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  • Fastest way to do a weighted tag search in SQL Server

    - by Hasan Khan
    My table is as follows ObjectID bigint Tag nvarchar(50) Weight float Type tinyint I want to get search for all objects that has tags 'big' or 'large' I want the objectid in order of sum of weights (so objects having both the tags will be on top) select objectid, row_number() over (order by sum(weight) desc) as rowid from tags where tag in ('big', 'large') and type=0 group by objectid the reason for row_number() is that i want paging over results. The query in its current form is very slow, takes a minute to execute over 16 million tags. What should I do to make it faster? I have a non clustered index (objectid, tag, type) Any suggestions?

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  • How can I get a COUNT(col) ... GROUP BY to use an index?

    - by thecoop
    I've got a table (col1, col2, ...) with an index on (col1, col2, ...). The table has got millions of rows in it, and I want to run a query: SELECT col1, COUNT(col2) WHERE col1 NOT IN (<couple of exclusions>) GROUP BY col1 Unfortunately, this is resulting in a full table scan of the table, which takes upwards of a minute. Is there any way of getting oracle to use the index on the columns to return the results much faster?

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  • how to avoid temporaries when copying weakly typed object

    - by Truncheon
    Hi. I'm writing a series classes that inherit from a base class using virtual. They are INT, FLOAT and STRING objects that I want to use in a scripting language. I'm trying to implement weak typing, but I don't want STRING objects to return copies of themselves when used in the following way (instead I would prefer to have a reference returned which can be used in copying): a = "hello "; b = "world"; c = a + b; I have written the following code as a mock example: #include <iostream> #include <string> #include <cstdio> #include <cstdlib> std::string dummy("<int object cannot return string reference>"); struct BaseImpl { virtual bool is_string() = 0; virtual int get_int() = 0; virtual std::string get_string_copy() = 0; virtual std::string const& get_string_ref() = 0; }; struct INT : BaseImpl { int value; INT(int i = 0) : value(i) { std::cout << "constructor called\n"; } INT(BaseImpl& that) : value(that.get_int()) { std::cout << "copy constructor called\n"; } bool is_string() { return false; } int get_int() { return value; } std::string get_string_copy() { char buf[33]; sprintf(buf, "%i", value); return buf; } std::string const& get_string_ref() { return dummy; } }; struct STRING : BaseImpl { std::string value; STRING(std::string s = "") : value(s) { std::cout << "constructor called\n"; } STRING(BaseImpl& that) { if (that.is_string()) value = that.get_string_ref(); else value = that.get_string_copy(); std::cout << "copy constructor called\n"; } bool is_string() { return true; } int get_int() { return atoi(value.c_str()); } std::string get_string_copy() { return value; } std::string const& get_string_ref() { return value; } }; struct Base { BaseImpl* impl; Base(BaseImpl* p = 0) : impl(p) {} ~Base() { delete impl; } }; int main() { Base b1(new INT(1)); Base b2(new STRING("Hello world")); Base b3(new INT(*b1.impl)); Base b4(new STRING(*b2.impl)); std::cout << "\n"; std::cout << b1.impl->get_int() << "\n"; std::cout << b2.impl->get_int() << "\n"; std::cout << b3.impl->get_int() << "\n"; std::cout << b4.impl->get_int() << "\n"; std::cout << "\n"; std::cout << b1.impl->get_string_ref() << "\n"; std::cout << b2.impl->get_string_ref() << "\n"; std::cout << b3.impl->get_string_ref() << "\n"; std::cout << b4.impl->get_string_ref() << "\n"; std::cout << "\n"; std::cout << b1.impl->get_string_copy() << "\n"; std::cout << b2.impl->get_string_copy() << "\n"; std::cout << b3.impl->get_string_copy() << "\n"; std::cout << b4.impl->get_string_copy() << "\n"; return 0; } It was necessary to add an if check in the STRING class to determine whether its safe to request a reference instead of a copy: Script code: a = "test"; b = a; c = 1; d = "" + c; /* not safe to request reference by standard */ C++ code: STRING(BaseImpl& that) { if (that.is_string()) value = that.get_string_ref(); else value = that.get_string_copy(); std::cout << "copy constructor called\n"; } If was hoping there's a way of moving that if check into compile time, rather than run time.

