file in memory as a string. Split the string into an array on spaces while ignoring punctuation. Use LINQ against the array to .GroupBy() and .Count(), then OrderBy() said count. I got this answer wrong for two reasons: Streaming an entire text file into memory could be disasterous. What if it was an entire encyclopedia? Instead I should stream one block at a time and begin building a hash table. LINQ is too expensive and requires too many processing cycles. I should have built a hash table instead and, for each iteration, only added a word to the hash table if it didn't otherwise exist and then increment it's count. The first reason seems, well, reasonable. But the second gives me more pause. I thought that one of the selling points of LINQ is that it simply abstracts away lower-level operations like hash tables but that, under the veil, it is still the same implementation. Question Aside from a few additional processing cycles to call any abstracted methods, does LINQ require significantly more processing cycles to accomplish a given data iteration task than a lower-level task (such as building a hash table) would?

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• Removing occurrences of characters in a string

  - by DmainEvent

  I am reading this book, programming Interviews exposed by John Wiley and sons and in chapter 6 they are discussing removing all instances of characters in a src string using a removal string... so removeChars(string str, string remove) In there writeup they sey the steps to accomplish this are to have a boolean lookup array with all values initially set to false, then loop through each character in remove setting the corresponding value in the lookup array to true (note: this could also be a hash if the possible character set where huge like Unicode-16 or something like that or if str and remove are both relatively small... < 100 characters I suppose). You then iterate through the str with a source and destination index, copying each character only if its corresponding value in the lookup array is false... Which makes sense... I don't understand the code that they use however... They have for(src = 0; src < len; ++src){ flags[r[src]] == true; } which is turning the flag value at the remove string indexed at src to true... so if you start out with PLEASE HELP as your str and LEA as your remove you will be setting in your flag table at 0,1,2... t|t|t but after that you will get an out of bounds exception because r doesn't have have anything greater than 2 in it... even using there example you get an out of bounds exception... Am is there code example unworkable? Entire function string removeChars( string str, string remove ){ char[] s = str.toCharArray(); char[] r = remove.toCharArray(); bool[] flags = new bool[128]; // assumes ASCII! int len = s.Length; int src, dst; // Set flags for characters to be removed for( src = 0; src < len; ++src ){ flags[r[src]] = true; } src = 0; dst = 0; // Now loop through all the characters, // copying only if they aren’t flagged while( src < len ){ if( !flags[ (int)s[src] ] ){ s[dst++] = s[src]; } ++src; } return new string( s, 0, dst ); } as you can see, r comes from the remove string. So in my example the remove string has only a size of 3 while my str string has a size of 11. len is equal to the length of the str string. So it would be 11. How can I loop through the r string since it is only size 3? I haven't compiled the code so I can loop through it, but just looking at it I know it won't work. I am thinking they wanted to loop through the r string... in other words they got the length of the wrong string here.

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• Genetic Algorithm new generation exponentially increasing

  - by Rdz

  I'm programming Genetic Algorithm in C++ and after searching all kind of ways of doing GA'a operators (selection, crossover, mutation) I came up with a doubt. Let's say I have an initial population of 500. My selection will consist in getting the top 20% of 500(based on best fitness). So I get 100 individuals to mate. When I do the crossover I'll get 2 children where both together have 50% of surviving. So far so good. I start the mutation, and everything's ok.. Now when I start choosing the Next generation, I see that I have a big number of children (in this case, 4950 if you wanna know). Now the thing is, every time I run GA, if I send all the children to the next generation, the number of individuals per generation will increase exponentially. So there must be a way of choosing the children to fulfill a new generation without getting out of this range of the initial population. What I'm asking here is if there is anyway of choosing the children to fill the new generations OR should I choose somehow (and maybe reduce) the parents to mate so I don't get so many children in the end. Thanks :)

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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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• Simple algorithm for a sudoku solver java

  - by user142050

  just a quick note first, I originally asked this question on stack overflow but was refered here instead. I've been stuck on this thing for a while, I just can't wrap my head around it. For a homework, I have to produce an algorithm for a sudoku solver that can check what number goes in a blank square in a row, in a column and in a block. It's a regular 9x9 sudoku and I'm assuming that the grid is already printed so I have to produce the part where it solves it. I've read a ton of stuff on the subject I just get stuck expressing it. I want the solver to do the following: If the value is smaller than 9, increase it by 1 If the value is 9, set it to zero and go back 1 If the value is invalid, increase by 1 I've already read about backtracking and such but I'm in the early stage of the class so I'd like to keep it as simple as possible. I'm more capable of writing in pseudo code but not so much with the algorithm itself and it's the algorithm that is needed for this exercise. Thanks in advance for your help guys.

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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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• 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 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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