Generating t-ary trees in A-order
Two ‘natural’ orders have been defined on the set of t-ary trees. Zaks (1980) referred to these orders as A-order and B-order. Many algorithms have been developed for generating binary and t-ary trees in B-order. Here we develop an algorithm for generating all t-ary trees with n nodes in (reverse) A...
Gespeichert in:
| Veröffentlicht in: | Information processing letters 1988-04, Vol.27 (4), p.205-213 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 213 |
|---|---|
| container_issue | 4 |
| container_start_page | 205 |
| container_title | Information processing letters |
| container_volume | 27 |
| creator | van Baronaigien, D.Roelants Ruskey, Frank |
| description | Two ‘natural’ orders have been defined on the set of
t-ary trees. Zaks (1980) referred to these orders as A-order and B-order. Many algorithms have been developed for generating binary and
t-ary trees in B-order. Here we develop an algorithm for generating all
t-ary trees with
n nodes in (reverse) A-order, as well as ranking and unranking algorithms. The generation algorithm produces each tree in constant average time. The analysis of the generation algorithm makes use of an interesting bijection on the set of
t-ary trees. The ranking algorithm runs in O(
tn) time and the unranking algorithm in O(
tn lg
n) time. |
| doi_str_mv | 10.1016/0020-0190(88)90027-0 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_24888673</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>0020019088900270</els_id><sourcerecordid>1136890</sourcerecordid><originalsourceid>FETCH-LOGICAL-c362t-542189792049af69c2fd24890fe0887aac8f65b46de0349f1562ee58e0480ad13</originalsourceid><addsrcrecordid>eNp9kMFKAzEQhoMoWKtv4GH1IHqITrLZ7OQilKJVKHjRc4jZWUlpd2uyFXx7UysePHgaBr7_Z-Zj7FTAtQChbwAkcBAGLhGvTN5qDntsJLCWXAth9tnoFzlkRyktAECrsh6xsxl1FN0Qurdi4C5-FkMkSkXoignvY0PxmB20bpno5GeO2cv93fP0gc-fZo_TyZz7UsuBV0oKNLWRoIxrtfGybaRCAy0BYu2cx1ZXr0o3BKUyrai0JKqQQCG4RpRjdrHrXcf-fUNpsKuQPC2XrqN-k2wuQ9R1mcHzP-Ci38Qu32ZlWcsKsZIZUjvIxz6lSK1dx7DK_1kBdivNbo3YrRGLaL-lWcix212M8qcfgaJNPlDnqQmR_GCbPvxf8AXBaW9d</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>237258852</pqid></control><display><type>article</type><title>Generating t-ary trees in A-order</title><source>Elsevier ScienceDirect Journals Complete</source><creator>van Baronaigien, D.Roelants ; Ruskey, Frank</creator><creatorcontrib>van Baronaigien, D.Roelants ; Ruskey, Frank</creatorcontrib><description>Two ‘natural’ orders have been defined on the set of
t-ary trees. Zaks (1980) referred to these orders as A-order and B-order. Many algorithms have been developed for generating binary and
t-ary trees in B-order. Here we develop an algorithm for generating all
t-ary trees with
n nodes in (reverse) A-order, as well as ranking and unranking algorithms. The generation algorithm produces each tree in constant average time. The analysis of the generation algorithm makes use of an interesting bijection on the set of
t-ary trees. The ranking algorithm runs in O(
tn) time and the unranking algorithm in O(
tn lg
n) time.</description><identifier>ISSN: 0020-0190</identifier><identifier>EISSN: 1872-6119</identifier><identifier>DOI: 10.1016/0020-0190(88)90027-0</identifier><identifier>CODEN: IFPLAT</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>A-order ; Algorithms ; Applications ; bijection ; combinatorial generation ; Mathematical analysis ; ranking ; t-ary tree ; Trees</subject><ispartof>Information processing letters, 1988-04, Vol.27 (4), p.205-213</ispartof><rights>1988</rights><rights>Copyright Elsevier Sequoia S.A. Apr 8, 1988</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c362t-542189792049af69c2fd24890fe0887aac8f65b46de0349f1562ee58e0480ad13</citedby><cites>FETCH-LOGICAL-c362t-542189792049af69c2fd24890fe0887aac8f65b46de0349f1562ee58e0480ad13</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/0020-0190(88)90027-0$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids></links><search><creatorcontrib>van Baronaigien, D.Roelants</creatorcontrib><creatorcontrib>Ruskey, Frank</creatorcontrib><title>Generating t-ary trees in A-order</title><title>Information processing letters</title><description>Two ‘natural’ orders have been defined on the set of
t-ary trees. Zaks (1980) referred to these orders as A-order and B-order. Many algorithms have been developed for generating binary and
t-ary trees in B-order. Here we develop an algorithm for generating all
