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  • Project Euler 20: (Iron)Python

    - by Ben Griswold
    In my attempt to learn (Iron)Python out in the open, here’s my solution for Project Euler Problem 20.  As always, any feedback is welcome. # Euler 20 # http://projecteuler.net/index.php?section=problems&id=20 # n! means n x (n - 1) x ... x 3 x 2 x 1 # Find the sum of digits in 100! import time start = time.time() def factorial(n): if n == 0: return 1 else: return n * factorial(n-1) print sum([int(i) for i in str(factorial(100))]) print "Elapsed Time:", (time.time() - start) * 1000, "millisecs" a=raw_input('Press return to continue')

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  • When to use typedef?

    - by futlib
    I'm a bit confused about if and when I should use typedef in C++. I feel it's a balancing act between readability and clarity. Here's a code sample without any typedefs: int sum(std::vector<int>::const_iterator first, std::vector<int>::const_iterator last) { static std::map<std::tuple<std::vector<int>::const_iterator, std::vector<int>::const_iterator>, int> lookup_table; std::map<std::tuple<std::vector<int>::const_iterator, std::vector<int>::const_iterator>, int>::iterator lookup_it = lookup_table.find(lookup_key); if (lookup_it != lookup_table.end()) return lookup_it->second; ... } Pretty ugly IMO. So I'll add some typedefs within the function to make it look nicer: int sum(std::vector<int>::const_iterator first, std::vector<int>::const_iterator last) { typedef std::tuple<std::vector<int>::const_iterator, std::vector<int>::const_iterator> Lookup_key; typedef std::map<Lookup_key, int> Lookup_table; static Lookup_table lookup_table; Lookup_table::iterator lookup_it = lookup_table.find(lookup_key); if (lookup_it != lookup_table.end()) return lookup_it->second; ... } The code is still a bit clumsy, but I get rid of most nightmare material. But there's still the int vector iterators, this variant gets rid of those: typedef std::vector<int>::const_iterator Input_iterator; int sum(Input_iterator first, Input_iterator last) { typedef std::tuple<Input_iterator, Input_iterator> Lookup_key; typedef std::map<Lookup_key, int> Lookup_table; static Lookup_table lookup_table; Lookup_table::iterator lookup_it = lookup_table.find(lookup_key); if (lookup_it != lookup_table.end()) return lookup_it->second; ... } This looks clean, but is it still readable? When should I use a typedef? As soon as I have a nightmare type? As soon as it occurs more than once? Where should I put them? Should I use them in function signatures or keep them to the implementation?

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  • F# Project Euler Problem 1

    - by MarkPearl
    Every now and then I give project Euler a quick browse. Since I have been playing with F# I have found it a great way to learn the basics of the language. Today I thought I would give problem 1 an attempt… Problem 1 If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 1000. My F# Solution I broke this problem into two functions… 1) be able to generate a collection of numbers that are multiples of a number but but are smaller than another number. let GenerateMultiplesOfXbelowY X Y = X |> Seq.unfold (fun i -> if (i<Y) then Some(i, i+X) else None) I then needed something that generated collections for multiples of 3 & 5 and then removed any duplicates. Once this was done I would need to sum these all together to get a result. I found the Seq object to be extremely useful to achieve this… let Multiples = Seq.append (GenerateMultiplesOfXbelowY 3 1000) (GenerateMultiplesOfXbelowY 5 1000) |> Seq.distinct |> Seq.fold(fun acc a -> acc + a) 0 |> Console.WriteLine |> Console.ReadLine My complete solution was … open System let GenerateMultiplesOfXbelowY X Y = X |> Seq.unfold (fun i -> if (i<Y) then Some(i, i+X) else None) let Multiples = Seq.append (GenerateMultiplesOfXbelowY 3 1000) (GenerateMultiplesOfXbelowY 5 1000) |> Seq.distinct |> Seq.fold(fun acc a -> acc + a) 0 |> Console.WriteLine |> Console.ReadLine   Which seemed to generate the correct result in a relatively short period of time although I am sure I will get some comments from the experts who know of some intrinsic method to achieve all of this in one method call.

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  • Naming conventions for newtype deconstructors (destructors?)

    - by Petr Pudlák
    Looking into Haskell's standard library we can see: newtype StateT s m a = StateT { runStateT :: s -> m (a, s) } newtype WrappedMonad m a = WrapMonad { unwrapMonad :: m a } newtype Sum a = Sum { getSum :: a } Apparently, there (at least) 3 different prefixes used to unwrap a value inside a newtype: un-, run- and get-. (Moreover run- and get- capitalizes the next letter while un- doesn't.) This seems confusing. Are there any reasons for that, or is that just a historical thing? If I design my own newtype, what prefix should I use and why?