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  • JavaScript Optimisation

    - by Jayie
    I am using JavaScript to work out all the combinations of badminton doubles matches from a given list of players. Each player teams up with everyone else. EG. If I have the following players a, b, c & d. Their combinations can be: a & b V c & d a & c V b & d a & d V b & c I am using the code below, which I wrote to do the job, but it's a little inefficient. It loops through the PLAYERS array 4 times finding every single combination (including impossible ones). It then sorts the game out into alphabetical order and stores it in the GAMES array if it doesn't already exist. I can then use the first half of the GAMES array to list all game combinations. The trouble is if I have any more than 8 players it runs really slowly because the combination growth is exponential. Does anyone know a better way or algorithm I could use? The more I think about it the more my brain hurts! var PLAYERS = ["a", "b", "c", "d", "e", "f", "g"]; var GAMES = []; var p1, p2, p3, p4, i1, i2, i3, i4, entry, found, i; var pos = 0; var TEAM1 = []; var TEAM2 = []; // loop through players 4 times to get all combinations for (i1 = 0; i1 < PLAYERS.length; i1++) { p1 = PLAYERS[i1]; for (i2 = 0; i2 < PLAYERS.length; i2++) { p2 = PLAYERS[i2]; for (i3 = 0; i3 < PLAYERS.length; i3++) { p3 = PLAYERS[i3]; for (i4 = 0; i4 < PLAYERS.length; i4++) { p4 = PLAYERS[i4]; if ((p1 != p2 && p1 != p3 && p1 != p4) && (p2 != p1 && p2 != p3 && p2 != p4) && (p3 != p1 && p3 != p2 && p3 != p4) && (p4 != p1 && p4 != p2 && p4 != p3)) { // sort teams into alphabetical order (so we can compare them easily later) TEAM1[0] = p1; TEAM1[1] = p2; TEAM2[0] = p3; TEAM2[1] = p4; TEAM1.sort(); TEAM2.sort(); // work out the game and search the array to see if it already exists entry = TEAM1[0] + " & " + TEAM1[1] + " v " + TEAM2[0] + " & " + TEAM2[1]; found = false; for (i=0; i < GAMES.length; i++) { if (entry == GAMES[i]) found = true; } // if the game is unique then store it if (!found) { GAMES[pos] = entry; document.write((pos+1) + ": " + GAMES[pos] + "<br>"); pos++; } } } } } } Thanks in advance. Jason.

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  • C++ DWORD* to BYTE*

    - by NomeSkavinski
    My issue, i am trying to convert and array of dynamic memory of type DWORD to a BYTE. Fair enough i can for loop through this and convert the DWORD into a BYTE per entry. But is their a faster way to do this? to take a pointer to DWORD data and convert the whole piece of data into a pointer to BYTE data? such as using a memcpy operation? I feel this is not possible, im not requesting an answer just an experienced opinion on my approach, as i have tried testing both approaches but seem to fail getting to a solution on my second solution. Thanks for any input, again no answers just a point in the right direction. Nor is this a homework question, i felt that had to be mentioned.

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  • How to properly cast a global memory array using the uint4 vector in CUDA to increase memory throughput?

    - by charis
    There are generally two techniques to increase the memory throughput of the global memory on a CUDA kernel; memory accesses coalescence and accessing words of at least 4 bytes. With the first technique accesses to the same memory segment by threads of the same half-warp are coalesced to fewer transactions while be accessing words of at least 4 bytes this memory segment is effectively increased from 32 bytes to 128. To access 16-byte instead of 1-byte words when there are unsigned chars stored in the global memory, the uint4 vector is commonly used by casting the memory array to uint4: uint4 *text4 = ( uint4 * ) d_text; var = text4[i]; In order to extract the 16 chars from var, i am currently using bitwise operations. For example: s_array[j * 16 + 0] = var.x & 0x000000FF; s_array[j * 16 + 1] = (var.x >> 8) & 0x000000FF; s_array[j * 16 + 2] = (var.x >> 16) & 0x000000FF; s_array[j * 16 + 3] = (var.x >> 24) & 0x000000FF; My question is, is it possible to recast var (or for that matter *text4) to unsigned char in order to avoid the additional overhead of the bitwise operations?

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  • Why this query is so slow?

    - by Silver Light
    This query appears in mysql slow query log: it takes 11 seconds. INSERT INTO record_visits ( record_id, visit_day ) VALUES ( '567', NOW() ); The table has 501043 records and it's structure looks like this: CREATE TABLE IF NOT EXISTS `record_visits` ( `id` int(11) NOT NULL AUTO_INCREMENT, `record_id` int(11) DEFAULT NULL, `visit_day` date DEFAULT NULL, `visit_cnt` bigint(20) DEFAULT '1', PRIMARY KEY (`id`), UNIQUE KEY `record_id_visit_day` (`record_id`,`visit_day`) ) ENGINE=MyISAM DEFAULT CHARSET=utf8 ; What could be wrong? Why this INSERT takes so long?

