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• Autodetect Presence of CSV Headers in a File

  - by banzaimonkey

  Short question: How do I automatically detect whether a CSV file has headers in the first row? Details: I've written a small CSV parsing engine that places the data into an object that I can access as (approximately) an in-memory database. The original code was written to parse third-party CSV with a predictable format, but I'd like to be able to use this code more generally. I'm trying to figure out a reliable way to automatically detect the presence of CSV headers, so the script can decide whether to use the first row of the CSV file as keys / column names or start parsing data immediately. Since all I need is a boolean test, I could easily specify an argument after inspecting the CSV file myself, but I'd rather not have to (go go automation). I imagine I'd have to parse the first 3 to ? rows of the CSV file and look for a pattern of some sort to compare against the headers. I'm having nightmares of three particularly bad cases in which: The headers include numeric data for some reason The first few rows (or large portions of the CSV) are null There headers and data look too similar to tell them apart If I can get a "best guess" and have the parser fail with an error or spit out a warning if it can't decide, that's OK. If this is something that's going to be tremendously expensive in terms of time or computation (and take more time than it's supposed to save me) I'll happily scrap the idea and go back to working on "important things". I'm working with PHP, but this strikes me as more of an algorithmic / computational question than something that's implementation-specific. If there's a simple algorithm I can use, great. If you can point me to some relevant theory / discussion, that'd be great, too. If there's a giant library that does natural language processing or 300 different kinds of parsing, I'm not interested.

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• Programmer Puzzle: Encoding a chess board state throughout a game

  - by Andrew Rollings

  Not strictly a question, more of a puzzle... Over the years, I've been involved in a few technical interviews of new employees. Other than asking the standard "do you know X technology" questions, I've also tried to get a feel for how they approach problems. Typically, I'd send them the question by email the day before the interview, and expect them to come up with a solution by the following day. Often the results would be quite interesting - wrong, but interesting - and the person would still get my recommendation if they could explain why they took a particular approach. So I thought I'd throw one of my questions out there for the Stack Overflow audience. Question: What is the most space-efficient way you can think of to encode the state of a chess game (or subset thereof)? That is, given a chess board with the pieces arranged legally, encode both this initial state and all subsequent legal moves taken by the players in the game. No code required for the answer, just a description of the algorithm you would use. EDIT: As one of the posters has pointed out, I didn't consider the time interval between moves. Feel free to account for that too as an optional extra :) EDIT2: Just for additional clarification... Remember, the encoder/decoder is rule-aware. The only things that really need to be stored are the player's choices - anything else can be assumed to be known by the encoder/decoder. EDIT3: It's going to be difficult to pick a winner here :) Lots of great answers!

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• Algorithms for finding a numerical record in a list of ordered numbers

  - by Ankur

  I have a list of incomplete ordered numbers. I want to find a particular number with as few steps as possible. Are there any improvements on this algorithm, I assume you can count the set size without difficulty - it will be stored and updated every time a new item is added. Your object is to get your cursor over the value x The first number (smallest) is s, and the last number (greatest) is g. Take the midpoint m1 of the set: calculate is x < m1, If yes then s <= x < m1 If no then m1 < x <= g If m1 = x then you're done. Keep repeating till you find x. Basically dividing the set into two parts with each iteration till you hit x. The purpose is to retrieve a numerical id from a very large table to then find the associated other records. I would imagine this is the most trivial kind of indexing available, are there improvements?

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• Please Help Me with my Homework Problem in C++

  - by sil3nt

  Hey there, this is part of a question i got in class, im at the final stretch but this has become a major problem. In it im given a certain value which is called the "gold value" and it is 40.5, this value changes in input. and i have these constants const int RUBIES_PER_DIAMOND = 5; // relative values. * const int EMERALDS_PER_RUBY = 2; const int GOLDS_PER_EMERALDS = 5; const int SILVERS_PER_GOLD = 4; const int COPPERS_PER_SILVER = 5; const int DIAMOND_VALUE = 50; // gold values. * const int RUBY_VALUE = 10; const int EMERALD_VALUE = 5; const float SILVER_VALUE = 0.25; const float COPPER_VALUE = 0.05; which means that basically for every diamond there are 5 rubies, and for every ruby there are 2 emeralds. So on and so forth. and the "gold value" for every diamond for example is 50 (diamond value = 50) this is how much one diamond is worth in golds. my problem is converting 40.5 into these diamonds and ruby values. I know the answer is 4rubies and 2silvers but how do i write the algorithm for this so that it gives the best estimate for every goldvalue that comes along??

