{"id":4717,"date":"2025-07-21T13:40:25","date_gmt":"2025-07-21T11:40:25","guid":{"rendered":"https:\/\/www.tutego.de\/blog\/javainsel\/?p=4717"},"modified":"2025-07-21T13:40:25","modified_gmt":"2025-07-21T11:40:25","slug":"inselraus-die-tuerme-von-hanoi","status":"publish","type":"post","link":"https:\/\/www.tutego.de\/blog\/javainsel\/2025\/07\/inselraus-die-tuerme-von-hanoi\/","title":{"rendered":"Inselraus: Die T\u00fcrme von Hanoi"},"content":{"rendered":"<style>\n<!-- \/* Font Definitions *\/ @font-face {font-family:Wingdings; panose-1:5 0 0 0 0 0 0 0 0 0; mso-font-charset:2; mso-generic-font-family:auto; mso-font-pitch:variable; mso-font-signature:0 268435456 0 0 -2147483648 0;} @font-face {font-family:\"Cambria Math\"; panose-1:2 4 5 3 5 4 6 3 2 4; mso-font-charset:0; mso-generic-font-family:roman; mso-font-pitch:variable; mso-font-signature:-536869121 1107305727 33554432 0 415 0;} @font-face {font-family:Calibri; panose-1:2 15 5 2 2 2 4 3 2 4; mso-font-charset:0; mso-generic-font-family:swiss; 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mso-style-unhide:no; vertical-align:super;} span.Kursiv {mso-style-name:Kursiv; mso-style-unhide:no; font-style:italic; mso-bidi-font-style:normal;} span.FunotentextZchn {mso-style-name:\"Fu\u00dfnotentext Zchn\"; mso-style-noshow:yes; mso-style-unhide:no; mso-style-locked:yes; mso-style-link:Fu\u00dfnotentext; mso-ansi-font-size:9.0pt; mso-bidi-font-size:11.0pt; font-family:\"Times New Roman\",serif; mso-ascii-font-family:\"Times New Roman\"; mso-fareast-font-family:\"Times New Roman\"; mso-hansi-font-family:\"Times New Roman\";} p.Listeunnummeriert, li.Listeunnummeriert, div.Listeunnummeriert {mso-style-name:\"Liste unnummeriert\"; mso-style-unhide:no; mso-style-parent:\"\"; margin-top:3.0pt; margin-right:0cm; margin-bottom:3.0pt; margin-left:17.85pt; text-align:justify; text-indent:-17.85pt; line-height:14.0pt; mso-line-height-rule:exactly; mso-pagination:widow-orphan; mso-list:l0 level1 lfo1; tab-stops:list 17.85pt; font-size:11.0pt; mso-bidi-font-size:12.0pt; font-family:\"Times New Roman\",serif; mso-fareast-font-family:\"Times New Roman\"; mso-ansi-language:DE; mso-fareast-language:DE;} .MsoChpDefault {mso-style-type:export-only; mso-default-props:yes; font-size:10.0pt; mso-ansi-font-size:10.0pt; mso-bidi-font-size:10.0pt; font-family:\"Calibri\",sans-serif; mso-ascii-font-family:Calibri; mso-fareast-font-family:Calibri; mso-hansi-font-family:Calibri; mso-ansi-language:DE; mso-fareast-language:DE;} \/* Page Definitions *\/ @page {mso-footnote-separator:url(\"file:\/\/\/C:\/Users\/CHRIST~1\/AppData\/Local\/Temp\/msohtmlclip1\/01\/clip_header.htm\") fs; mso-footnote-continuation-separator:url(\"file:\/\/\/C:\/Users\/CHRIST~1\/AppData\/Local\/Temp\/msohtmlclip1\/01\/clip_header.htm\") fcs; mso-endnote-separator:url(\"file:\/\/\/C:\/Users\/CHRIST~1\/AppData\/Local\/Temp\/msohtmlclip1\/01\/clip_header.htm\") es; mso-endnote-continuation-separator:url(\"file:\/\/\/C:\/Users\/CHRIST~1\/AppData\/Local\/Temp\/msohtmlclip1\/01\/clip_header.htm\") ecs;} @page