Hanojski stolp z usmerjenimi premiki diskov

Golob, Martina

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Title:	Hanojski stolp z usmerjenimi premiki diskov
Authors:	ID Golob, Martina (Author) ID Klavžar, Sandi (Mentor) More about this mentor... ID Petr, Ciril (Comentor)
Files:	UN_Golob_Martina_2016.pdf (541,41 KB) MD5: 5462EB1B266065A3B5E478C3A4BD971A
Language:	Slovenian
Work type:	Undergraduate thesis
Typology:	2.11 - Undergraduate Thesis
Organization:	FNM - Faculty of Natural Sciences and Mathematics
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:	Hanojski stolp, graf, digraf, rekurzija, iteracija, število premikov, optimalne rešitve.
Place of publishing:	Maribor
Publisher:	[M. Golob]
Year of publishing:	2016
PID:	20.500.12556/DKUM-63944
UDC:	519.1(043.2)
COBISS.SI-ID:	22724360
NUK URN:	URN:SI:UM:DK:X5SFNXUN
Publication date in DKUM:	11.11.2016
Views:	2582
Downloads:	171
Metadata:
Categories:	FNM
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Secondary language

Language:	English
Title:	The Tower of Hanoi with forbidden moves
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.
Keywords:	The Tower of Hanoi, graph, digraph, recursion, iteration, number of moves, optimal solutions.

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