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Title:Lomljena drevesa : magistrsko delo
Authors:ID Turnšek, Nina (Author)
ID Taranenko, Andrej (Mentor) More about this mentor... New window
Files:.pdf MAG_Turnsek_Nina_2022.pdf (2,11 MB)
MD5: D3AA5969DFA66CDB018B83B7DD18B2F4
 
.zip MAG_Turnsek_Nina_2022.zip (1,65 MB)
MD5: ECC18427629994D40EDC17413E1D3E14
 
Language:Slovenian
Work type:Master's thesis/paper
Typology:2.09 - Master's Thesis
Organization:FNM - Faculty of Natural Sciences and Mathematics
Abstract:V magistrskem delu je predstavljena podatkovna struktura imenovana lomljeno drevo. Gre za dvojiško iskalno drevo, kjer se oblika drevesa spremeni po vsakem posegu (operaciji) v drevo. Vozlišče, nad katerim izvajamo poljubno operacijo, je na koncu operacije vedno v korenu drevesa. Postopku, ki vozlišče premakne v koren drevesa, pravimo \emph{lomljenje}. Namen lomljenih dreves je, da so podatki, ki jih pogosto uporabljamo, hitro dostopni. Tako podatki, ki jih večkrat uporabljamo, ostanejo bližje vrha drevesa in jih ob naslednji uporabi hitreje najdemo. Podatki, ki so redko v uporabi, se nahajajo nižje v drevesu. Na podlagi amortizirane časovne zahtevnosti je analizirana hitrost delovanja osnovnih operacij lomljenih dreves. Amortizirana časovna zahtevnost je povprečen čas posamezne operacije v najslabšem zaporedju operacij. V magistrskem delu je predstavljen tudi implementiran program za lomljena drevesa, v katerem so definirane osnovne operacije na lomljenih drevesih. Nazadnje je narejena še analiza hitrosti delovanja operacij implementiranega programa za lomljena drevesa in primerjava lomljenih dreves z drugimi uravnoteženimi drevesi.
Keywords:lomljeno drevo, lomljenje, amortizirana časovna zahtevnost, uravnotežena drevesa
Place of publishing:Maribor
Place of performance:Maribor
Publisher:[N. Turnšek]
Year of publishing:2022
Number of pages:VIII, 82 f.
PID:20.500.12556/DKUM-81869 New window
UDC:519.6(043.2)
COBISS.SI-ID:127465475 New window
Publication date in DKUM:28.10.2022
Views:955
Downloads:80
Metadata:XML DC-XML DC-RDF
Categories:FNM
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Licences

License:CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Link:http://creativecommons.org/licenses/by-nc-nd/4.0/
Description:The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.
Licensing start date:12.06.2022

Secondary language

Language:English
Title:Splay trees : na študijskem programu 2. stopnje Matematika
Abstract:The master's thesis presents the data structure called splay tree. It is a binary search tree, where the shape of the tree changes after each intervention (operation) in the tree. At the end of each operation, the node over which the operation is performed is always in the root of the tree. The process of moving a node to the root of a tree is called \emph{splaying}. The purpose of splay trees is to make frequently used data quickly accessible. Thus, the data we use multiple times remains near the top of the tree and is then found faster. Data that is rarely used is located lower in the tree. Using the amortized time complexity, we analyse the speed of basic operations on splay trees. Amortized time complexity is the average time of an individual operation in the worst sequence of operations. In the master's thesis an implementation for splay trees is also presented. Finally, the time complexity analysis is made for the operations of the implementation and a comparison of splay trees with other balanced trees is given.
Keywords:splay tree, splaying, amortized time complexity, balanced trees


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