WordSection1 {size:612.0pt 792.0pt; margin:70.85pt 70.85pt 2.0cm 70.85pt; mso-header-margin:36.0pt; mso-footer-margin:36.0pt; mso-paper-source:0;} div.WordSection1 {page:WordSection1;} \/* List Definitions *\/ @list l0 {mso-list-id:915476229; mso-list-type:simple; mso-list-template-ids:251568122;} @list l0:level1 {mso-level-number-format:bullet; mso-level-style-link:\"Liste unnummeriert\"; mso-level-text:\uf0a7; mso-level-tab-stop:17.85pt; mso-level-number-position:left; margin-left:17.85pt; text-indent:-17.85pt; mso-ansi-font-size:8.0pt; mso-bidi-font-size:8.0pt; font-family:Wingdings; color:black; mso-ansi-font-weight:normal; mso-ansi-font-style:normal;} ol {margin-bottom:0cm;} ul {margin-bottom:0cm;} --><br \/>\n<\/style>\n<p class=\"MsoNormal\"><span lang=\"DE\">Die Legende der T\u00fcrme von Hanoi soll erstmalig von Ed Lucas in einem Artikel in der franz\u00f6sischen Zeitschrift \u00bbCosmo\u00ab im Jahre 1890 ver\u00f6ffentlicht worden sein.<a style=\"mso-footnote-id: ftn1;\" title=\"\" href=\"#_ftn1\" name=\"_ftnref1\"><span class=\"MsoFootnoteReference\"><span style=\"mso-special-character: footnote;\"><!-- [if !supportFootnotes]--><span class=\"MsoFootnoteReference\"><span lang=\"DE\" style=\"font-size: 11.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: DE; mso-fareast-language: DE; mso-bidi-language: AR-SA;\">[1]<\/span><\/span><!--[endif]--><\/span><\/span><\/a> Der Legende nach standen vor langer Zeit im Tempel von Hanoi drei S\u00e4ulen. Die erste war aus Kupfer, die zweite aus Silber und die dritte aus Gold. Auf der Kupfers\u00e4ule waren einhundert Scheiben aufgestapelt. Die Scheiben hatten in der Mitte ein Loch und waren aus Porphyr<a style=\"mso-footnote-id: ftn2;\" title=\"\" href=\"#_ftn2\" name=\"_ftnref2\"><span class=\"MsoFootnoteReference\"><span style=\"mso-special-character: footnote;\"><!-- [if !supportFootnotes]--><span class=\"MsoFootnoteReference\"><span lang=\"DE\" style=\"font-size: 11.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: DE; mso-fareast-language: DE; mso-bidi-language: AR-SA;\">[2]<\/span><\/span><!--[endif]--><\/span><\/span><\/a>. Die Scheibe mit dem gr\u00f6\u00dften Umfang lag unten, und alle kleiner werdenden Scheiben lagen obenauf. Ein alter M\u00f6nch stellte sich die Aufgabe, den Turm der Scheiben von der Kupfers\u00e4ule zur Golds\u00e4ule zu bewegen. In einem Schritt sollte aber nur eine Scheibe bewegt werden, und zudem war die Bedingung, dass eine gr\u00f6\u00dfere Scheibe niemals auf eine kleinere bewegt werden durfte. Der M\u00f6nch erkannte schnell, dass er die Silbers\u00e4ule nutzen musste; er setzte sich an einen Tisch, machte einen Plan, \u00fcberlegte und kam zu einer Entscheidung. Er konnte sein Problem in drei Schritten l\u00f6sen. Am n\u00e4chsten Tag schlug der M\u00f6nch die L\u00f6sung an die Tempelt\u00fcr:<\/span><\/p>\n<p class=\"Listeunnummeriert\" style=\"mso-list: l0 level1 lfo1;\"><!