[{"data":1,"prerenderedAt":234},["ShallowReactive",2],{"tag-二叉树-1":3},{"title":4,"articles":5,"hot_article":19,"month_arch":82,"total":230,"cover":231},"二叉树 - 独孤影的博客",[6],{"id":7,"title":8,"uri":8,"author":9,"tags":10,"created_at":16,"view_count":17,"content":18},15,"二叉树非递归解汉诺塔","duguying",[11,12,13,14,15],"汉诺塔","非递归","算法","数据结构","二叉树","2014-10-09 19:50:34",6613,"\u003Cp>解汉诺塔最常见的方法是递归法，记得上数据结构那门课的时候老师说过，递归法通常情况下都能够找到一种非递归的方法来实现，汉诺塔也有非递归的方法解决。\u003C\u002Fp>\u003Cp>\u003Cstrong>递归方法：\u003C\u002Fstrong>\u003C\u002Fp>\u003Cp>首先把三根柱子按顺序排成品字型，把所有的圆盘按从大到小的顺序放在柱子A上，根据圆盘的数量确定柱子的排放顺序：若n为偶数，按顺时针方向依次摆放 A B C；\u003Cspan style=\"font-size: 12.5px;\">若n为奇数，按顺时针方向依次摆放 A C B。\u003Cbr\u002F>\u003C\u002Fspan>\u003C\u002Fp>\u003Col class=\" list-paddingleft-2\" style=\"list-style-type: decimal;\">\u003Cli>\u003Cp>\u003Cspan style=\"font-size: 12.5px;\">按顺时针方向把圆盘1从现在的柱子移动到下一根柱子，即当n为偶数时，若圆盘1在柱子A，则把它移动到B；若圆盘1在柱子B，则把它移动到C；若圆盘1在柱子C，则把它移动到A。\u003Cbr\u002F>\u003C\u002Fspan>\u003C\u002Fp>\u003C\u002Fli>\u003Cli>\u003Cp>\u003Cspan style=\"font-size: 12.5px;\">接着，把另外两根柱子上可以移动的圆盘移动到新的柱子上。即把非空柱子上的圆盘移动到空柱子上，当两根柱子都非空时，移动较小的圆盘。这一步没有明确规定移动哪个圆盘，你可能以为会有多种可能性，其实不然，可实施的行动是唯一的。\u003Cbr\u002F>\u003C\u002Fspan>\u003C\u002Fp>\u003C\u002Fli>\u003Cli>\u003Cp>\u003Cspan style=\"font-size: 12.5px;\">反复进行1、2操作，最后就能按规定完成汉诺塔的移动。\u003Cbr\u002F>\u003C\u002Fspan>\u003C\u002Fp>\u003C\u002Fli>\u003C\u002Fol>\u003Cp>\u003Cspan style=\"font-size: 12.5px;\">所以结果非常简单，就是按照移动规则向一个方向移动金片：\u003Cbr\u002F>\u003C\u002Fspan>\u003Cspan style=\"font-size: 12.5px;\">如3阶汉诺塔的移动：A→C,A→B,C→B,A→C,B→A,B→C,A→C\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"color: rgb(255, 0, 0);\">\u003Cstrong>非递归方法\u003C\u002Fstrong>\u003C\u002Fspan>\u003Cstrong>：\u003C\u002Fstrong>\u003Cbr\u002F>\u003C\u002Fp>\u003Col class=\" list-paddingleft-2\" style=\"list-style-type: decimal;\">\u003Cli>\u003Cp>确定起点塔、终点塔，确定层数n\u003C\u002Fp>\u003C\u002Fli>\u003Cli>\u003Cp>若由A到C，画出其下分支\u003C\u002Fp>\u003Cp>                 A\u003Cspan style=\"line-height: 23px;\">→C                          1\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>        A\u003Cspan style=\"line-height: 23px;\">→B          B\u003Cspan style=\"line-height: 23px;\">→C                  2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">A\u003Cspan style=\"line-height: 23px;\">→C   C\u003Cspan style=\"line-height: 23px;\">→B    B\u003Cstrong>\u003Cspan style=\"line-height: 23px;\">→\u003C\u002Fspan>\u003C\u002Fstrong>\u003Cspan style=\"line-height: 23px;\">A   A\u003Cspan style=\"line-height: 23px;\">→C           3\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fp>\u003C\u002Fli>\u003Cli>\u003Cp>\u003Cem>\u003Cstrong>\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">中序遍历得到结果\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fstrong>\u003C\u002Fem>\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">：\u003Cspan style=\"line-height: 23px;\">A\u003C\u002Fspan>\u003Cspan style=\"line-height: 23px;\">→C,\u003Cspan style=\"line-height: 23px;\"> A\u003C\u002Fspan>\u003Cspan style=\"line-height: 23px;\">→B,\u003Cspan style=\"line-height: 23px;\"> C\u003C\u002Fspan>\u003Cspan style=\"line-height: 23px;\">→B,\u003Cspan style=\"line-height: 23px;\"> A\u003C\u002Fspan>\u003Cspan