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• Fuzzy Search on Material Descriptions including numerical sizes & general descriptions of material t

  - by Kyle

  We're looking to provide a fuzzy search on an electrical materials database (i.e. conduit, cable, etc.). The problem is that, because of a lack of consistency across all material types, we could not split sizes into separate fields from the text description because some materials are rated by things other than size. I've attempted a combination of a full text search & a SQL CLR implementation of the Levenshtein search algorithm (for assistance in ranking), but my results are a little funky (i.e. they are not sorting correctly due to improper ranking). For example, if the search term is "3/4" ABCD Conduit", I'll might get back several irrelevant results in the following order: 1/2" Conduit 1/4" X 3/4" Cable 1/4" Cable Ties 3/4" DFC Conduit Tees 3/4" ABCD Conduit 3/4" Conduit I believe I've nailed the problem down to the fact that these two search algorithms do not factor in the relevance of punctuation & numeric. That is, in such a search, I'd expect the size to take precedence over any fuzzy match on the rest of the description, but my results don't reflect that. My question is: Can anyone recommend better search algorithms or different approaches that may be better suited for searching a combination of alphanumerics & punctuation characters?

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• Finding subsets that can be completed to tuples without duplicates

  - by Jules

  We have a collection of sets A_1,..,A_n. The goal is to find new sets for each of the old sets. newA_i = {a_i in A_i such that there exist (a_1,..,a_n) in (A1,..,An) with no a_k = a_j for all k and j} So in words this says that we remove all the elements from A_i that can't be used to form a tuple (a_1,..a_n) from the sets (A_1,..,A_n) such that the tuple doesn't contain duplicates. My question is how to compute these new sets quickly. If you just implement this definition by generating all possible v's this will take exponential time. Do you know a better algorithm? Edit: here's an example. Take A_1 = {1,2,3,4} A_2 = {2}. Now the new sets look like this: newA_1 = {1,3,4} newA_2 = {2} The 2 has been removed from A_1 because if you choose it the tuple will always be (2,2) which is invalid because it contains duplicates. On the other hand 1,3,4 are valid because (1,2), (3,2) and (4,2) are valid tuples. Another example: A_1 = {1,2,3} A_2 = {1,4,5} A_3 = {2,4,5} A_4 = {1,2,3} A_5 = {1,2,3} Now the new sets are: newA_1 = {1,2,3} newA_2 = {4,5} newA_3 = {4,5} newA_4 = {1,2,3} newA_5 = {1,2,3} The 1 and 2 are removed from sets 2 and 3 because if you choose the 1 or 2 from these sets you'll only have 2 values left for sets 1, 4 and 5, so you will always have duplicates in tuples that look like (_,1,_,_,_) or like (_,_,2,_,_).

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• A function where small changes in input always result in large changes in output

  - by snowlord

  I would like an algorithm for a function that takes n integers and returns one integer. For small changes in the input, the resulting integer should vary greatly. Even though I've taken a number of courses in math, I have not used that knowledge very much and now I need some help... An important property of this function should be that if it is used with coordinate pairs as input and the result is plotted (as a grayscale value for example) on an image, any repeating patterns should only be visible if the image is very big. I have experimented with various algorithms for pseudo-random numbers with little success and finally it struck me that md5 almost meets my criteria, except that it is not for numbers (at least not from what I know). That resulted in something like this Python prototype (for n = 2, it could easily be changed to take a list of integers of course): import hashlib def uniqnum(x, y): return int(hashlib.md5(str(x) + ',' + str(y)).hexdigest()[-6:], 16) But obviously it feels wrong to go over strings when both input and output are integers. What would be a good replacement for this implementation (in pseudo-code, python, or whatever language)?

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• Count all lists of adjacent nodes stored in an array.