-- [if !supportLists]--><span lang=\"DE\" style=\"font-size: 8.0pt; font-family: Wingdings; mso-fareast-font-family: Wingdings; mso-bidi-font-family: Wingdings; color: black;\"><span style=\"mso-list: Ignore;\">\u00a7<span style=\"font: 7.0pt 'Times New Roman';\">\u00a0\u00a0 <\/span><\/span><\/span><!--[endif]--><span lang=\"DE\">Falls der Turm aus mehr als einer Scheibe besteht, bitte deinen \u00e4ltesten Sch\u00fcler, einen Turm von (<span class=\"Kursiv\">N<\/span> \u2013 1) Scheiben von der ersten zur dritten S\u00e4ule unter Verwendung der zweiten S\u00e4ule umzusetzen.<\/span><\/p>\n<p class=\"Listeunnummeriert\" style=\"mso-list: l0 level1 lfo1;\"><!-- [if !supportLists]--><span lang=\"DE\" style=\"font-size: 8.0pt; font-family: Wingdings; mso-fareast-font-family: Wingdings; mso-bidi-font-family: Wingdings; color: black;\"><span style=\"mso-list: Ignore;\">\u00a7<span style=\"font: 7.0pt 'Times New Roman';\">\u00a0\u00a0 <\/span><\/span><\/span><!--[endif]--><span lang=\"DE\">Trage selbst die erste Scheibe von einer zur anderen S\u00e4ule.<\/span><\/p>\n<p class=\"Listeunnummeriert\" style=\"mso-list: l0 level1 lfo1;\"><!-- [if !supportLists]--><span lang=\"DE\" style=\"font-size: 8.0pt; font-family: Wingdings; mso-fareast-font-family: Wingdings; mso-bidi-font-family: Wingdings; color: black;\"><span style=\"mso-list: Ignore;\">\u00a7<span style=\"font: 7.0pt 'Times New Roman';\">\u00a0\u00a0 <\/span><\/span><\/span><!--[endif]--><span lang=\"DE\">Falls der Turm aus mehr als einer Scheibe besteht, bitte deinen \u00e4ltesten Sch\u00fcler, einen Turm aus (<span class=\"Kursiv\">N<\/span> \u2013 1) Scheiben von der dritten zu der anderen S\u00e4ule unter Verwendung der ersten S\u00e4ule zu transportieren.<\/span><\/p>\n<p class=\"MsoNormal\"><span lang=\"DE\">Und so rief der alte M\u00f6nch seinen \u00e4ltesten Sch\u00fcler zu sich und trug ihm auf, den Turm aus 99\u00a0Scheiben von der Kupfers\u00e4ule zur Golds\u00e4ule unter Verwendung der Silbers\u00e4ule umzuschichten und ihm den Vollzug zu melden. Nach der Legende w\u00fcrde das Ende der Welt nahe sein, bis der M\u00f6nch seine Arbeit beendet h\u00e4tte.<\/span><\/p>\n<p class=\"MsoNormal\"><span lang=\"DE\">Nun, so weit die Geschichte. Wollen wir den Algorithmus zur Umschichtung der Porphyrscheiben in Java programmieren, so ist eine rekursive L\u00f6sung recht einfach. Werfen wir einen Blick auf das folgende Programm, das die Umschichtungen \u00fcber die drei Pfl\u00f6cke (engl. <span class=\"Kursiv\">pegs<\/span>) vornimmt:<\/span><\/p>\n<div><\/div>\n<div>\n<style>\n<!-- \/* Font Definitions *\/ @font-face {font-family:\"Cambria Math\"; panose-1:2 4 5 3 5 4 6 3 2 4; mso-font-charset:0; mso-generic-font-family:roman; mso-font-pitch:variable; mso-font-signature:-536869121 1107305727 33554432 0 415 0;} @font-face {font-family:Calibri; panose-1:2 15 5 2 2 2 4 3 2 4; mso-font-charset:0; mso-generic-font-family:swiss; mso-font-pitch:variable; mso-font-signature:-469750017 -1040178053 9 0 511 0;} \/* Style Definitions *\/ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-unhide:no; mso-style-qformat:yes; mso-style-parent:\"\"; margin-top:0cm; margin-right:0cm; margin-bottom:3.0pt; margin-left:0cm; text-align:justify; line-height:13.5pt; mso-pagination:widow-orphan; tab-stops:17.85pt; font-size:11.0pt; font-family:\"Times New Roman\",serif; mso-fareast-font-family:\"Times New Roman\"; 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color:purple; mso-ansi-language:DE; mso-fareast-language:DE; mso-no-proof:yes;} p.ListingStandardCxSpLast, li.ListingStandardCxSpLast, div.ListingStandardCxSpLast {mso-style-name:\"Listing StandardCxSpLast\"; mso-style-priority:1; mso-style-unhide:no; mso-style-parent:\"\"; mso-style-type:export-only; margin-top:0cm; margin-right:-22.7pt; margin-bottom:3.0pt; margin-left:0cm; mso-add-space:auto; line-height:14.0pt; mso-line-height-rule:exactly; mso-pagination:widow-orphan; font-size:9.0pt; font-family:\"Courier New\"; mso-fareast-font-family:\"Times New Roman\"; mso-bidi-font-family:\"Times New Roman\"; color:purple; mso-ansi-language:DE; mso-fareast-language:DE; mso-no-proof:yes;} span.ListingZeichenFett {mso-style-name:\"Listing Zeichen Fett\"; mso-style-priority:1; mso-style-unhide:no; mso-style-qformat:yes; mso-ansi-font-size:9.0pt; font-family:\"Courier New\"; mso-ascii-font-family:\"Courier New\"; mso-hansi-font-family:\"Courier New\"; color:purple; border:none; background:#F2F2F2; mso-shading-themecolor:background1; mso-shading-themeshade:242; font-weight:bold; mso-bidi-font-weight:normal;} .MsoChpDefault {mso-style-type:export-only; mso-default-props:yes; font-size:10.0pt; mso-ansi-font-size:10.0pt; mso-bidi-font-size:10.0pt; font-family:\"Calibri\",sans-serif; mso-ascii-font-family:Calibri; mso-fareast-font-family:Calibri; mso-hansi-font-family:Calibri; mso-ansi-language:DE; mso-fareast-language:DE;} @page WordSection1 {size:612.0pt 792.0pt; margin:70.85pt 70.85pt 2.0cm 70.85pt; mso-header-margin:36.0pt; mso-footer-margin:36.0pt; mso-paper-source:0;} div.WordSection1 {page:WordSection1;} --><br \/>\n<\/style>\n<pre class=\"ListingJava\"><span style=\"mso-ansi-language: EN-US;\">class TowerOfHanoi {\r\n\r\n<span style=\"mso-spacerun: yes;\">\u00a0<\/span>static void <span class=\"ListingZeichenFett\"><span style=\"mso-bidi-font-family: 'Times New Roman'; border: none;\"><span style=\"border: none;\">move( int n, String fromPeg, String\r\ntoPeg, String usingPeg )<\/span><\/span><\/span> {\r\n\r\n<span style=\"mso-spacerun: yes;\">\u00a0 <\/span>if ( n &gt; 1 ) {\r\n<span style=\"mso-spacerun: yes;\">\u00a0\u00a0 <\/span><span class=\"ListingZeichenFett\"><span style=\"mso-bidi-font-family: 'Times New Roman'; border: none;\"><span style=\"border: none;\">move( n - 1, fromPeg, usingPeg, toPeg );<\/span><\/span><\/span>\r\n<span style=\"mso-spacerun: yes;\">\u00a0\u00a0 <\/span>System.out.printf( \"Move disk %d\r\nfrom %s to %s.