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  • Euler Problem 20

    - by MarkPearl
    This was probably one of the easiest ones to complete – a quick bash got me the following… The Problem n! means n (n 1) ... 3 2 1 For example, 10! = 10 9 ... 3 2 1 = 3628800, and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27. Find the sum of the digits in the number 100! The Solution   private static BigInteger Factorial(int num) { if (num > 1) return (BigInteger)num * Factorial(num - 1); else return 1; } private static BigInteger SumDigits(string digits) { BigInteger result = 0; foreach (char number in digits) { result += Convert.ToInt32(number)-48; } return result; } static void Main(string[] args) { Console.WriteLine(SumDigits(Factorial(100).ToString())); Console.ReadLine(); }

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  • T-SQL Snack: How Much Free Storage Space is Available?

    - by andyleonard
    Introduction Ever have a need to calculate the total available storage space for a server? Recently I did. Here's a solution I came up with - I bet someone can do this better! xp_fixeddrives There's a handy stored procedure called xp_fixeddrives that reports the available storage space: exec xp_fixeddrives This returns: drive MB free ----- ----------- C 6998 E 201066 Problem solved right? Maybe. The Sum What I really want is the sum total of all available space presented to the server. I built this...(read more)

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  • Is it correct to add booleans in order to count the number of true values in a vector?

    - by gerrit
    Is it conceptually correct to sum a vector of booleans? From a mathematical point of view, I would argue it's not: True + True != 2. But it's quite practical to do so still! Example using the vectorised Python library numpy: In [1]: X = rand(10) In [2]: large = X>0.6 In [3]: large.dtype Out[3]: dtype('bool') In [4]: large.sum() Out[4]: 7 I don't like it, but it's very practical. Is this a good practice? Update: the aim is to count the number of true values in a vector.

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  • Help me alter this query to get the desired results - New*

    - by sandeepan
    Please dump these data first CREATE TABLE IF NOT EXISTS `all_tag_relations` ( `id_tag_rel` int(10) NOT NULL AUTO_INCREMENT, `id_tag` int(10) unsigned NOT NULL DEFAULT '0', `id_tutor` int(10) DEFAULT NULL, `id_wc` int(10) unsigned DEFAULT NULL, PRIMARY KEY (`id_tag_rel`), KEY `All_Tag_Relations_FKIndex1` (`id_tag`), KEY `id_wc` (`id_wc`) ) ENGINE=InnoDB DEFAULT CHARSET=latin1 AUTO_INCREMENT=19 ; INSERT INTO `all_tag_relations` (`id_tag_rel`, `id_tag`, `id_tutor`, `id_wc`) VALUES (1, 1, 1, NULL), (2, 2, 1, NULL), (3, 6, 2, NULL), (4, 7, 2, NULL), (8, 3, 1, 1), (9, 4, 1, 1), (10, 5, 2, 2), (11, 4, 2, 2), (15, 8, 1, 3), (16, 9, 1, 3), (17, 10, 1, 4), (18, 4, 1, 4), (19, 1, 2, 5), (20, 4, 2, 5); CREATE TABLE IF NOT EXISTS `tags` ( `id_tag` int(10) unsigned NOT NULL AUTO_INCREMENT, `tag` varchar(255) DEFAULT NULL, PRIMARY KEY (`id_tag`), UNIQUE KEY `tag` (`tag`), KEY `id_tag` (`id_tag`), KEY `tag_2` (`tag`), KEY `tag_3` (`tag`), KEY `tag_4` (`tag`), FULLTEXT KEY `tag_5` (`tag`) ) ENGINE=MyISAM DEFAULT CHARSET=latin1 AUTO_INCREMENT=11 ; INSERT INTO `tags` (`id_tag`, `tag`) VALUES (1, 'Sandeepan'), (2, 'Nath'), (3, 'first'), (4, 'class'), (5, 'new'), (6, 'Bob'), (7, 'Cratchit'), (8, 'more'), (9, 'fresh'), (10, 'second'); CREATE TABLE IF NOT EXISTS `webclasses` ( `id_wc` int(10) NOT NULL AUTO_INCREMENT, `id_author` int(10) NOT NULL, `name` varchar(50) DEFAULT NULL, PRIMARY KEY (`id_wc`) ) ENGINE=InnoDB DEFAULT CHARSET=latin1 AUTO_INCREMENT=5 ; INSERT INTO `webclasses` (`id_wc`, `id_author`, `name`) VALUES (1, 1, 'first class'), (2, 2, 'new class'), (3, 1, 'more fresh'), (4, 1, 'second class'), (5, 2, 'sandeepan class'); About the system - The system consists of tutors and classes. - The data in the table All_Tag_Relations stores tag relations for each tutor registered and each class created by a tutor. The tag relations are used for searching classes. The current data dump corresponds to tutor "Sandeepan Nath" who has created classes named "first class", "more fresh", "second class" and tutor "Bob Cratchit" who has created classes "new class" and "Sandeepan class". I am trying for a search query performs AND logic on the search keywords and returns wvery such class for which the search terms are present in the class name or its tutor name To make it easy, following is the list of search terms and desired results:- Search term result classes (check the id_wc in the results) first class 1 Sandeepan Nath class 1 Sandeepan Nath 1,3 Bob Cratchit 2 Sandeepan Nath bob none Sandeepan Class 1,4,5 I have so far reached upto this query -- Two keywords search SET @tag1 = 4, @tag2 = 1; -- Setting some user variables to see where the ids go. SELECT wc.id_wc, sum( DISTINCT ( wtagrels.id_tag = @tag1 ) ) AS key_1_class_matches, sum( DISTINCT ( wtagrels.id_tag = @tag2 ) ) AS key_2_class_matches, sum( DISTINCT ( ttagrels.id_tag = @tag1 ) ) AS key_1_tutor_matches, sum( DISTINCT ( ttagrels.id_tag = @tag2 ) ) AS key_2_tutor_matches, sum( DISTINCT ( ttagrels.id_tag = wtagrels.id_tag ) ) AS key_class_tutor_matches FROM WebClasses as wc join all_tag_relations AS wtagrels on wc.id_wc = wtagrels.id_wc join all_tag_relations as ttagrels on (wc.id_author = ttagrels.id_tutor) WHERE ( wtagrels.id_tag = @tag1 OR wtagrels.id_tag = @tag2 OR ttagrels.id_tag = @tag1 OR ttagrels.id_tag = @tag2 ) GROUP BY wtagrels.id_wc LIMIT 0 , 20 For search with 1 or 3 terms, remove/add the variable part in this query. Tabulating my observation of the values of key_1_class_matches, key_2_class_matches,key_1_tutor_matches (say, class keys),key_2_tutor_matches for various cases (say, tutor keys). Search term expected result Observation first class 1 for class 1, all class keys+all tutor keys =1 Sandeepan Nath class 1 for class 1, one class key+ all tutor keys = 1 Sandeepan Nath 1,3 both tutor keys =1 for these classes Bob Cratchit 2 both tutor keys = 1 Sandeepan Nath bob none no complete tutor matches for any class I found a pattern that, for any case, the class(es) which should appear in the result have the highest number of matches (all class keys and tutor keys). E.g. searching "first class", only for class =1, total of key matches = 4(1+1+1+1) searching "Sandeepan Nath", for classes 1, 3,4(all classes by Sandeepan Nath) have all the tutor keys matching. But no pattern in the search for "Sandeepan Class" - classes 1,4,5 should match. Now, how do I put a condition into the query, based on that pattern so that only those classes are returned. Do I need to use full text search here because it gives a scoring/rank value indicating the strength of the match? Any sample query would help. Please note - I have already found solution for showing classes when any/all of the search terms match with the class name. http://stackoverflow.com/questions/3030022/mysql-help-me-alter-this-search-query-to-get-desired-results But if all the search terms are in tutor name, it does not work. So, I am modifying the query and experimenting.