  - by Ben Brodie

  There are many naive approaches to this problem, but I'm looking for a good solution. Here is the problem (will be implemented in Java): You have a function foo(int a, int b) that returns true if 'a' is "adjacent" to 'b' and false if 'a' is not adjacent to 'b'. You have an array such as this [1,4,5,9,3,2,6,15,89,11,24], but in reality has a very long length, like 120, and will be repeated over and over (its a genetic algorithm fitness function) which is why efficiency is important. I want a function that returns the length of each possible 'list' of adjacencies in the array, but not including the 'lists' which simply subsets of a larger list. For example, if foo(1,4) - true, foo(4,5) - true, foo(5,9)- false, foo(9,3) & foo(3,2) & foo(2,6), foo(6,15) - true, then there are 'lists' (1,4,5) and (9,3,2,6), so length 3 and 4. I don't want it to return (3,2,6), though, because this is simply a subset of 9,3,2,6. Thanks.

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• How to find minimum cut-sets for several subgraphs of a graph of degrees 2 to 4

  - by Tore

  I have a problem, Im trying to make A* searches through a grid based game like pacman or sokoban, but i need to find "enclosures". What do i mean by enclosures? subgraphs with as few cut edges as possible given a maximum size and minimum size for number of vertices that act as soft constraints. Alternatively you could say i am looking to find bridges between subgraphs, but its generally the same problem. Given a game that looks like this, what i want to do is find enclosures so that i can properly find entrances to them and thus get a good heuristic for reaching vertices inside these enclosures. So what i want is to find these colored regions on any given map. The reason for me bothering to do this and not just staying content with the performance of a simple manhattan distance heuristic is that an enclosure heuristic can give more optimal results and i would not have to actually do the A* to get some proper distance calculations and also for later adding competitive blocking of opponents within these enclosures when playing sokoban type games. Also the enclosure heuristic can be used for a minimax approach to finding goal vertices more properly. Do you know of a good algorithm for solving this problem or have any suggestions in things i should explore?

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• Random Pairings that don't Repeat

  - by Andrew Robinson

  This little project / problem came out of left field for me. Hoping someone can help me here. I have some rough ideas but I am sure (or at least I hope) a simple, fairly efficient solution exists. Thanks in advance.... pseudo code is fine. I generally work in .NET / C# if that sheds any light on your solution. Given: A pool of n individuals that will be meeting on a regular basis. I need to form pairs that have not previously meet. The pool of individuals will slowly change over time. For the purposes of pairing, (A & B) and (B & A) constitute the same pair. The history of previous pairings is maintained. For the purpose of the problem, assume an even number of individuals. For each meeting (collection of pairs) and individual will only pair up once. Is there an algorithm that will allow us to form these pairs? Ideally something better than just ordering the pairs in a random order, generating pairings and then checking against the history of previous pairings. In general, randomness within the pairing is ok.

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• Time complexity with bit cost

  - by Keyser

  I think I might have completely misunderstood bit cost analysis. I'm trying to wrap my head around the concept of studying an algorithm's time complexity with respect to bit cost (instead of unit cost) and it seems to be impossible to find anything on the subject. Is this considered to be so trivial that no one ever needs to have it explained to them? Well I do. (Also, there doesn't even seem to be anything on wikipedia which is very unusual). Here's what I have so far: The bit cost of multiplication and division of two numbers with n bits is O(n^2) (in general?) So, for example: int number = 2; for(int i = 0; i < n; i++ ){ number = i*i; } has a time complexity with respect to bit cost of O(n^3), because it does n multiplications (right?) But in a regular scenario we want the time complexity with respect to the input. So, how does that scenario work? The number of bits in i could be considered a constant. Which would make the time complexity the same as with unit cost except with a bigger constant (and both would be linear). Also, I'm guessing addition and subtraction can be done in constant time, O(1). Couldn't find any info on it but it seems reasonable since it's one assembler operation.

