{"title":"随机Weyl树的研究","authors":"L. Devroye, Amar Goudjil","doi":"10.1002/(SICI)1098-2418(199805)12:3%3C271::AID-RSA4%3E3.0.CO;2-S","DOIUrl":null,"url":null,"abstract":"We study binary search trees constructed from Weyl sequences fnng; n 1, where is an irrational and f:g denotes \\mod 1\". We explore various properties of the structure of these trees, and relate them to the continued fraction expansion of. If H n is the height of the tree with n nodes when is chosen at random and uniformly on 0; 1], then we show that in probability, H n (12== 2) log n log log n.","PeriodicalId":303496,"journal":{"name":"Random Struct. Algorithms","volume":"31 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1998-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"A study of random Weyl trees\",\"authors\":\"L. Devroye, Amar Goudjil\",\"doi\":\"10.1002/(SICI)1098-2418(199805)12:3%3C271::AID-RSA4%3E3.0.CO;2-S\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study binary search trees constructed from Weyl sequences fnng; n 1, where is an irrational and f:g denotes \\\\mod 1\\\". We explore various properties of the structure of these trees, and relate them to the continued fraction expansion of. If H n is the height of the tree with n nodes when is chosen at random and uniformly on 0; 1], then we show that in probability, H n (12== 2) log n log log n.\",\"PeriodicalId\":303496,\"journal\":{\"name\":\"Random Struct. Algorithms\",\"volume\":\"31 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1998-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Random Struct. Algorithms\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1002/(SICI)1098-2418(199805)12:3%3C271::AID-RSA4%3E3.0.CO;2-S\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Random Struct. Algorithms","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/(SICI)1098-2418(199805)12:3%3C271::AID-RSA4%3E3.0.CO;2-S","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5
摘要
研究了基于Weyl序列的二叉搜索树;N 1，其中是无理数，f:g表示\mod 1 '。我们探索了这些树结构的各种性质，并将它们与的连分式展开联系起来。设H n为n节点树的高度，在0上随机均匀选择;1]，然后我们证明在概率中，H n (12== 2) log n log n。
We study binary search trees constructed from Weyl sequences fnng; n 1, where is an irrational and f:g denotes \mod 1". We explore various properties of the structure of these trees, and relate them to the continued fraction expansion of. If H n is the height of the tree with n nodes when is chosen at random and uniformly on 0; 1], then we show that in probability, H n (12== 2) log n log log n.
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