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  • Help me alter this query to get the desired results

    - by sandeepan
    Please dump these data first CREATE TABLE IF NOT EXISTS `all_tag_relations` ( `id_tag_rel` int(10) NOT NULL AUTO_INCREMENT, `id_tag` int(10) unsigned NOT NULL DEFAULT '0', `id_tutor` int(10) DEFAULT NULL, `id_wc` int(10) unsigned DEFAULT NULL, PRIMARY KEY (`id_tag_rel`), KEY `All_Tag_Relations_FKIndex1` (`id_tag`), KEY `id_wc` (`id_wc`) ) ENGINE=InnoDB DEFAULT CHARSET=latin1 AUTO_INCREMENT=19 ; INSERT INTO `all_tag_relations` (`id_tag_rel`, `id_tag`, `id_tutor`, `id_wc`) VALUES (1, 1, 1, NULL), (2, 2, 1, NULL), (3, 6, 2, NULL), (4, 7, 2, NULL), (8, 3, 1, 1), (9, 4, 1, 1), (10, 5, 2, 2), (11, 4, 2, 2), (15, 8, 1, 3), (16, 9, 1, 3), (17, 10, 1, 4), (18, 4, 1, 4), (19, 1, 2, 5), (20, 4, 2, 5); CREATE TABLE IF NOT EXISTS `tags` ( `id_tag` int(10) unsigned NOT NULL AUTO_INCREMENT, `tag` varchar(255) DEFAULT NULL, PRIMARY KEY (`id_tag`), UNIQUE KEY `tag` (`tag`), KEY `id_tag` (`id_tag`), KEY `tag_2` (`tag`), KEY `tag_3` (`tag`), KEY `tag_4` (`tag`), FULLTEXT KEY `tag_5` (`tag`) ) ENGINE=MyISAM DEFAULT CHARSET=latin1 AUTO_INCREMENT=11 ; INSERT INTO `tags` (`id_tag`, `tag`) VALUES (1, 'Sandeepan'), (2, 'Nath'), (3, 'first'), (4, 'class'), (5, 'new'), (6, 'Bob'), (7, 'Cratchit'), (8, 'more'), (9, 'fresh'), (10, 'second'); CREATE TABLE IF NOT EXISTS `webclasses` ( `id_wc` int(10) NOT NULL AUTO_INCREMENT, `id_author` int(10) NOT NULL, `name` varchar(50) DEFAULT NULL, PRIMARY KEY (`id_wc`) ) ENGINE=InnoDB DEFAULT CHARSET=latin1 AUTO_INCREMENT=5 ; INSERT INTO `webclasses` (`id_wc`, `id_author`, `name`) VALUES (1, 1, 'first class'), (2, 2, 'new class'), (3, 1, 'more fresh'), (4, 1, 'second class'), (5, 2, 'sandeepan class'); About the system - The system consists of tutors and classes. - The data in the table All_Tag_Relations stores tag relations for each tutor registered and each class created by a tutor. The tag relations are used for searching classes. The current data dump corresponds to tutor "Sandeepan Nath" who has created classes named "first class", "more fresh", "second class" and tutor "Bob Cratchit" who has created classes "new class" and "Sandeepan class". I am trying for a search query performs AND logic on the search keywords and returns wvery such class for which the search terms are present in the class name or its tutor name To make it easy, following is the list of search terms and desired results:- Search term result classes (check the id_wc in the results) first class 1 Sandeepan Nath class 1 Sandeepan Nath 1,3 Bob Cratchit 2 Sandeepan Nath bob none Sandeepan Class 1,4,5 I have so far reached upto this query -- Two keywords search SET @tag1 = 4, @tag2 = 1; -- Setting some user variables to see where the ids go. SELECT wc.id_wc, sum( DISTINCT ( wtagrels.id_tag = @tag1 ) ) AS key_1_class_matches, sum( DISTINCT ( wtagrels.id_tag = @tag2 ) ) AS key_2_class_matches, sum( DISTINCT ( ttagrels.id_tag = @tag1 ) ) AS key_1_tutor_matches, sum( DISTINCT ( ttagrels.id_tag = @tag2 ) ) AS key_2_tutor_matches, sum( DISTINCT ( ttagrels.id_tag = wtagrels.id_tag ) ) AS key_class_tutor_matches FROM WebClasses as wc join all_tag_relations AS wtagrels on wc.id_wc = wtagrels.id_wc join all_tag_relations as ttagrels on (wc.id_author = ttagrels.id_tutor) WHERE ( wtagrels.id_tag = @tag1 OR wtagrels.id_tag = @tag2 OR ttagrels.id_tag = @tag1 OR ttagrels.id_tag = @tag2 ) GROUP BY wtagrels.id_wc LIMIT 0 , 20 For search with 1 or 3 terms, remove/add the variable part in this query. Tabulating my observation of the values of key_1_class_matches, key_2_class_matches,key_1_tutor_matches (say, class keys),key_2_tutor_matches for various cases (say, tutor keys). Search term expected result Observation first class 1 for class 1, all class keys+all tutor keys =1 Sandeepan Nath class 1 for class 1, one class