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  • MySQL query paralyzes site

    - by nute
    Once in a while, at random intervals, our website gets completely paralyzed. Looking at SHOW FULL PROCESSLIST;, I've noticed that when this happens, there is a specific query that is "Copying to tmp table" for a loooong time (sometimes 350 seconds), and almost all the other queries are "Locked". The part I don't understand is that 90% of the time, this query runs fine. I see it going through in the process list and it finishes pretty quickly most of the time. This query is being called by an ajax call on our homepage to display product recommendations based your browsing history (a la amazon). Just sometimes, randomly (but too often), it gets stuck at "copying to tmp table". Here is a caught instance of the query that was up 109 seconds when I looked: SELECT DISTINCT product_product.id, product_product.name, product_product.retailprice, product_product.imageurl, product_product.thumbnailurl, product_product.msrp FROM product_product, product_xref, product_viewhistory WHERE ( (product_viewhistory.productId = product_xref.product_id_1 AND product_xref.product_id_2 = product_product.id) OR (product_viewhistory.productId = product_xref.product_id_2 AND product_xref.product_id_1 = product_product.id) ) AND product_product.outofstock='N' AND product_viewhistory.cookieId = '188af1efad392c2adf82' AND product_viewhistory.productId IN (24976, 25873, 26067, 26073, 44949, 16209, 70528, 69784, 75171, 75172) ORDER BY product_xref.hits DESC LIMIT 10 Of course the "cookieId" and the list of "productId" changes dynamically depending on the request. I use php with PDO.

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  • How to get REALLY fast python over a simple loop

    - by totallymike
    I'm working on a spoj problem, INTEST. The goal is to specify the number of test cases (n) and a divisor (k), then feed your program n numbers. The program will accept each number on a newline of stdin and after receiving the nth number, will tell you how many were divisible by k. The only challenge in this problem is getting your code to be FAST because it k can be anything up to 10^7 and the test cases can be as high as 10^9. I'm trying to write it in python and having trouble speeding it up. Any ideas? import sys first_in = raw_input() thing = first_in.split() n = int(thing[0]) k = int(thing[1]) total = 0 i = 0 for line in sys.stdin: t = int(line) if t % k == 0: total += 1 print total

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  • Overhead of serving pages - JSPs vs. PHP vs. ASPXs vs. C

    - by John Shedletsky
    I am interested in writing my own internet ad server. I want to serve billions of impressions with as little hardware possible. Which server-side technologies are best suited for this task? I am asking about the relative overhead of serving my ad pages as either pages rendered by PHP, or Java, or .net, or coding Http responses directly in C and writing some multi-socket IO monster to serve requests (I assume this one wins, but if my assumption is wrong, that would actually be most interesting). Obviously all the most efficient optimizations are done at the algorithm level, but I figure there has got to be some speed differences at the end of the day that makes one method of serving ads better than another. How much overhead does something like apache or IIS introduce? There's got to be a ton of extra junk in there I don't need. At some point I guess this is more a question of which platform/language combo is best suited - please excuse the in-adroitly posed question, hopefully you understand what I am trying to get at.

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  • Creating objects makes the VM faster?

    - by Sudhir Jonathan
    Look at this piece of code: MessageParser parser = new MessageParser(); for (int i = 0; i < 10000; i++) { parser.parse(plainMessage, user); } For some reason, it runs SLOWER (by about 100ms) than for (int i = 0; i < 10000; i++) { MessageParser parser = new MessageParser(); parser.parse(plainMessage, user); } Any ideas why? The tests were repeated a lot of times, so it wasn't just random. How could creating an object 10000 times be faster than creating it once?

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  • Has anyone ever successfully make index merge work for MySQL?

