algorithm - How to determine the runtime of this function -


i'm having trouble basic runtime understanding, maybe can clarify me. how go determining runtime of function?

i need determine rather f = o(g) or f = omega(g) or f = theta(g)

f(n) = 100n + logn
g(n) = n + (logn)2

so 100n , n in same order; , linear time > log time; @ point still need @ log part? or can determine f = theta(g)?

you can safely determine same order of magnitude. there no need @ "log part".

here formal proof specific case, general proof can shown limit arithmetic.

let's @ function h(n) = f(n)/g(n) n approaches infinity, if stays bounded above 0 , below number m know f(x) = theta(g(x)) (because of how theta defined).

so have h(n) = (100n + logn)/(n + logn^2)

we know if show for real x, holds natural numbers too. enough show for:

h(x) = (100x + logx)/(x + logx^2)

we know l'hospital's rule if derivatives of nominator , denominator exist , converge limit of original function exists , equals same number too. let's apply , get:

lim x-> infinity , h(x) = (100x + logx)/(x + logx^2) =   lim x-> infinity , (100+1/x) / (1 + (2log(x) / x) )

we know 1/x approaches 0 x approaches infinity, , (2logx)/x approaches 0 x approaches infinity (in words (time > log time)). limit arithmetic

lim x-> infinity h(x) = 100/1 = 100

since limit exists in r , nonzero f(x) = theta(g(x)) wanted show.


Comments

Post a Comment

Popular posts from this blog

SPSS keyboard combination alters encoding -

my question not have programming practical issue on spss. accident keyword combination cannot remember because did not intend press changed encoding in spss , text in data in different language english shown small boxes. nevertheless, when kind of analysis performed different language text shown in output. does know reason? tried change encoding did not produce result. first, @ edit > options , see whether setting unicode or locale. might fix it. if have text in multiple languages, want unicode. otherwise, may have specific locale set wrong. can change set locale, need know locale want use.
Read more

Add new record to the table by click on the button in Microsoft Access -

in ms access form want implement separate button, adds new record table. in order added button , attached button event: private sub btnaddrec_click() refresh codecontextobject on error resume next docmd.gotorecord , , acnewrec if err.number <> 0 btnaddrec.enabled = false end if end end sub everything ok when open window , click btnaddrec button, problem when first of perform navigation through existed records , after click on button. got runtime error: 2105: «you can't go specified record. may @ end of recordset» . how solve issue, need have ability add new record on click on specific button, no matter, have walked or not walked through records before. thanks. i created simple form field call description (and autonumber) , created button code follows click event. filled number of records , navigated through them, clicked addnewrec button. form navigated new record without issues. able click addnewrec button directly after
Read more

CSS3 Transition to highlight new elements created in JQuery -

i want use css3 color transition apply highlight-fading color effect (yellow transparent) new elements appended markup using jquery. css #content div { background-color:transparent; -moz-transition:background-color 2s; -webkit-transition:background-color 2s; -o-transition:background-color 2s; transition:background-color 2s; } #content div.new { background-color:yellow; } html <div id="content"></div> <a id="add-element" href="#">add new element</a> js $('#add-element').click(function() { var newelement = $('<div class="new">new element</div>'); $('#content').append(newelement); newelement.removeclass('new'); }); when click link, new element created. class "new" (background color yellow) , it's appended html markup. should able remove "new" class trigger background color transition transparent (or whate
Read more