key+ all tutor keys = 1 Sandeepan Nath 1,3 both tutor keys =1 for these classes Bob Cratchit 2 both tutor keys = 1 Sandeepan Nath bob none no complete tutor matches for any class I found a pattern that, for any case, the class(es) which should appear in the result have the highest number of matches (all class keys and tutor keys). E.g. searching "first class", only for class =1, total of key matches = 4(1+1+1+1) searching "Sandeepan Nath", for classes 1, 3,4(all classes by Sandeepan Nath) have all the tutor keys matching. But no pattern in the search for "Sandeepan Class" - classes 1,4,5 should match. Now, how do I put a condition into the query, based on that pattern so that only those classes are returned. Do I need to use full text search here because it gives a scoring/rank value indicating the strength of the match? Any sample query would help. Please note - I have already found solution for showing classes when any/all of the search terms match with the class name. http://stackoverflow.com/questions/3030022/mysql-help-me-alter-this-search-query-to-get-desired-results But if all the search terms are in tutor name, it does not work. So, I am modifying the query and experimenting.

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  • Getting timing consistency in Linux

    - by Jim Hunziker
    I can't seem to get a simple program (with lots of memory access) to achieve consistent timing in Linux. I'm using a 2.6 kernel, and the program is being run on a dual-core processor with realtime priority. I'm trying to disable cache effects by declaring the memory arrays as volatile. Below are the results and the program. What are some possible sources of the outliers? Results: Number of trials: 100 Range: 0.021732s to 0.085596s Average Time: 0.058094s Standard Deviation: 0.006944s Extreme Outliers (2 SDs away from mean): 7 Average Time, excluding extreme outliers: 0.059273s Program: #include <stdio.h> #include <stdlib.h> #include <math.h> #include <sched.h> #include <sys/time.h> #define NUM_POINTS 5000000 #define REPS 100 unsigned long long getTimestamp() { unsigned long long usecCount; struct timeval timeVal; gettimeofday(&timeVal, 0); usecCount = timeVal.tv_sec * (unsigned long long) 1000000; usecCount += timeVal.tv_usec; return (usecCount); } double convertTimestampToSecs(unsigned long long timestamp) { return (timestamp / (double) 1000000); } int main(int argc, char* argv[]) { unsigned long long start, stop; double times[REPS]; double sum = 0; double scale, avg, newavg, median; double stddev = 0; double maxval = -1.0, minval = 1000000.0; int i, j, freq, count; int outliers = 0; struct sched_param sparam; sched_getparam(getpid(), &sparam); sparam.sched_priority = sched_get_priority_max(SCHED_FIFO); sched_setscheduler(getpid(), SCHED_FIFO, &sparam); volatile float* data; volatile float* results; data = calloc(NUM_POINTS, sizeof(float)); results = calloc(NUM_POINTS, sizeof(float)); for (i = 0; i < REPS; ++i) { start = getTimestamp(); for (j = 0; j < NUM_POINTS; ++j) { results[j] = data[j]; } stop = getTimestamp(); times[i] = convertTimestampToSecs(stop-start); } free(data); free(results); for (i = 0; i < REPS; i++) { sum += times[i]; if (times[i] > maxval) maxval = times[i]; if (times[i] < minval) minval = times[i]; } avg = sum/REPS; for (i = 0; i < REPS; i++) stddev += (times[i] - avg)*(times[i] - avg); stddev /= REPS; stddev = sqrt(stddev); for (i = 0; i < REPS; i++) { if (times[i] > avg + 2*stddev || times[i] < avg - 2*stddev) { sum -= times[i]; outliers++; } } newavg = sum/(REPS-outliers); printf("Number of trials: %d\n", REPS); printf("Range: %fs to %fs\n", minval, maxval); printf("Average Time: %fs\n", avg); printf("Standard Deviation: %fs\n", stddev); printf("Extreme Outliers (2 SDs away from mean): %d\n", outliers); printf("Average Time, excluding extreme outliers: %fs\n", newavg); return 0; }