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• Dealing with Imprecise Drawing in CAD Drawing

  - by Graviton

  I have a CAD application, that allows user to draw lines and polygons and all that. One thorny problem that I face is user drawing can be highly imprecise, for example, a user might want to draw two rectangles that are connected to each other. Hence there should be one line shared by two rectangles. However, it's easy for user to, instead of draw a line, draw two lines that are very close to each other, so close to each other that when look from the screen, you would be mistaken that they are the same line, except that they aren't when you zoom in a little bit. My application would require user to properly draw the lines ( or my preprocessing must be able to do auto correction), or else my internal algorithm would not be able to process the inputs correctly. What is the best strategy to combat this kind of problem? I am thinking about rounding the point coordinates to a certain degree of precision, but although I can't exactly pinpoint the problem of this approach, but I feel that this is not the correct way of doing things, that this will introduce a new set of problem. Any idea?

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• Log 2 N generic comparison tree

  - by Morano88

  Hey! I'm working on an algorithm for Redundant Binary Representation (RBR) where every two bits represent a digit. I designed the comparator that takes 4 bits and gives out 2 bits. I want to make the comparison in log 2 n so If I have X and Y .. I compare every 2 bits of X with every 2 bits of Y. This is smooth if the number of bits of X or Y equals n where (n = 2^X) i.e n = 2,4,8,16,32,... etc. Like this : However, If my input let us say is 6 or 10 .. then it becomes not smooth and I have to take into account some odd situations like this : I have a shallow experience in algorithms .. is there a generic way to do it .. so at the end I get only 2 bits no matter what the input is ? I just need hints or pseudo-code. If my question is not appropriate here .. so feel free to flag it or tell me to remove it. I'm using VHDL by the way!

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• sort outer array based on values in inner array, javascript

  - by ptrn

  I have an array with arrays in it, where I want to sort the outer arrays based on values in a specific column in the inner. I bet that sounded more than a bit confusing, so I'll skip straight to an example. Initial data: var data = [ [ "row_1-col1", "2-row_1-col2", "c-row_1-coln" ], [ "row_2-col1", "1-row_2-col2", "b-row_2-coln" ], [ "row_m-col1", "3-row_m-col2", "a-row_m-coln" ] ]; Sort data, based on column with index 1 data.sortFuncOfSomeKind(1); where the object then would look like this; var data = [ [ "row_2-col1", "1-row_2-col2", "b-row_2-coln" ], [ "row_1-col1", "2-row_1-col2", "c-row_1-coln" ], [ "row_m-col1", "3-row_m-col2", "a-row_m-coln" ] ]; Sort data, based on column with index 2 data.sortFuncOfSomeKind(2); where the object then would look like this; var data = [ [ "row_m-col1", "3-row_m-col2", "a-row_m-coln" ], [ "row_2-col1", "1-row_2-col2", "b-row_2-coln" ], [ "row_1-col1", "2-row_1-col2", "c-row_1-coln" ] ]; The big Q Is there an existing solution to this that you know of, or would I have to write one myself? If so, which would be the easiest sort algorithm to use? QuickSort? _L

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• How should I generate the partitions / pairs for the Chinese Postman problem?

  - by Simucal

  I'm working on a program for class that involves solving the Chinese Postman problem. Our assignment only requires us to write a program to solve it for a hard-coded graph but I'm attempting to solve it for the general case on my own. The part that is giving me trouble is generating the partitions of pairings for the odd vertices. For example, if I had the following labeled odd verticies in a graph: 1 2 3 4 5 6 I need to find all the possible pairings / partitions I can make with these vertices. I've figured out I'll have i paritions given: n = num of odd verticies k = n / 2 i = ((2k)(2k-1)(2k-2)...(k+1))/2 So, given the 6 odd verticies above, we will know that we need to generate i = 15 partitions. The 15 partions would look like: 1 2 3 4 5 6 1 2 3 5 4 6 1 2 3 6 4 5 ... 1 6 ... Then, for each partition, I take each pair and find the shortest distance between them and sum them for that partition. The partition with the total smallest distance between its pairs is selected, and I then double all the edges between the shortest path between the odd vertices (found in the selected partition). These represent the edges the postman will have to walk twice. At first I thought I had worked out an appropriate algorithm for generating these partitions / pairs but it is flawed. I found it wasn't a simple permutation/combination problem. Does anyone who has studied this problem before have any tips that can help point me in the right direction for generating these partitions?

