- , 6- Persistent Data Structures : : Rebuild subtree T Example History , attire : - Preserves prior states of , Samak , Sleater ," . Let Tzbenew subtree : - Driscoll " " " t ' splay - First serious Tarjan ( 1986 ) trees data structure PBJ Tree : BJ Tree : Nino - Allows searches in history theoretical analysis I . " lost ! t.is ① → Applied to geometric was Jane Smith enrolled unlinked " → in spring Approach : whenever a modification search ( time is coordinate ) " in UMD 2016 ? - Fulll Partial Persistence : made - save old contents tuse - change can be made temporal node to distinguish Approaches : - . to anykurrent version . . - write : Whenever you change att Copy - on : Drew ↳ Persisten ¥ SearchTreesw modify , make a copy o → very inefficient ! Example : - log * 6 ¥ change a list of Make Command : Tinie : : * recent updates . - - - et - insert IAD 01 FD → slow to process insert BWI 03 ¥ ~ TkCase study . Fat nodes ( Node copying : PBJ Tree insert SFO 05 : When changes occur , save Persistent weight - Balanced delete BWI 07 just modified portions . . . time : . Jackhammer trees op op op g , → Temporal node : New node in IAD BWI BWI IAD → A partially persistent i. IAD , IAD in i SFO type pro i ④ ⇐ time ÷ , . . . . ; not found find IAD at ! BJ tree o : post " I :{ tenets → Uses rebuilding to balance pre { ybntfeenf . find IAD ato ? found ! " . . subtrees - min : BWI get at 04 on crafter ' prior to time . → Allows weighted . . time t t . : IAD . entries get - min at 08 ° ,
↳ - , PBJ Tree Private ) Data : ⇐ PBJ Tree : Tech specs Few More Things : - final float ALPHA , BETA , check that - Before insert Node structure : Node : weight t > last Insert Time - maxwt ( float ) as BJ Tree ↳ same - Node → else Error ! ↳ Temp Node : time ( int ) - root : null root → init - int first Insert Tinie } - set last Insert Time ← t pre , post ( Node ) . , > init : Int Node : key - Note : Partial persistence - int last Inserttiine , right , left Ext Node : key , value - Rebalance → NEXT - ⑧ Insertion ( without rebalancing ) . If mention ) IPersistentssearchtreeswT-empmna.ge ? tgnf :xgYf ¥ mw ¥ . . . Updating weights ? : Node insert ( x. v. w ,t ) Helper wt-left.wttright.wt-I.ro → insert ( xn ) of wt wat t Int Node : .li ? ornighti-t.eI-root--newExtNodelx,v,w)&# , - Post ! - post . maxwt - maxwtc s - s s s - reach Ext Node @ tempipfostc-pos-t.int/weighttmaxWt - → Int : left c- left . insert . . ) . → Update node - search for x . - right . Example : | in tree rights . insert . . . ) " )tmiY% insert 'D . . : Duplicate key sit ,g y ⇒ Error . ( later ) ," ? . % , " ⑤ ⑤ oty mtaybe " ¥ 7 a - maybe Into It ' ⑤ @ i , " ⑤ " . . ② ③ . Ds weight . so " ' ⑤ , " I ⑦ letter right " maxwt ? " ⑤ " ' ⑤ ④ ÷ " ( or post ) . goofy bis . . . child i. copy ° ,
⇐ - , Internal Node Rebalance :-# tindlx.tl.fnidvplx.tl , getminlt ) . Rebalancing after insertion : . . - starting at root as before but for temporal - T est a ,p condition , retrace - same nodes visit prelpost based out search path ( same as BJ tree ) - Recursive helper - If unbalanced , compile - check whether tcfirstupdatetime : A- of extern nodes Node rebalance ( x ,t ) → if list → null ③ - toe memorially : Apply to left for current tree → Internal c- " - - - T - original tree getpreordwlistltlgettullpreorderlistl ) x ⇒ key right based on on post side " ' temporalities .to#..-kistcgetsepmre::dgrnliostesagtimet strewn tree - . : IPersistentSearchTreesyT - second gets full preorder list temporal ⑨ " od " Call nodes ) Delete Hear : Not implemented ) Temporal Node Rebalance : b t 't - Not required ! ( A bit messy ) - Recuse on post side : - 88 - . rebalance Cx ,t ) f ⇒ Example : ④ - post post - On return : % , D8 " → rebuild at is temporal ) . if ( post child , , ? ⑤ in ' . as " - perform left rotation I. update weights ⑤ QI , , ⑤ " " " ⑤ ⑤ " ' ⑤ YO ⇒ ⑤ ' ' . . . shallow or root of subtree a . ⑤ ⑥ return ' n ⑤ vis " ai why ? Don't like long post chains , ⑤ " ⑤ I " ⑤ deep copy ? " ' ' " ⑤ ⑤ " ⑤ " ' ⑤ Itcngteaimnpitgrea 'iJ ¥ i sis → we did , → → oesitdemraiter ? one . no newest - - ' " - - ← - - - - - - - - - . .
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