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  • Matrix Multiplication with Threads: Why is it not faster?

    - by prelic
    Hey all, So I've been playing around with pthreads, specifically trying to calculate the product of two matrices. My code is extremely messy because it was just supposed to be a quick little fun project for myself, but the thread theory I used was very similar to: #include <pthread.h> #include <stdio.h> #include <stdlib.h> #define M 3 #define K 2 #define N 3 #define NUM_THREADS 10 int A [M][K] = { {1,4}, {2,5}, {3,6} }; int B [K][N] = { {8,7,6}, {5,4,3} }; int C [M][N]; struct v { int i; /* row */ int j; /* column */ }; void *runner(void *param); /* the thread */ int main(int argc, char *argv[]) { int i,j, count = 0; for(i = 0; i < M; i++) { for(j = 0; j < N; j++) { //Assign a row and column for each thread struct v *data = (struct v *) malloc(sizeof(struct v)); data->i = i; data->j = j; /* Now create the thread passing it data as a parameter */ pthread_t tid; //Thread ID pthread_attr_t attr; //Set of thread attributes //Get the default attributes pthread_attr_init(&attr); //Create the thread pthread_create(&tid,&attr,runner,data); //Make sure the parent waits for all thread to complete pthread_join(tid, NULL); count++; } } //Print out the resulting matrix for(i = 0; i < M; i++) { for(j = 0; j < N; j++) { printf("%d ", C[i][j]); } printf("\n"); } } //The thread will begin control in this function void *runner(void *param) { struct v *data = param; // the structure that holds our data int n, sum = 0; //the counter and sum //Row multiplied by column for(n = 0; n< K; n++){ sum += A[data->i][n] * B[n][data->j]; } //assign the sum to its coordinate C[data->i][data->j] = sum; //Exit the thread pthread_exit(0); } source: http://macboypro.com/blog/2009/06/29/matrix-multiplication-in-c-using-pthreads-on-linux/ For the non-threaded version, I used the same setup (3 2-d matrices, dynamically allocated structs to hold r/c), and added a timer. First trials indicated that the non-threaded version was faster. My first thought was that the dimensions were too small to notice a difference, and it was taking longer to create the threads. So I upped the dimensions to about 50x50, randomly filled, and ran it, and I'm still not seeing any performance upgrade with the threaded version. What am I missing here?

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  • Calculate the number of ways to roll a certain number