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• Fastest way to modify a decimal-keyed table in MySQL?

  - by javanix

  I am dealing with a MySQL table here that is keyed in a somewhat unfortunate way. Instead of using an auto increment table as a key, it uses a column of decimals to preserve order (presumably so its not too difficult to insert new rows while preserving a primary key and order). Before I go through and redo this table to something more sane, I need to figure out how to rekey it without breaking everything. What I would like to do is something that takes a list of doubles (the current keys) and outputs a list of integers (which can be cast down to doubles for rekeying). For example, input {1.00, 2.00, 2.50, 2.60, 3.00} would give output {1, 2, 3, 4, 5). Since this is a database, I also need to be able to update the rows nicely: UPDATE table SET `key`='3.00' WHERE `key`='2.50'; Can anyone think of a speedy algorithm to do this? My current thought is to read all of the doubles into a vector, take the size of the vector, and output a new vector with values from 1 => doubleVector.size. This seems pretty slow, since you wouldn't want to read every value into the vector if, for instance, only the last n/100 elements needed to be modified. I think there is probably something I can do in place, since only values after the first non-integer double need to be modified, but I can't for the life of me figure anything out that would let me update in place as well. For instance, setting 2.60 to 3.00 the first time you see 2.50 in the original key list would result in an error, since the key value 3.00 is already used for the table.

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• Ranking/ weighing search result

  - by biso

  I am trying to build an application that has a smart adaptive search engine (lets say for cars). If I search for for 4x4 then the DB will return all the 4x4 cars I have (100 cars) - but as time goes by and I start checking out cars, liking them, commenting on them, etc the order of the search result should be the different. That means 1 month later when searching for 4x4, I should get the same result set ordered differently as per my previous interaction with the site. If I was mainly liking and commenting on German cars, BMW should be on the top and Land cruiser should be further down. This ranking should be based on attributes that I captureduring user interaction (eg: car origin, user age, user location, car type[4x4, coupe, hatchback], price range). So for each car result I get, I will be weighing it based on how well it is performing on the 5 attributes above. I intend to use the DB just as a repository and do the ranking and the thinking on the server. My question is, what kind of algorithm should I be using to weigh/rank my search result? Thanks.

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• Does anyone knows the algorithm how Facebook detects the images when adding a link

  - by Edelcom

  When you add a link to your Facebook page, after some processing, Facebook presents you a next/prev button to choose an image linked to the url your are inserting. Obviously, Facebook reads the html-page and displays the images found on the url you insert. Does anyone knows what algorithm Facebook uses to decide what images to show ? If I insert a link to : http://www.staplijst.be/lachende-wandelaars-aalter-aktivia-003.asp, only 11 images are detected. The one I want, the one at the top right corner, is not included in the list. If I insert a link to http://www.staplijst.be/stichting-kennedymars-rijsbergen-zundert-nederland-knblo-nl-81996.asp, 19 images are displayed (including the one I want (the one at the right top corner of the text area). Both pages are build using asp code but are functionally the same. I thought that it has something to do with the image size, but can't find any deciding factor there. I will investigate some furhter, because if I know what Facebook is looking for, I can make sure that the correct images are included on the page (since they are dynamic pages build with classic asp). But if anyone has any idea ? Help would be appreciated.

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• Fastest way to convert a list of doubles to a unique list of integers?

  - by javanix

  I am dealing with a MySQL table here that is keyed in a somewhat unfortunate way. Instead of using an auto increment table as a key, it uses a column of decimals to preserve order (presumably so its not too difficult to insert new rows while preserving a primary key and order). Before I go through and redo this table to something more sane, I need to figure out how to rekey it without breaking everything. What I would like to do is something that takes a list of doubles (the current keys) and outputs a list of integers (which can be cast down to doubles for rekeying). For example, input {1.00, 2.00, 2.50, 2.60, 3.00} would give output {1, 2, 3, 4, 5). Since this is a database, I also need to be able to update the rows nicely: UPDATE table SET `key`='3.00' WHERE `key`='2.50'; Can anyone think of a speedy algorithm to do this? My current thought is to read all of the doubles into a vector, take the size of the vector, and output a new vector with values from 1 => doubleVector.size. This seems pretty slow, since you wouldn't want to read every value into the vector if, for instance, only the last n/100 elements needed to be modified. I think there is probably something I can do in place, since only values after the first non-integer double need to be modified, but I can't for the life of me figure anything out that would let me update in place as well. For instance, setting 2.60 to 3.00 the first time you see 2.50 in the original key list would result in an error, since the key value 3.00 is already used for the table.