    - by user198729
    Setup: mysql> create table t(a integer unsigned,b integer unsigned); mysql> insert into t(a,b) values (1,2),(1,3),(2,4); mysql> create index i_t_a on t(a); mysql> create index i_t_b on t(b); mysql> explain select * from t where a=1 or b=4; +----+-------------+-------+------+---------------+------+---------+------+------+-------------+ | id | select_type | table | type | possible_keys | key | key_len | ref | rows | Extra | +----+-------------+-------+------+---------------+------+---------+------+------+-------------+ | 1 | SIMPLE | t | ALL | i_t_a,i_t_b | NULL | NULL | NULL | 3 | Using where | +----+-------------+-------+------+---------------+------+---------+------+------+-------------+ Is there something I'm missing? Update mysql> explain select * from t where a=1 or b=4; +----+-------------+-------+------+---------------+------+---------+------+------+-------------+ | id | select_type | table | type | possible_keys | key | key_len | ref | rows | Extra | +----+-------------+-------+------+---------------+------+---------+------+------+-------------+ | 1 | SIMPLE | t | ALL | i_t_a,i_t_b | NULL | NULL | NULL | 1863 | Using where | +----+-------------+-------+------+---------------+------+---------+------+------+-------------+ Version: mysql> select version(); +----------------------+ | version() | +----------------------+ | 5.1.36-community-log | +----------------------+ Has anyone ever successfully make index merge work for MySQL? I'll be glad to see successful stories here:)

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  • Ternary Operators in JavaScript Without an "Else"

    - by Oscar Godson
    I've been using them forever, and I love them. To me they see cleaner and i can scan faster, but ever since I've been using them i've always had to put null in the else conditions that don't have anything. Is there anyway around it? E.g. condition ? x=true : null ; basically, is there a way to do: condition ? x=true; Now it shows up as a syntax error...

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  • Anything wrong with this MySQL quert? takes 10 seconds+ to load

    - by user345426
    I have a search that is taking 10 seconds+ to execute! Keep in mind it is also searching over 200,000 products in the database. I posted the explain and MySQL query here. 1 SIMPLE p ref PRIMARY,products_status,prod_prodid_status,product... products_status 1 const 9048 Using where; Using temporary; Using filesort 1 SIMPLE v ref PRIMARY,vendors_id,vendors_vendorid vendors_vendorid 4 rhinomar_rhinomartnew.p.vendors_id 1 1 SIMPLE s ref products_id products_id 4 rhinomar_rhinomartnew.p.products_id 1 1 SIMPLE pd ref PRIMARY,products,prod_desc_prodid_prodname prod_desc_prodid_prodname 4 rhinomar_rhinomartnew.p.products_id 1 1 SIMPLE p2c ref PRIMARY,ptc_catidx PRIMARY 4 rhinomar_rhinomartnew.p.products_id 1 Using where; Using index 1 SIMPLE c eq_ref PRIMARY PRIMARY 4 rhinomar_rhinomartnew.p2c.categories_id 1 Using where MySQL Query: select p.products_id, p.products_image, p.products_price, p.products_weight, p.products_unit_quantity, s.specials_new_products_price, s.status, pd.products_name, pd.products_img_alt from products p left join vendors v ON v.vendors_id = p.vendors_id left join specials s on s.products_id = p.products_id left join products_description pd on pd.products_id = p.products_id left join products_to_categories p2c on p2c.products_id = p.products_id left join categories c on c.categories_id = p2c.categories_id where ( ( pd.products_name like '%apparel%' ) or p2c.categories_id IN (773, 132, 135, 136, 119, 122, 124, 125, 126, 1749, 1753, 1747, 123, 127, 130, 131, 178, 137, 140, 164, 165, 166, 167, 168, 169, 832, 2045 ) or p.products_id = 'apparel' or p.products_model = 'apparel' or CONCAT(v.vendors_prefix, '-') = 'apparel' or CONCAT( v.vendors_prefix, '-', p.products_id ) = 'apparel' ) and p.products_status = '1' and c.categories_status = '1' group by p.products_id order by pd.products_name

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  • Java - Optimize finding a string in a list

    - by Mark
    I have an ArrayList of objects where each object contains a string 'word' and a date. I need to check to see if the date has passed for a list of 500 words. The ArrayList could contain up to a million words and dates. The dates I store as integers, so the problem I have is attempting to find the word I am looking for in the ArrayList. Is there a way to make this faster? In python I have a dict and mWords['foo'] is a simple lookup without looping through the whole 1 million items in the mWords array. Is there something like this in java? for (int i = 0; i < mWords.size(); i++) { if ( word == mWords.get(i).word ) { mLastFindIndex = i; return mWords.get(i); } }

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  • Why does the order of the loops affect performance when iterating over a 2D array? [closed]