    - by helloworld
    I'm a high school Computer Science student, and today I was given a problem to: Program Description: There is a belief among dice players that in throwing three dice a ten is easier to get than a nine. Can you write a program that proves or disproves this belief? Have the computer compute all the possible ways three dice can be thrown: 1 + 1 + 1, 1 + 1 + 2, 1 + 1 + 3, etc. Add up each of these possibilities and see how many give nine as the result and how many give ten. If more give ten, then the belief is proven. I quickly worked out a brute force solution, as such int sum,tens,nines; tens=nines=0; for(int i=1;i<=6;i++){ for(int j=1;j<=6;j++){ for(int k=1;k<=6;k++){ sum=i+j+k; //Ternary operators are fun! tens+=((sum==10)?1:0); nines+=((sum==9)?1:0); } } } System.out.println("There are "+tens+" ways to roll a 10"); System.out.println("There are "+nines+" ways to roll a 9"); Which works just fine, and a brute force solution is what the teacher wanted us to do. However, it doesn't scale, and I am trying to find a way to make an algorithm that can calculate the number of ways to roll n dice to get a specific number. Therefore, I started generating the number of ways to get each sum with n dice. With 1 die, there is obviously 1 solution for each. I then calculated, through brute force, the combinations with 2 and 3 dice. These are for two: There are 1 ways to roll a 2 There are 2 ways to roll a 3 There are 3 ways to roll a 4 There are 4 ways to roll a 5 There are 5 ways to roll a 6 There are 6 ways to roll a 7 There are 5 ways to roll a 8 There are 4 ways to roll a 9 There are 3 ways to roll a 10 There are 2 ways to roll a 11 There are 1 ways to roll a 12 Which looks straightforward enough; it can be calculated with a simple linear absolute value function. But then things start getting trickier. With 3: There are 1 ways to roll a 3 There are 3 ways to roll a 4 There are 6 ways to roll a 5 There are 10 ways to roll a 6 There are 15 ways to roll a 7 There are 21 ways to roll a 8 There are 25 ways to roll a 9 There are 27 ways to roll a 10 There are 27 ways to roll a 11 There are 25 ways to roll a 12 There are 21 ways to roll a 13 There are 15 ways to roll a 14 There are 10 ways to roll a 15 There are 6 ways to roll a 16 There are 3 ways to roll a 17 There are 1 ways to roll a 18 So I look at that, and I think: Cool, Triangular numbers! However, then I notice those pesky 25s and 27s. So it's obviously not triangular numbers, but still some polynomial expansion, since it's symmetric. So I take to Google, and I come across this page that goes into some detail about how to do this with math. It is fairly easy(albeit long) to find this using repeated derivatives or expansion, but it would be much harder to program that for me. I didn't quite understand the second and third answers, since I have never encountered that notation or those concepts in my math studies before. Could someone please explain how I could write a program to do this, or explain the solutions given on that page, for my own understanding of combinatorics? EDIT: I'm looking for a mathematical way to solve this, that gives an exact theoretical number, not by simulating dice

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  • Strange behaviour of CUDA kernel

    - by username_4567
    I'm writing code for calculating prefix sum. Here is my kernel __global__ void prescan(int *indata,int *outdata,int n,long int *sums) { extern __shared__ int temp[]; int tid=threadIdx.x; int offset=1,start_id,end_id; int *global_sum=&temp[n+2]; if(tid==0) { temp[n]=blockDim.x*blockIdx.x; temp[n+1]=blockDim.x*(blockIdx.x+1)-1; start_id=temp[n]; end_id=temp[n+1]; //cuPrintf("Value of start %d and end %d\n",start_id,end_id); } __syncthreads(); start_id=temp[n]; end_id=temp[n+1]; temp[tid]=indata[start_id+tid]; temp[tid+1]=indata[start_id+tid+1]; for(int d=n>>1;d>0;d>>=1) { __syncthreads(); if(tid<d) { int ai=offset*(2*tid+1)-1; int bi=offset*(2*tid+2)-1; temp[bi]+=temp[ai]; } offset*=2; } if(tid==0) { sums[blockIdx.x]=temp[n-1]; temp[n-1]=0; cuPrintf("sums %d\n",sums[blockIdx.x]); } for(int d=1;d<n;d*=2) { offset>>=1; __syncthreads(); if(tid<d) { int ai=offset*(2*tid+1)-1; int bi=offset*(2*tid+2)-1; int t=temp[ai]; temp[ai]=temp[bi]; temp[bi]+=t; } } __syncthreads(); if(tid==0) { outdata[start_id]=0; } __threadfence_block(); __syncthreads(); outdata[start_id+tid]=temp[tid]; outdata[start_id+tid+1]=temp[tid+1]; __syncthreads(); if(tid==0) { temp[0]=0; outdata[start_id]=0; } __threadfence_block(); __syncthreads(); if(blockIdx.x==0 && threadIdx.x==0) { for(int i=1;i<gridDim.x;i++) { sums[i]=sums[i]+sums[i-1]; } } __syncthreads(); __threadfence(); if(blockIdx.x==0 && threadIdx.x==0) { for(int i=0;i<gridDim.x;i++) { cuPrintf("****sums[%d]=%d ",i,sums[i]); } } __syncthreads(); __threadfence(); if(blockIdx.x!=gridDim.x-1) { int tid=(blockIdx.x+1)*blockDim.x+threadIdx.x; if(threadIdx.x==0) cuPrintf("Adding %d \n",sums[blockIdx.x]); outdata[tid]+=sums[blockIdx.x]; } __syncthreads(); } In above kernel, sums array will accumulate prefix sum per block and and then first thread will calculate prefix sum of this sum array. Now if I print this sum array from device side it'll show correct results while in cuPrintf("Adding %d \n",sums[blockIdx.x]); this line it prints that it is taking old value. What could be the reason?