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• Find min. "join" operations for sequence

  - by utyle

  Let's say, we have a list/an array of positive integers x1, x2, ... , xn. We can do a join operation on this sequence, that means that we can replace two elements that are next to each other with one element, which is sum of these elements. For example: - array/list: [1;2;3;4;5;6] we can join 2 and 3, and replace them with 5; we can join 5 and 6, and replace them with 11; we cannot join 2 and 4; we cannot join 1 and 3 etc. Main problem is to find minimum join operations for given sequence, after which this sequence will be sorted in increasing order. Note: empty and one-element sequences are sorted in increasing order. Basic examples: for [4; 6; 5; 3; 9] solution is 1 (we join 5 and 3) for [1; 3; 6; 5] solution is also 1 (we join 6 and 5) What I am looking for, is an algorithm that solve this problem. It could be in pseudocode, C, C++, PHP, OCaml or similar (I mean: I woluld understand solution, if You wrote solution in one of these languages). I would appreciate Your help.

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• Good PHP / MYSQL hashing solution for large number of text values

  - by Dave

  Short descriptio: Need hashing algorithm solution in php for large number of text values. Long description. PRODUCT_OWNER_TABLE serial_number (auto_inc), product_name, owner_id OWNER_TABLE owner_id (auto_inc), owener_name I need to maintain a database of 200000 unique products and their owners (AND all subsequent changes to ownership). Each product has one owner, but an owner may have MANY different products. Owner names are "Adam Smith", "John Reeves", etc, just text values (quite likely to be unicode as well). I want to optimize the database design, so what i was thinking was, every week when i run this script, it fetchs the owner of a proudct, then checks against a table i suppose similar to PRODUCT_OWNER_TABLE, fetching the owner_id. It then looks up owner_id in OWNER_TABLE. If it matches, then its the same, so it moves on. The problem is when its different... To optimize the database, i think i should be checking against the other "owner_name" entries in OWNER_TABLE to see if that value exists there. If it does, then i should use that owner_id. If it doesnt, then i should add another entry. Note that there is nothing special about the "name". as long as i maintain the correct linkagaes AND make the OWNER_TABLE "read-only, append-new" type table - I should be able create a historical archive of ownership. I need to do this check for 200000 entries, with i dont know how many unique owner names (~50000?). I think i need a hashing solution - the OWNER_TABLE wont be sorted, so search algos wont be optimal. programming language is PHP. database is MYSQL.

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• how to implement a really efficient bitvector sorting in python

  - by xiao

  Hello guys! Actually this is an interesting topic from programming pearls, sorting 10 digits telephone numbers in a limited memory with an efficient algorithm. You can find the whole story here What I am interested in is just how fast the implementation could be in python. I have done a naive implementation with the module bitvector. The code is as following: from BitVector import BitVector import timeit import random import time import sys def sort(input_li): return sorted(input_li) def vec_sort(input_li): bv = BitVector( size = len(input_li) ) for i in input_li: bv[i] = 1 res_li = [] for i in range(len(bv)): if bv[i]: res_li.append(i) return res_li if __name__ == "__main__": test_data = range(int(sys.argv[1])) print 'test_data size is:', sys.argv[1] random.shuffle(test_data) start = time.time() sort(test_data) elapsed = (time.time() - start) print "sort function takes " + str(elapsed) start = time.time() vec_sort(test_data) elapsed = (time.time() - start) print "sort function takes " + str(elapsed) start = time.time() vec_sort(test_data) elapsed = (time.time() - start) print "vec_sort function takes " + str(elapsed) I have tested from array size 100 to 10,000,000 in my macbook(2GHz Intel Core 2 Duo 2GB SDRAM), the result is as following: test_data size is: 1000 sort function takes 0.000274896621704 vec_sort function takes 0.00383687019348 test_data size is: 10000 sort function takes 0.00380706787109 vec_sort function takes 0.0371489524841 test_data size is: 100000 sort function takes 0.0520560741425 vec_sort function takes 0.374383926392 test_data size is: 1000000 sort function takes 0.867373943329 vec_sort function takes 3.80475401878 test_data size is: 10000000 sort function takes 12.9204008579 vec_sort function takes 38.8053860664 What disappoints me is that even when the test_data size is 100,000,000, the sort function is still faster than vec_sort. Is there any way to accelerate the vec_sort function?

