Hanojski stolp z usmerjenimi premiki diskov

diplomsko delo

Martina Golob (Author), Sandi Klavžar (Mentor), Ciril Petr (Co-mentor)

Abstract

Igra Hanojski stolp spada v področje razvedrilne matematike. Rešujemo jo tako, da premikamo diske iz začetne palice na končno palico po določenih pravilih. Cilj igre je uporabiti najmanjše število premikov. V diplomskem delu obravnavamo Hanojski stolp z usmerjenimi premiki diskov, kar pomeni, da obstajajo omejitve pri premikih. Ločimo pet različnih primerov Hanojskega stolpa, ki jih ponazorimo z digrafi. Vsak digraf ima tri vozlišča, med katerimi obstajajo usmerjene povezave. V prvem delu bomo najprej predstavili Hanojski stolp in podali osnovne definicije o grafih. V naslednjem poglavju se bomo osredotočili na rekurzivno in iterativno rešitev problema. Jedro diplomskega dela predstavljajo optimalne rešitve za vsak digraf ter izračunano število premikov. V zaključku bomo z digrafi stanj vizualizirali prepovedane, dovoljene ter uporabljene premike pri iskanju optimalne rešitve. Končna ugotovitev kaže na to, da podan algoritem za reševanje Hanojskega stolpa z omejenimi premiki daje optimalne rešitve problema. Vsaka druga rešitev daje nujno večje število premikov. Za vsak digraf bomo zapisali natančno formulo za izračun števila premikov.

Keywords

diplomska dela;Hanojski stolp;grafi;diagrafi;rekruzije;iteracije;število premikov;optimalne rešitve;

Data

Language:	Slovenian
Year of publishing:	2016
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[M. Golob]
UDC:	519.1(043.2)
COBISS:	22724360
Views:	2029
Downloads:	114
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	The Tower of Hanoi with forbidden moves
Secondary abstract:	The game the Tower of Hanoi falls within the area of recreational mathematics. We solve it by moving discs from the initial position to the final position according to certain rules. The objective is to use minimal number of moves. In this graduation thesis we deal with the Tower of Hanoi with forbidden moves, which means that there are certain limited moves. We investigate five different cases of Hanoi Tower, which are represented by digraphs. Every digraph is a digraph on three vertices, between which there can be directed edges. In the first part we will introduce the Tower of Hanoi and present basic definitions of graphs. In the next chapter we will deal with the recursive and the iterative solution. The focus of this graduation thesis is on optimal solution of every digraph and calculated number of moves. In the last chapter we will visualize forbidden, allowed and used moves in the search of the optimal solution. The final results show, that the given algorithm for solving Hanoi Tower with forbidden moves provides optimal solution of the problem. Moreover, every distinct solution takes strictly more moves than the given algorithm. We will write down a precise formula for the number of moves for every digraph.
Secondary keywords:	theses;the tower of Hanoi;graphs;diagraphs;recursions;iterations;number of moves;optimal solutions;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	IX, 40 f.
ID:	9170479