algorithm - Sorting a partially sorted array -

-

possible duplicate:
interview q: sorting sorted array (elements misplaced no more k)

i have partially sorted array property every element within d units of sorted position. wondering if there way sort array -- exploiting fact -- in less n log n time.

off top of head...

create "sliding window" of size 2d.

start @ [0,2d). sort elements in window; elements 0 through d-1 guaranteed correct.

slide window forward d, it's [d,3d). sort elements, guaranteeing elements d through 2d-1 correct.

slide forward d, [2d,4d). sort those. , on.

each sort o(d log d), , takes n/d steps end, o(n/d * d log d) = o(n log d). if d constant, that's o(n).

[edit]

you make point in comment; did not prove each iteration preserves property every element within d units of proper position.

so...

lemma: if array property every element within d units of proper position, , sort contiguous subsequence within create array a', every element in a' within d units of proper position.

proof: since lemma properties of sort (not performance), not matter algorithm use sort. use bubble sort. find 2 elements in subsequence out of order, , swap them. there 3 cases: both elements before proper positions in array; both after proper positions in array; or between proper positions in array.

for example, suppose a[i] belongs @ position i' , a[j] belongs @ position j', < j, a[i] > a[j]. follows i' > j' (because elements "belong", , a[i] > a[j]). case 1: suppose i' , j' both greater , j; is, order goes < j < j' < i'. hypothesis, i' d units i, entire range d units wide @ most. j within d units of i' , within d units of j', when swap a[i] a[j], both elements still within d of belong. analysis case 2 , case 3 similar.

so each step of bubble sort -- on subsequence of -- preserve desired property, follows entire bubble sort preserve desired property, follows any sort preserve desired property. q.e.d.


Comments

Post a Comment

Popular posts from this blog

linux - Using a Cron Job to check if my mod_wsgi / apache server is running and restart -

-
my group , running server based upon django , uses mod_wsgi run apache server. not working on project after over, attempting set cronjob similar functionality check if apache server has shut down(system restart or power failure), , if has, restart server me. i've found documentation on how check if apache server down , restart server if is, our server uses https , our start command pretty verbose. can use functionality provided in these examples: https://askubuntu.com/questions/277389/cron-job-to-restart-apache https://www.digitalocean.com/community/tutorials/how-to-use-a-simple-bash-script-to-restart-server-programs or need more complicated process make happen? the command use start server is python manage.py runmodwsgi --host 0.0.0.0 --port 8001 --https-port 8000 --ssl-certificate (certificate location) --server-name (domain name) i'm pretty new linux , using both mod-wsgi apache appreciated. you better off using --setup-only option mod_wsgi-expres...
Read more

actionscript 3 - TweenLite does not work with object -

-
i got following problem: i have object called tempscore game. this object blitted canvas renderer via copypixels method. object not display object. it's score-object (self made). score-object extends object called basicblitarrayobject. basicblitarrayobject extends eventdispatcher (therefore no display object). i tried apply several different tweenlite-plugins tempscore-object (i.e. transformaroundcenter, colormatrixfilter, etc.). nothing happens. absolutely nothing. sometimes error messages (when plugin requires display object , object not display object). far good. according greensock (maker of tweenlite) engine can tween numeric property of object. when plugin transformaroundcenter requires display object tweening have modify plugin working non-display object (tempscore). can't because it's way hard me. my game rests upon code: http://www.8bitrocket.com/book/ch11_blastermines.zip try apply tweenlite object called tempmine inside game class blastermines. ...
Read more

jQuery Ajax Render Fragments OR Whole Page -

-
i'm in throes of building application wraps mess of legacy code. page working on, need substitute fragment divs constructed on back-end -- or else need replace entire page altogether. idea there dynamically controlled flow needs satisfied before can forward legacy product. substituting fragments works fine, seen in below my_body_content swap. trouble comes when i'm trying render not fragment, whole page, in "body" swap. @ point page goes blank. i want similar errors returned server. want nice rest 404 error messages displayed on screen, legacy-product 404s show in legacy-product 404 page. yes, requirements project weird. that's not problem can fix. here's jquery invocation, names changed protect guilty: $.ajax({ url: "places/things", type: "post", data: json.stringify(somebadassobject), datatype: "text", accepts: "text/html", contenttype: "application/json; charset=...
Read more