Kurt Hoffmann, Kurt Mehlhorn, Pierre Rosenstiehl, Robert E. Tarjan
{"title":"排序约旦序列在线性时间使用水平链接搜索树","authors":"Kurt Hoffmann, Kurt Mehlhorn, Pierre Rosenstiehl, Robert E. Tarjan","doi":"10.1016/S0019-9958(86)80033-X","DOIUrl":null,"url":null,"abstract":"<div><p>For a Jordan curve <em>C</em> in the plane nowhere tangent to the <em>x</em> axis, let <em>x</em><sub>1</sub>, <em>x</em><sub>2</sub>,…, <em>x<sub>n</sub></em> be the abscissas of the intersection points of <em>C</em> with the <em>x</em> axis, listed in the order the points occur on <em>C.</em> We call <em>x</em><sub>1</sub>, <em>x</em><sub>2</sub>,…, <em>x<sub>n</sub></em> a <em>Jordan sequence</em>. In this paper we describe an <em>O</em>(<em>n</em>)-time algorithm for recognizing and sorting Jordan sequences. The problem of sorting such sequences arises in computational geometry and computational geography. Our algorithm is based on a reduction of the recognition and sorting problem to a list-splitting problem. To solve the list-splitting problem we use level-linked search trees.</p></div>","PeriodicalId":38164,"journal":{"name":"信息与控制","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1986-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0019-9958(86)80033-X","citationCount":"121","resultStr":"{\"title\":\"Sorting jordan sequences in linear time using level-linked search trees\",\"authors\":\"Kurt Hoffmann, Kurt Mehlhorn, Pierre Rosenstiehl, Robert E. Tarjan\",\"doi\":\"10.1016/S0019-9958(86)80033-X\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>For a Jordan curve <em>C</em> in the plane nowhere tangent to the <em>x</em> axis, let <em>x</em><sub>1</sub>, <em>x</em><sub>2</sub>,…, <em>x<sub>n</sub></em> be the abscissas of the intersection points of <em>C</em> with the <em>x</em> axis, listed in the order the points occur on <em>C.</em> We call <em>x</em><sub>1</sub>, <em>x</em><sub>2</sub>,…, <em>x<sub>n</sub></em> a <em>Jordan sequence</em>. In this paper we describe an <em>O</em>(<em>n</em>)-time algorithm for recognizing and sorting Jordan sequences. The problem of sorting such sequences arises in computational geometry and computational geography. Our algorithm is based on a reduction of the recognition and sorting problem to a list-splitting problem. To solve the list-splitting problem we use level-linked search trees.</p></div>\",\"PeriodicalId\":38164,\"journal\":{\"name\":\"信息与控制\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1986-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0019-9958(86)80033-X\",\"citationCount\":\"121\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"信息与控制\",\"FirstCategoryId\":\"1093\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S001999588680033X\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"信息与控制","FirstCategoryId":"1093","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S001999588680033X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Sorting jordan sequences in linear time using level-linked search trees
For a Jordan curve C in the plane nowhere tangent to the x axis, let x1, x2,…, xn be the abscissas of the intersection points of C with the x axis, listed in the order the points occur on C. We call x1, x2,…, xn a Jordan sequence. In this paper we describe an O(n)-time algorithm for recognizing and sorting Jordan sequences. The problem of sorting such sequences arises in computational geometry and computational geography. Our algorithm is based on a reduction of the recognition and sorting problem to a list-splitting problem. To solve the list-splitting problem we use level-linked search trees.