    - by Mark
    Possible Duplicate: Which of these two for loops is more efficient in terms of time and cache performance Below are two programs that are almost identical except that I switched the i and j variables around. They both run in different amounts of time. Could someone explain why this happens? Version 1 #include <stdio.h> #include <stdlib.h> main () { int i,j; static int x[4000][4000]; for (i = 0; i < 4000; i++) { for (j = 0; j < 4000; j++) { x[j][i] = i + j; } } } Version 2 #include <stdio.h> #include <stdlib.h> main () { int i,j; static int x[4000][4000]; for (j = 0; j < 4000; j++) { for (i = 0; i < 4000; i++) { x[j][i] = i + j; } } }

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  • Sorting a list of numbers with modified cost

    - by David
    First, this was one of the four problems we had to solve in a project last year and I couldn’t find a suitable algorithm so we handle in a brute force solution. Problem: The numbers are in a list that is not sorted and supports only one type of operation. The operation is defined as follows: Given a position i and a position j the operation moves the number at position i to position j without altering the relative order of the other numbers. If i j, the positions of the numbers between positions j and i - 1 increment by 1, otherwise if i < j the positions of the numbers between positions i+1 and j decreases by 1. This operation requires i steps to find a number to move and j steps to locate the position to which you want to move it. Then the number of steps required to move a number of position i to position j is i+j. We need to design an algorithm that given a list of numbers, determine the optimal (in terms of cost) sequence of moves to rearrange the sequence. Attempts: Part of our investigation was around NP-Completeness, we make it a decision problem and try to find a suitable transformation to any of the problems listed in Garey and Johnson’s book: Computers and Intractability with no results. There is also no direct reference (from our point of view) to this kind of variation in Donald E. Knuth’s book: The art of Computer Programing Vol. 3 Sorting and Searching. We also analyzed algorithms to sort linked lists but none of them gives a good idea to find de optimal sequence of movements. Note that the idea is not to find an algorithm that orders the sequence, but one to tell me the optimal sequence of movements in terms of cost that organizes the sequence, you can make a copy and sort it to analyze the final position of the elements if you want, in fact we may assume that the list contains the numbers from 1 to n, so we know where we want to put each number, we are just concerned with minimizing the total cost of the steps. We tested several greedy approaches but all of them failed, divide and conquer sorting algorithms can’t be used because they swap with no cost portions of the list and our dynamic programing approaches had to consider many cases. The brute force recursive algorithm takes all the possible combinations of movements from i to j and then again all the possible moments of the rest of the element’s, at the end it returns the sequence with less total cost that sorted the list, as you can imagine the cost of this algorithm is brutal and makes it impracticable for more than 8 elements. Our observations: n movements is not necessarily cheaper than n+1 movements (unlike swaps in arrays that are O(1)). There are basically two ways of moving one element from position i to j: one is to move it directly and the other is to move other elements around i in a way that it reaches the position j. At most you make n-1 movements (the untouched element reaches its position alone). If it is the optimal sequence of movements then you didn’t move the same element twice.

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  • Initializing a C++ vector to random values... fast

    - by Flamewires
    Hey, id like to make this as fast as possible because it gets called A LOT in a program i'm writing, so is there any faster way to initialize a C++ vector to random values than: double range;//set to the range of a particular function i want to evaluate. std::vector<double> x(30, 0.0); for (int i=0;i<x.size();i++) { x.at(i) = (rand()/(double)RAND_MAX)*range; } EDIT:Fixed x's initializer.

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  • How do I select a random record efficiently in MySQL?

    - by user198729
    mysql> EXPLAIN SELECT * FROM urls ORDER BY RAND() LIMIT 1; +----+-------------+-------+------+---------------+------+---------+------+-------+---------------------------------+ | id | select_type | table | type | possible_keys | key | key_len | ref | rows | Extra | +----+-------------+-------+------+---------------+------+---------+------+-------+---------------------------------+ | 1 | SIMPLE | urls | ALL | NULL | NULL | NULL | NULL | 62228 | Using temporary; Using filesort | +----+-------------+-------+------+---------------+------+---------+------+-------+---------------------------------+ The above doesn't qualify as efficient,how should I do it properly?

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  • How do I know if my PHP application is using too much memory?