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  • Will disabling hyperthreading improve performance on our SQL Server install

    - by Sam Saffron
    Related to: Current wisdom on SQL Server and Hyperthreading Recently we upgraded our Windows 2008 R2 database server from an X5470 to a X5560. The theory is both CPUs have very similar performance, if anything the X5560 is slightly faster. However, SQL Server 2008 R2 performance has been pretty bad over the last day or so and CPU usage has been pretty high. Page life expectancy is massive, we are getting almost 100% cache hit for the pages, so memory is not a problem. When I ran: SELECT * FROM sys.dm_os_wait_stats order by signal_wait_time_ms desc I got: wait_type waiting_tasks_count wait_time_ms max_wait_time_ms signal_wait_time_ms ------------------------------------------------------------ -------------------- -------------------- -------------------- -------------------- XE_TIMER_EVENT 115166 2799125790 30165 2799125065 REQUEST_FOR_DEADLOCK_SEARCH 559393 2799053973 5180 2799053973 SOS_SCHEDULER_YIELD 152289883 189948844 960 189756877 CXPACKET 234638389 2383701040 141334 118796827 SLEEP_TASK 170743505 1525669557 1406 76485386 LATCH_EX 97301008 810738519 1107 55093884 LOGMGR_QUEUE 16525384 2798527632 20751319 4083713 WRITELOG 16850119 18328365 1193 2367880 PAGELATCH_EX 13254618 8524515 11263 1670113 ASYNC_NETWORK_IO 23954146 6981220 7110 1475699 (10 row(s) affected) I also ran -- Isolate top waits for server instance since last restart or statistics clear WITH Waits AS ( SELECT wait_type, wait_time_ms / 1000. AS [wait_time_s], 100. * wait_time_ms / SUM(wait_time_ms) OVER() AS [pct], ROW_NUMBER() OVER(ORDER BY wait_time_ms DESC) AS [rn] FROM sys.dm_os_wait_stats WHERE wait_type NOT IN ('CLR_SEMAPHORE','LAZYWRITER_SLEEP','RESOURCE_QUEUE', 'SLEEP_TASK','SLEEP_SYSTEMTASK','SQLTRACE_BUFFER_FLUSH','WAITFOR','LOGMGR_QUEUE', 'CHECKPOINT_QUEUE','REQUEST_FOR_DEADLOCK_SEARCH','XE_TIMER_EVENT','BROKER_TO_FLUSH', 'BROKER_TASK_STOP','CLR_MANUAL_EVENT','CLR_AUTO_EVENT','DISPATCHER_QUEUE_SEMAPHORE', 'FT_IFTS_SCHEDULER_IDLE_WAIT','XE_DISPATCHER_WAIT', 'XE_DISPATCHER_JOIN')) SELECT W1.wait_type, CAST(W1.wait_time_s AS DECIMAL(12, 2)) AS wait_time_s, CAST(W1.pct AS DECIMAL(12, 2)) AS pct, CAST(SUM(W2.pct) AS DECIMAL(12, 2)) AS running_pct FROM Waits AS W1 INNER JOIN Waits AS W2 ON W2.rn <= W1.rn GROUP BY W1.rn, W1.wait_type, W1.wait_time_s, W1.pct HAVING SUM(W2.pct) - W1.pct < 95; -- percentage threshold And got wait_type wait_time_s pct running_pct CXPACKET 554821.66 65.82 65.82 LATCH_EX 184123.16 21.84 87.66 SOS_SCHEDULER_YIELD 37541.17 4.45 92.11 PAGEIOLATCH_SH 19018.53 2.26 94.37 FT_IFTSHC_MUTEX 14306.05 1.70 96.07 That shows huge amounts of time synchronizing queries involving parallelism (high CXPACKET). Additionally, anecdotally many of these problem queries are being executed on multiple cores (we have no MAXDOP hints anywhere in our code) The server has not been under load for more than a day or so. We are experiencing a large amount of variance with query executions, typically many queries appear to be slower that they were on our previous DB server and CPU is really high. Will disabling Hyperthreading help at reducing our CPU usage and increase throughput?

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  • Pivot tables: How can I total the subtotal?

    - by Mike
    Person A needs £115, Person D £234 and Person G £789, but how do I SUM that and get it to show on the same ROW as the subtotal? The Rows are subscription names. The Value field holds the Cost per subscription. the Columns holds the name of the person who receives the subscription. I have GROUPED on YEAR & MONTH, and have a subtotal that shows me how much each person will need to pay each month for all their subscriptions, but I need a figure showing me the total of all the subscriptions per month. I've tried adding calculated fields, but I want to SUM the subtotals so I'm struggling to see the field I need to use. I've tried Grand Totals but that SUMS all rows and I really only want SUM the Subtotal Total Row. I need a nice neat report that my managers won't go white at when looking at it...to many numbers = fear and confusion. Anyway it got messy, so I've come for help. Cheers Mike.

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  • How flexible is the 'indirect' function?

