Primerjava algoritmov za izračun Fibonaccijevih števil

diplomsko delo

Gašper Močnik (Author), Jurij Mihelič (Mentor)

Abstract

V diplomski nalogi so predstavljeni in analizirani načini algoritmičnega izračuna Fibonaccijevih števil. V prvem delu je predstavljeno teoretično ozadje računanja elementov Fibonaccijevega zaporedja in aritmetika v poljubni natančnosti, ki nam omogoča operiranje s števili, ki velikostno presegajo dolžino procesorskih registrov. Opisani so algoritmi, ki temeljijo na osnovni rekurzivni zvezi Fibonaccijevega zaporedja, matrični algoritmi, algoritmi na podlagi Binetove formule in algoritem, ki pri izračunu uporablja binomske koeficiente. V drugem delu so predstavljeni rezultati eksperimentalne primerjave predstavljenih algoritmov, ki smo jih implementirali v programskem jeziku C, za izvajanje aritmetike v poljubni natančnosti pa je bila uporabljena knjižnica GNU MP.

Keywords

Fibonaccijeva števila;aritmetika poljubne natančnosti;časovna zahtevnost;rekurzija;univerzitetni študij;diplomske naloge;

Data

Language:	Slovenian
Year of publishing:	2022
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FRI - Faculty of Computer and Information Science
Publisher:	[G. Močnik]
UDC:	004:51(043.2)
COBISS:	97925635
Views:	164
Downloads:	39
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Comparison of algorithms for computing Fibonacci numbers
Secondary abstract:	In this thesis, we present and analyse ways of algorithmically computing Fibonacci numbers. In the first part we describe theoretical background of computing elements of the Fibonacci sequence. We also describe arbitrary precision arithmetic that allows us to do mathematical operations on numbers that are larger than the length of processor registers. We describe algorithms that are based on the Fibonacci sequence recursive relation, matrix algorithms, algorithms that calculate Binet’s formula and an algorithm that uses binomial coefficients. In the second part we present the results of experimental comparison of the above algorithms which were implemented in C programming language using GNU MP library for arbitrary precision arithmetic.
Secondary keywords:	Fibonacci numbers;arbitrary precision arithmetic;time complexity;recursion;computer science;diploma;Računalništvo;Univerzitetna in visokošolska dela;
Type (COBISS):	Bachelor thesis/paper
Study programme:	1000468
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za računalništvo in informatiko
Pages:	60 str.
ID:	14444843