    - by John
    I'm working on a PHP web application that let's users network with each other, book events, message etc... I launched it a few months ago and at the moment, there's only about 100 users. I set up the application on a VPS with ubuntu 9.10, apache 2, mysql 5 and php 5. I had 360 Mb of RAM, but upgraded to 720 MB a few minutes ago. Lately, my web application has been experiencing outages due to excessive memory usage. From what I can tell in error logs, it seems the server automatically kills apache processes that consume too much memory. As a result, I upgraded memory from 360 MB to 720 MB as a stop-gap measure. So my question is, how do I go about resolving these outage issues? How do I know if my website's need for more memory is due to poor code or if it's part of the website's natural growth? What's the most efficient way to determine which PHP scripts consume the most memory?

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  • Calculating Growth-Rates by applying log-differences

    - by mropa
    I am trying to transform my data.frame by calculating the log-differences of each column and controlling for the rows id. So basically I like to calculate the growth rates for each id's variable. So here is a random df with an id column, a time period colum p and three variable columns: df <- data.frame (id = c("a","a","a","c","c","d","d","d","d","d"), p = c(1,2,3,1,2,1,2,3,4,5), var1 = rnorm(10, 5), var2 = rnorm(10, 5), var3 = rnorm(10, 5) ) df id p var1 var2 var3 1 a 1 5.375797 4.110324 5.773473 2 a 2 4.574700 6.541862 6.116153 3 a 3 3.029428 4.931924 5.631847 4 c 1 5.375855 4.181034 5.756510 5 c 2 5.067131 6.053009 6.746442 6 d 1 3.846438 4.515268 6.920389 7 d 2 4.910792 5.525340 4.625942 8 d 3 6.410238 5.138040 7.404533 9 d 4 4.637469 3.522542 3.661668 10 d 5 5.519138 4.599829 5.566892 Now I have written a function which does exactly what I want BUT I had to take a detour which is possibly unnecessary and can be removed. However, somehow I am not able to locate the shortcut. Here is the function and the output for the posted data frame: fct.logDiff <- function (df) { df.log <- dlply (df, "code", function(x) data.frame (p = x$p, log(x[, -c(1,2)]))) list.nalog <- llply (df.log, function(x) data.frame (p = x$p, rbind(NA, sapply(x[,-1], diff)))) ldply (list.nalog, data.frame) } fct.logDiff(df) id p var1 var2 var3 1 a 1 NA NA NA 2 a 2 -0.16136569 0.46472004 0.05765945 3 a 3 -0.41216720 -0.28249264 -0.08249587 4 c 1 NA NA NA 5 c 2 -0.05914281 0.36999681 0.15868378 6 d 1 NA NA NA 7 d 2 0.24428771 0.20188025 -0.40279188 8 d 3 0.26646102 -0.07267311 0.47041227 9 d 4 -0.32372771 -0.37748866 -0.70417351 10 d 5 0.17405309 0.26683625 0.41891802 The trouble is due to the added NA-rows. I don't want to collapse the frame and reduce it, which would be automatically done by the diff() function. So I had 10 rows in my original frame and am keeping the same amount of rows after the transformation. In order to keep the same length I had to add some NAs. I have taken a detour by transforming the data.frame into a list, add the NAs, and afterwards transform the list back into a data.frame. That looks tedious. Any ideas to avoid the data.frame-list-data.frame class transformation and optimize the function?

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  • Thin down jQuery

    - by Taylor Satula
    Hi, I have been optimizing my website but the one problem that stands in my way is all the jQuery functions that I do not use. The only ones that I use are for a smooth page scroller. It just seems like such a waste of download time. My question is: Is there any script or program that will remove the jQuery code that I do not need and leave the 1 or 2 functions that I do need.

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  • Iterative Reduction to Null Matrix

    - by user1459032
    Here's the problem: I'm given a matrix like Input: 1 1 1 1 1 1 1 1 1 At each step, I need to find a "second" matrix of 1's and 0's with no two 1's on the same row or column. Then, I'll subtract the second matrix from the original matrix. I will repeat the process until I get a matrix with all 0's. Furthermore, I need to take the least possible number of steps. I need to print all the "second" matrices in O(n) time. In the above example I can get to the null matrix in 3 steps by subtracting these three matrices in order: Expected output: 1 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1 1 0 0 I have coded an attempt, in which I am finding the first maximum value and creating the second matrices based on the index of that value. But for the above input I am getting 4 output matrices, which is wrong: My output: 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 My solution works for most of the test cases but fails for the one given above. Can someone give me some pointers on how to proceed, or find an algorithm that guarantees optimality? Test case that works: Input: 0 2 1 0 0 0 3 0 0 Output 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0

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