algorithm - O(n log n) vs O(n) -- practical differences in time complexity -


n log n > n -- pseudo-linear relationship. if n=1 billion, log n ~ 30;

so n log n 30 billion, 30 x n, order of n. wondering if time complexity difference between n log n , n significant in real life.

eg: quick select on finding kth element in unsorted array o(n) using quickselect algorithm.

if sort array , find kth element, o(n log n). sort array 1 trillion elements, 60 times slower if quicksort , index it. me sounds not big difference, need opinion of experts here.

the main purpose of big-o notation let estimates ones did in post, , decide if spending effort coding typically more advanced algorithm worth additional cpu cycles going buy code improvement. depending on circumstances, may different answer, when data set relatively small:

  • if running on mobile device, , algorithm represents significant portion of execution time, cutting down use of cpu translates extending battery life
  • if running in all-or-nothing competitive environment, such high-frequency trading system, micro-optimization may differentiate between making money , losing money
  • when profiling shows algorithm in question dominates execution time in server environment, switching faster algorithm may improve performance clients.

another thing big-o notation hides constant multiplication factor. example, quick select has reasonable multiplier, making time savings employing on extremely large data sets worth trouble of implementing it.

another thing need keep in mind space complexity. often, algorithms o(n*log n) time complexity have o(log n) space complexity. may present problem extremely large data sets, example when recursive function runs on system limited stack capacity.


-

Comments

Post a Comment

Popular posts from this blog

html - Sizing a high-res image (~8MB) to display entirely in a small div (circular, diameter 100px) -

first of all, thank being patient know simple question more couple of weeks' experience figure out. i've seen folks persevere , helpful on here , hope you're willing me. here fiddle: http://jsfiddle.net/65uzf/ here 1 of places searched answers on here: ( vertically center image thumbnails fix-sized div ) tried solutions on there , didn't work out me. i've searched ~4 or 5 others, , been unsuccessful those, too. what want take large image (what linked background-image #ysypic , #tabpic divs) , display thumbnail version of image in confines of divs have set it. is, using background properties have laid out in css, portion of image displays inside of circular divs. without these properties, display defaults smaller section of image [presumably pi*(50^2) area in top left] terrible resolution. i not care if entire image doesn't display inside of circles (it won't, given difference in shape), , overflow not being displayed fine. want able see figu
Read more

java - IntelliJ - No such instance method -

using intellij's 12 ultimate, i'm running following code in debugger: java import play.api.libs.json.jsvalue; public class foo { ... public jsvalue tojson() { ... } public class fooexample { ... foo foo = new foo(); system.out.println("...); //<-- breakpoint at breakpoint, right-clicked source code , picked "evaluate expression," typing in: foo.tojson() . but following error showed up: no such instance method: play.api.libs.json.jsvalue$class.com.foo.foo.tojson () am doing wrong? foo#tojson calls scala code, if matters. edit had breakpoint after instantiation of foo. downvoted it, deserved it. edit my answer no longer valid after op modified question (i.e. moved breakpoint actual is).. a breakpoint hit before line executed. in case foo has not yet been declared or instantiated (i.e. foo constructor has not yet been called). you'll need put breakpoint @ next line (or step on current line) if want evaluate foo .
Read more

identifier - Is it possible for an html5 document to have two ids? -

i wondering if html5 element can have 2 ids, this: <button id="thing1" id="thing2" name="button1" onclick="change()">click here</button> or this: <button id="thing1, thing2" name="button1" onclick="change()">click here</button> also, if 1 of ids said 1 thing, , other id said thing, 1 used? tl;dr : no. in versions of html, each element can have 1 id. see the spec : the id attribute specifies element's unique identifier (id). [dom] the value must unique amongst ids in element's home subtree , must contain @ least 1 character. the value must not contain space characters. note: there no other restrictions on form id can take; in particular, ids can consist of digits, start digit, start underscore, consist of punctuation , etc. note: element's unique identifier can used variety of purposes, notably way link specific parts of document usin
Read more