%n\", n, fromPeg, toPeg );\r\n<span style=\"mso-spacerun: yes;\">\u00a0\u00a0 <\/span><span class=\"ListingZeichenFett\"><span style=\"mso-bidi-font-family: 'Times New Roman'; border: none;\"><span style=\"border: none;\">move( n - 1, usingPeg, toPeg, fromPeg );<\/span><\/span><\/span>\r\n<span style=\"mso-spacerun: yes;\">\u00a0 <\/span>}\r\n<span style=\"mso-spacerun: yes;\">\u00a0 <\/span>else\r\n<span style=\"mso-spacerun: yes;\">\u00a0\u00a0 <\/span>System.out.printf( \"Move disk %d\r\nfrom %s to %s.%n\", n, fromPeg, toPeg );\r\n<span style=\"mso-spacerun: yes;\">\u00a0<\/span>}\r\n\r\n<span style=\"mso-spacerun: yes;\">\u00a0<\/span>public static void main( String[] args )\r\n{\r\n<span style=\"mso-spacerun: yes;\">\u00a0\u00a0 <\/span><span class=\"ListingZeichenFett\"><span style=\"mso-bidi-font-family: 'Times New Roman'; border: none;\"><span style=\"border: none;\">move( 4, \"copper peg\", \"gold peg\",\r\n\"silver peg\" )<span style=\"border: none;\">;<\/span><\/span><\/span><\/span>\r\n<span style=\"mso-spacerun: yes;\">\u00a0<\/span>}\r\n}<\/span><\/pre>\n<p class=\"MsoNormal\"><span lang=\"DE\">Starten wir das Programm mit vier Scheiben, so bekommen wir folgende Ausgabe:<\/span><\/p>\n<p class=\"ListingStandard\"><span style=\"mso-ansi-language: EN-US;\">Move disk 1 from copper peg to silver peg.<br \/>\nMove disk 2 from copper peg to gold peg.<br \/>\nMove disk 1 from silver peg to gold peg.<br \/>\nMove disk 3 from copper peg to silver peg.<br \/>\nMove disk 1 from gold peg to copper peg.<br \/>\nMove disk 2 from gold peg to silver peg.<br \/>\nMove disk 1 from copper peg to silver peg.<br \/>\nMove disk 4 from copper peg to gold peg.<br \/>\nMove disk 1 from silver peg to gold peg.<br \/>\nMove disk 2 from silver peg to copper peg.<br \/>\nMove disk 1 from gold peg to copper peg.<br \/>\nMove disk 3 from silver peg to gold peg.<br \/>\nMove disk 1 from copper peg to silver peg.<br \/>\nMove disk 2 from copper peg to gold peg.<br \/>\n<\/span><span lang=\"DE\">Move disk 1 from silver peg to gold peg.<\/span><\/p>\n<p><span lang=\"DE\" style=\"font-size: 11.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: DE; mso-fareast-language: DE; mso-bidi-language: AR-SA;\">Schon bei vier Scheiben haben wir 15 Bewegungen. Selbst wenn unser Prozessor mit vielen Millionen Operationen pro Sekunde arbeitet, ben\u00f6tigt ein Computer f\u00fcr die Abarbeitung von 100 Scheiben Tausende geologischer Erdzeitalter. An diesem Beispiel wird eines deutlich: Viele Dinge sind im Prinzip berechenbar, nur praktisch ist ein solcher Algorithmus nicht.<\/span><\/p>\n<\/div>\n<div style=\"mso-element: footnote-list;\">\n<p><!-- [if !supportFootnotes]--><\/p>\n<hr align=\"left\" size=\"1\" width=\"33%\" \/>\n<p><!--[endif]--><\/p>\n<div id=\"ftn1\" style=\"mso-element: footnote;\">\n<p class=\"MsoFootnoteText\"><a style=\"mso-footnote-id: ftn1;\" title=\"\" href=\"#_ftnref1\" name=\"_ftn1\"><span class=\"MsoFootnoteReference\"><span lang=\"DE\"><span style=\"mso-special-character: footnote;\"><!-- [if !supportFootnotes]--><span class=\"MsoFootnoteReference\"><span lang=\"DE\" style=\"font-size: 9.0pt; mso-bidi-font-size: 11.