    - by Chuck
    My curiosity pushes me to ask this question. If I were to have a series of functions that referenced a different column in a worksheet but all ended on the same row of data is there a way to point the 'row' part of a cell reference to a blank cell and use it has a variable to show the results of the functions up to a desired row simultaneously? Example: =Average('worksheet 1'.$A$1:'worksheet 1'.$A100) =Max('worksheet 1'.$B$1:'worksheet 1'.$B100) =Min('worksheet 1'.$C$1:'worksheet 1'.$C100) =Sum('worksheet 1'.$D$1:'worksheet 1'.$D100) Pseudo formulas... =Average('worksheet 1'.$A$1:'worksheet 1'.$A*('worksheet 2'.$A$1)*) =Max('worksheet 1'.$B$1:'worksheet 1'.$B*('worksheet 2'.$A$1)*) =Min('worksheet 1'.$C$1:'worksheet 1'.$C*('worksheet 2'.$A$1)*) =Sum('worksheet 1'.$D$1:'worksheet 1'.$D*('worksheet 2'.$A$1)*) Where 'worksheet 2'.$A$1 would only contain a number corresponding to a row in 'worksheet 1'. After stumbling upon and playing with the indirect() function I have only been able to replace the entire cell reference (Column and Row) with any success. The formula so far =SUM('worksheet 1'.C3:INDIRECT(A1)) Where A1 is on 'worksheet 2' and contains a full cell reference pointing to 'worksheet 1'. Any pointers?

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  • How do I convert an INT into HH:mm:ss using SSRS 2005

    - by user293249
    Ok I need to display total talk time of an agent that is coming into SRSS 2005 from SQL 2005 as an INT. For the life of me I cannot figure out what combination of expression editing or format editing I need to use. For the detail portion I can use: =DATEADD("s", SUM(Fields!Talk_Time.Value), CDate("00:00")) And it will return: 1/1/0001 12:00:14 AM Now I can use =LEFT(DATEADD("s", SUM(Fields!Talk_Time.Value), CDate("00:00")),8) Which will return: 12:00:14 But really what I need is: 00:00:14 Please help!

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  • Zend DB returning NULL value

    - by davykiash
    I have the following query that extends from Zend_DB_Table_Abstract $select = $this->select() ->from('expense_details', array('SUM(expense_details_amount) AS total')) ->where('YEAR(expense_details_date) = ?', '2010') ->where('MONTH(expense_details_date) = ?', '01') ->where('expense_details_linkemail = ?', '[email protected]'); However it returning a NULL value despite its "equivalent" returning the desired value SELECT SUM(expense_details_amount) AS total FROM expense_details WHERE YEAR(expense_details_date) = '2010' AND MONTH(expense_details_date) = '01' AND expense_details_linkemail = '[email protected]' Is my Zend_DB_Table construct above correct?

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  • Linq to sql, summing timespan?

    - by DaRKoN_
    I have a time field in a mssql 2008 database that I want to do something to the effect of: Timespent = x.sum(x => x.AmountOfTime); Where AmountOfTime is a time MSSQL field. Sum seems to only work on decimals, how can I add these columns?

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  • Invoking methods on objects in java.

    - by David
    If i have a class called Dice which contains this method: public void roll () { this.x = randNum(1, this.sum.length) ; this.sum[x] ++ ; } And i am in a diferent class how do i invoke this method? I am currently trying InstanceOfObjectName.Dice.roll and its not working. What should i do?

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  • ActiveRecord + CodeIgniter - Return single value from query, not in array form.

    - by txmail
    Say you construct an activerecord query that will always just return a single value, how do you just address that single value instead of getting an array in return? For instance I am using an ActiveRecord query to return the SUM of a single column, it will only return this one single SUM, instead of having to parse the array is there a way to assign the value as a function return equal to that value instead of getting an array?

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  • Operations on Python hashes

    - by cdecker
    I've got a rather strange problem. For a Distributed Hash Table I need to be able to do some simple math operations on MD5 hashes. These include a sum (numeric sum represented by the hash) and a modulo operation. Now I'm wondering what the best way to implement these operations is. I'm using hashlib to calculate the hashes, but since the hashes I get are then string, how do I calculate with them?

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  • Objective C: CoreData and aggregation

    - by Ralf
    Given a CoreData-Entity with an date (days) and an ammount called Transaction. Is it with CoreData possible (and how) to aggregate/group the 'table' (with all Transactions) by Date and calculate the sum of the day in a second column/attribute? (the SQL-Solution would be SELECT date, sum(ammount) FROM transaction GROUP BY date)

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  • Adding custom query to paginator (KNP Paginator) in Symfony2?

    - by Unni
    I have the following query , how to write these query in Symfony2 SELECT Inventory_Stock.id, Inventory_Stock.quantity, SUM(InventoryUsage.quantity) ,Inventory_Stock.quantity - SUM(InventoryUsage.quantity) AS Stock FROM Inventory_Stock LEFT JOIN InventoryUsage ON Inventory_Stock.id = InventoryUsage.InventoryStock_id WHERE Inventory_Stock.id = 26 OR Inventory_Stock.id = 27 GROUP BY Inventory_Stock.id ORDER BY Stock DESC I need to paginate this as well Would be great if any one could help me out as this has been pulling my hair out for couple of days.

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  • Oneliner-question

    - by sid_com
    I proudly present a solution to the problem: perl -00 -F"\n" -anE '$_ = ( split / /, $F[1] )[0]; if ( !/error/ ) { $sum += $_; $c++ } } { say $sum / $c' file The problem: the first field of the second line of each paragraph if it is not error. How could I do this without the paragraph-mode? perl -anE 'say $F[0] if not /error/ and the second /\S+/ after /^$/' file

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