Primerjava algoritmov za izračun Fibonaccijevih števil

MOČNIK, GAŠPER (author), Mihelič, Jurij (mentor)

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.

• Language: Slovenian
• Keywords: Fibonaccijeva števila, aritmetika poljubne natančnosti, časovna zahtevnost, rekurzija
• Work type: Bachelor thesis/paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FRI - Faculty of Computer and Information Science
• Year: 2022
• PID: 20.500.12556/RUL-134822
• COBISS.SI-ID: 97925635
• Publication date in RUL: 03.02.2022

MOČNIK, GAŠPER, 2022, Primerjava algoritmov za izračun Fibonaccijevih števil [online]. Bachelor’s thesis. [Accessed 18 April 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=134822

Secondary language

• Language: English
• Title: Comparison of algorithms for computing Fibonacci numbers

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.

• Keywords: Fibonacci numbers, arbitrary precision arithmetic, time complexity, recursion