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: DE; mso-fareast-language: DE; mso-bidi-language: AR-SA;\">[1]<\/span><\/span><!--[endif]--><\/span><\/span><\/span><\/a><span lang=\"DE\"> Wir halten uns hier an eine \u00dcberlieferung von C. H. A. Koster aus dem Buch \u00bbTop-down Programming with Elan\u00ab von Ellis Horwood (Verlag Ellis Horwood Ltd, ISBN 0139249370, 1987).<\/span><\/p>\n<\/div>\n<div id=\"ftn2\" style=\"mso-element: footnote;\">\n<p class=\"MsoFootnoteText\"><a style=\"mso-footnote-id: ftn2;\" title=\"\" href=\"#_ftnref2\" name=\"_ftn2\"><span class=\"MsoFootnoteReference\"><span lang=\"DE\"><span style=\"mso-special-character: footnote;\"><!-- [if !supportFootnotes]--><span class=\"MsoFootnoteReference\"><span lang=\"DE\" style=\"font-size: 9.0pt; mso-bidi-font-size: 11.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: DE; mso-fareast-language: DE; mso-bidi-language: AR-SA;\">[2]<\/span><\/span><!--[endif]--><\/span><\/span><\/span><\/a><span lang=\"DE\"> Gestein vulkanischen Ursprungs. Besondere Eigenschaften von Porphyr sind: hohe Bruchfestigkeit, hohe Best\u00e4ndigkeit gegen physikalisch-chemische Wirkstoffe und hohe W\u00e4lz- und Gleitreibung.<\/span><\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Die Legende der T\u00fcrme von Hanoi soll erstmalig von Ed Lucas in einem Artikel in der franz\u00f6sischen Zeitschrift \u00bbCosmo\u00ab im Jahre 1890 ver\u00f6ffentlicht worden sein.[1] Der Legende nach standen vor langer Zeit im Tempel von Hanoi drei S\u00e4ulen. Die erste war aus Kupfer, die zweite aus Silber und die dritte aus Gold. Auf der Kupfers\u00e4ule [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","_links_to":"","_links_to_target":""},"categories":[1],"tags":[],"class_list":["post-4717","post","type-post","status-publish","format-standard","hentry","category-allgemein"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.tutego.de\/blog\/javainsel\/wp-json\/wp\/v2\/posts\/4717","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.tutego.de\/blog\/javainsel\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.tutego.de\/blog\/javainsel\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.tutego.de\/blog\/javainsel\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.tutego.de\/blog\/javainsel\/wp-json\/wp\/v2\/comments?post=4717"}],"version-history":[{"count":1,"href":"https:\/\/www.tutego.de\/blog\/javainsel\/wp-json\/wp\/v2\/posts\/4717\/revisions"}],"predecessor-version":[{"id":4718,"href":"https:\/\/www.tutego.de\/blog\/javainsel\/wp-json\/wp\/v2\/posts\/4717\/revisions\/4718"}],"wp:attachment":[{"href":"https:\/\/www.tutego.de\/blog\/javainsel\/wp-json\/wp\/v2\/media?parent=4717"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.tutego.de\/blog\/javainsel\/wp-json\/wp\/v2\/categories?post=4717"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.tutego.de\/blog\/javainsel\/wp-json\/wp\/v2\/tags?post=4717"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}