t-ary trees with
n nodes in (reverse) A-order, as well as ranking and unranking algorithms. The generation algorithm produces each tree in constant average time. The analysis of the generation algorithm makes use of an interesting bijection on the set of
t-ary trees. The ranking algorithm runs in O(
tn) time and the unranking algorithm in O(
tn lg
n) time.</description><subject>A-order</subject><subject>Algorithms</subject><subject>Applications</subject><subject>bijection</subject><subject>combinatorial generation</subject><subject>Mathematical analysis</subject><subject>ranking</subject><subject>t-ary tree</subject><subject>Trees</subject><issn>0020-0190</issn><issn>1872-6119</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1988</creationdate><recordtype>article</recordtype><recordid>eNp9kMFKAzEQhoMoWKtv4GH1IHqITrLZ7OQilKJVKHjRc4jZWUlpd2uyFXx7UysePHgaBr7_Z-Zj7FTAtQChbwAkcBAGLhGvTN5qDntsJLCWXAth9tnoFzlkRyktAECrsh6xsxl1FN0Qurdi4C5-FkMkSkXoignvY0PxmB20bpno5GeO2cv93fP0gc-fZo_TyZz7UsuBV0oKNLWRoIxrtfGybaRCAy0BYu2cx1ZXr0o3BKUyrai0JKqQQCG4RpRjdrHrXcf-fUNpsKuQPC2XrqN-k2wuQ9R1mcHzP-Ci38Qu32ZlWcsKsZIZUjvIxz6lSK1dx7DK_1kBdivNbo3YrRGLaL-lWcix212M8qcfgaJNPlDnqQmR_GCbPvxf8AXBaW9d</recordid><startdate>19880408</startdate><enddate>19880408</enddate><creator>van Baronaigien, D.Roelants</creator><creator>Ruskey, Frank</creator><general>Elsevier B.V</general><general>Elsevier Sequoia S.A</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>19880408</creationdate><title>Generating t-ary trees in A-order</title><author>van Baronaigien, D.Roelants ; Ruskey, Frank</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c362t-542189792049af69c2fd24890fe0887aac8f65b46de0349f1562ee58e0480ad13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1988</creationdate><topic>A-order</topic><topic>Algorithms</topic><topic>Applications</topic><topic>bijection</topic><topic>combinatorial generation</topic><topic>Mathematical analysis</topic><topic>ranking</topic><topic>t-ary tree</topic><topic>Trees</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>van Baronaigien, D.Roelants</creatorcontrib><creatorcontrib>Ruskey, Frank</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Information processing letters</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>van Baronaigien, D.Roelants</au><au>Ruskey, Frank</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Generating t-ary trees in A-order</atitle><jtitle>Information processing letters</jtitle><date>1988-04-08</date><risdate>1988</risdate><volume>27</volume><issue>4</issue><spage>205</spage><epage>213</epage><pages>205-213</pages><issn>0020-0190</issn><eissn>1872-6119</eissn><coden>IFPLAT</coden><abstract>Two ‘natural’ orders have been defined on the set of
t-ary trees. Zaks (1980) referred to these orders as A-order and B-order. Many algorithms have been developed for generating binary and
t-ary trees in B-order. Here we develop an algorithm for generating all
t-ary trees with
n nodes in (reverse) A-order, as well as ranking and unranking algorithms. The generation algorithm produces each tree in constant average time. The analysis of the generation algorithm makes use of an interesting bijection on the set of
t-ary trees. The ranking algorithm runs in O(
tn) time and the unranking algorithm in O(
tn lg
n) time.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/0020-0190(88)90027-0</doi><tpages>9</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0020-0190 |
| ispartof | Information processing letters, 1988-04, Vol.27 (4), p.205-213 |
| issn | 0020-0190 1872-6119 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_24888673 |
| source | Elsevier ScienceDirect Journals Complete |
| subjects | A-order Algorithms Applications bijection combinatorial generation Mathematical analysis ranking t-ary tree Trees |
| title | Generating t-ary trees in A-order |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-25T22%3A43%3A05IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Generating%20t-ary%20trees%20in%20A-order&rft.jtitle=Information%20processing%20letters&rft.au=van%20Baronaigien,%20D.Roelants&rft.date=1988-04-08&rft.volume=27&rft.issue=4&rft.spage=205&rft.epage=213&rft.pages=205-213&rft.issn=0020-0190&rft.eissn=1872-6119&rft.coden=IFPLAT&rft_id=info:doi/10.1016/0020-0190(88)90027-0&rft_dat=%3Cproquest_cross%3E1136890%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=237258852&rft_id=info:pmid/&rft_els_id=0020019088900270&rfr_iscdi=true |