math - What does the O(1) in "ln ln n / ln 2 + O(1)" mean? -

-

i have difficulty understand o(1) notation in formula, stand constant? why people use big-o notation this?

formula

this formula comes paper "balanced allocations" azar et al., , formulas used in abstract:

abstract

here, term o(1) means "some term o(1)," meaning term n goes infinity bounded above constant. example, might 137, or sin n, or 1 / n2. value described therefore might ln ln n / ln 2 + 137, or ln ln n / ln 2 + sin n, etc.

this use of big-o notation common in formal mathematics when discussing low order terms in formula contribute small amount overall total. authors have written entire expression o(ln ln n), less precise ln ln n / ln 2 + o(1) because obscures fact coefficient on ln ln n 1 / ln 2 , low-order growth term bounded above constant. explicitly writing out " + o(1)", authors able give better precision.

hope helps!


Comments

Post a Comment

Popular posts from this blog

java - Jmockit String final length method mocking Issue -

-
using jmockit 1.2 jar, trying mock string's length method getting unexpected invocation exception: failed: test java.lang.illegalstateexception: missing invocation mocked type @ point; please make sure such invocations appear after declaration of suitable mock field or parameter @ stringdemo.testa$1.<init>(testa.java:17) @ stringdemo.testa.test(testa.java:13) i using testng: @test public void test() throws exception { new expectations() { @mocked("length") string astring; { astring.length(); result = 2; } }; system.out.println(a.showa("test")); } } actual class a: public class { public static int showa(string str){ int a= str.length(); return a; } } this wrong way of recording expected results. shouldn't mock , record string's length() method, record showa() instead. here solution @suppresswarnings("unused...
Read more

What is the difference between data design and data model(ERD) -

-
i have google question , find answer in day. know, data design many many table have list column,and mark pk , fk. why er-diagram have find this? data design process of designing database. main output of data design detailed logical data model of database. some people data design includes of needed logical , physical design choices , physical storage parameters needed generate design in data definition language. technically, database analysis, database analysts (dbas) trained do. while person can both data design , database analysis, these 2 different tasks. data design models data. database analysis takes model , applies 1 or more database engines (relational, hierarchical, nosql). a logical data model 1 of main outputs of data design. data model represented entity relationship diagram, or er diagram.
Read more

ios - Can NSManagedObject conform to NSCoding -

-
i need transfer single object across device. right converting nsmanagedobject dictionary , archiving , sending nsdata. upon receiving unarchiving it. transfer nsmanagedobject archiving , unarchiving instead of creating intermediate data object. @interface test : nsmanagedobject<nscoding> @property (nonatomic, retain) nsstring * title; @end @implementation test @dynamic title; - (id)initwithcoder:(nscoder *)coder { self = [super init]; if (self) { self.title = [coder decodeobjectforkey:@"title"]; //<crash } return self; } - (void)encodewithcoder:(nscoder *)coder { [coder encodeobject:self.title forkey:@"title"]; } @end nsdata *archivedobjects = [nskeyedarchiver archiveddatawithrootobject:testobj]; nsdata *objectsdata = archivedobjects; if ([objectsdata length] > 0) { nsarray *objects = [nskeyedunarchiver unarchiveobjectwithdata:objectsdata]; } the problem above code is. crashes @ self.title in initwithcoder sa...
Read more