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• Reversing permutation of an array in Java efficiently

  - by HansDampf

  Okay, here is my problem: Im implementing an algorithm in Java and part of it will be following: The Question is to how to do what I will explain now in an efficient way. given: array a of length n integer array perm, which is a permutation of [1..n] now I want to shuffle the array a, using the order determined by array perm, i.e. a=[a,b,c,d], perm=[2,3,4,1] ------ shuffledA[b,c,d,a], I figured out I can do that by iterating over the array with: shuffledA[i]=a[perm[i-1]], (-1 because the permutation indexes in perm start with 1 not 0) Now I want to do some operations on shuffledA... And now I want to do the reverse the shuffle operation. This is where I am not sure how to do it. Note that a can hold an item more than once, i.e. a=[a,a,a,a] If that was not the case, I could iterate perm, and find the corresponding indexes to the values. Now I thought that using a Hashmap instead of the the perm array will help. But I am not sure if this is the best way to do.

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• more problems with the LAG function is SAS

  - by SAS_learner

  The following bit of SAS code is supposed to read from a dataset which contains a numeric variable called 'Radvalue'. Radvalue is the temperature of a radiator, and if a radiator is switched off but then its temperature increases by 2 or more it's a sign that it has come on, and if it is on but its temperature decreases by 2 or more it's a sign that it's gone off. Radstate is a new variable in the dataset which indicates for every observation whether the radiator is on or off, and it's this I'm trying to fill in automatically for the whole dataset. So I'm trying to use the LAG function, trying to initialise the first row, which doesn't have a dif_radvalue, and then trying to apply the algorithm I just described to row 2 onwards. Any idea why the columns Radstate and l_radstate come out completely blank? Thanks everso much!! Let me know if I haven't explained the problem clearly. Data work.heating_algorithm_b; Input ID Radvalue; Datalines; 1 15.38 2 15.38 3 20.79 4 33.47 5 37.03 ; DATA temp.heating_algorithm_c; SET temp.heating_algorithm_b; DIF_Radvalue = Radvalue - lag(Radvalue); l_Radstate = lag(Radstate); if missing(dif_radvalue) then do; dif_radvalue = 0; radstate = "off"; end; else if l_Radstate = "off" & DIF_Radvalue > 2 then Radstate = "on"; else if l_Radstate = "on" & DIF_Radvalue < -2 then Radstate = "off"; else Radstate = l_Radstate; run;

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• Designing small comparable objects

  - by Thomas Ahle

  Intro Consider you have a list of key/value pairs: (0,a) (1,b) (2,c) You have a function, that inserts a new value between two current pairs, and you need to give it a key that keeps the order: (0,a) (0.5,z) (1,b) (2,c) Here the new key was chosen as the average between the average of keys of the bounding pairs. The problem is, that you list may have milions of inserts. If these inserts are all put close to each other, you may end up with keys such to 2^(-1000000), which are not easily storagable in any standard nor special number class. The problem How can you design a system for generating keys that: Gives the correct result (larger/smaller than) when compared to all the rest of the keys. Takes up only O(logn) memory (where n is the number of items in the list). My tries First I tried different number classes. Like fractions and even polynomium, but I could always find examples where the key size would grow linear with the number of inserts. Then I thought about saving pointers to a number of other keys, and saving the lower/greater than relationship, but that would always require at least O(sqrt) memory and time for comparison. Extra info: Ideally the algorithm shouldn't break when pairs are deleted from the list.

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