style=\"line-height: 23px;\">→C, \u003Cspan style=\"line-height: 23px;\">B\u003C\u002Fspan>\u003Cstrong style=\"line-height: 23px; white-space: normal;\">→\u003C\u002Fstrong>\u003Cspan style=\"line-height: 23px;\">A ,\u003Cspan style=\"line-height: 23px;\"> B\u003C\u002Fspan>\u003Cspan style=\"line-height: 23px;\">→C,\u003Cspan style=\"line-height: 23px;\"> A\u003C\u002Fspan>\u003Cspan style=\"line-height: 23px;\">→C\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fp>\u003C\u002Fli>\u003C\u002Fol>\u003Cp>\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Ca href=\"\u002F\u002Fduguying.oss-cn-qingdao.aliyuncs.com\u002F2014\u002F10\u002F9\u002Ftree-script.jpg\">\u003Cimg src=\"\u002F\u002Fduguying.oss-cn-qingdao.aliyuncs.com\u002F2014\u002F10\u002F9\u002Ftree-script.jpg\" title=\"\" alt=\"tree-script.jpg\"\u002F>\u003C\u002Fa>\u003Cbr\u002F>5阶汉诺塔二叉树(演算手稿)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fp>\u003Cp>\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">\u003Cspan style=\"line-height: 23px;\">这种非递归的方法在手工演算方面着实简易，只需列出这棵二叉树便能够迅速写出答案。哈哈，挺适合做试卷的。不过，用此方法编程从理解上到也是比较容易的，比起递归法可能代码稍多但理解较易。\u003Cbr\u002F>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fp>",{"title":20,"list":21},"最热文章",[22,28,34,40,46,52,58,64,70,76],{"id":23,"title":24,"uri":25,"author":9,"created_at":26,"view_count":27},28,"docker容器目录与主机目录同步","\u002Farticle\u002Fdocker容器目录与主机目录同步","2014-12-31 12:34:08",15570,{"id":29,"title":30,"uri":31,"author":9,"created_at":32,"view_count":33},21,"beego中使用fis","\u002Farticle\u002Fbeego中使用fis","2014-12-03 10:47:56",9250,{"id":35,"title":36,"uri":37,"author":9,"created_at":38,"view_count":39},20,"用github登录，oauth开发","\u002Farticle\u002F用github登录，oauth开发","2014-11-23 13:33:37",9113,{"id":41,"title":42,"uri":43,"author":9,"created_at":44,"view_count":45},18,"windows服务注册工具nssm","\u002Farticle\u002Fwindows服务注册工具nssm","2014-10-31 21:34:39",9047,{"id":47,"title":48,"uri":49,"author":9,"created_at":50,"view_count":51},49,"用latex排版中文书籍","\u002Farticle\u002F用latex排版中文书籍","2016-10-31 11:12:02",8634,{"id":53,"title":54,"uri":55,"author":9,"created_at":56,"view_count":57},19,"texlive中文书签乱码","\u002Farticle\u002Ftexlive中文书签乱码","2014-11-15 02:54:01",8461,{"id":59,"title":60,"uri":61,"author":9,"created_at":62,"view_count":63},6,"Windows上的软件包管理器chocolatey","\u002Farticle\u002FWindows上的软件包管理器chocolatey","2014-08-10 15:55:22",8009,{"id":65,"title":66,"uri":67,"author":9,"created_at":68,"view_count":69},3,"利用开源和免费资源搭建CI环境","\u002Farticle\u002F利用开源和免费资源搭建CI环境","2014-07-04 16:54:58",7732,{"id":71,"title":72,"uri":73,"author":9,"created_at":74,"view_count":75},16,"php-fpm网站目录权限配置","\u002Farticle\u002Fphp-fpm网站目录权限配置","2014-10-18 01:36:10",7274,{"id":77,"title":78,"uri":79,"author":9,"created_at":80,"view_count":81},27,"sublime text 2插件开发，外部修改文件无法重新加载","\u002Farticle\u002Fsublime text 2插件开发，外部修改文件无法重新加载","2014-12-26 20:24:13",7054,{"title":83,"list":84},"按月归档",[85,89,92,95,98,101,104,108,112,115,118,121,125,128,131,135,138,141,144,148,151,154,157,160,163,166,169,172,175,178,181,184,187,190,193,196,199,202,205,208,212,215,218,221,224,227],{"title":86,"uri":87,"view_count":88},"2026年7月","\u002Farchive\u002F2026\u002F7\u002F1","[1]",{"title":90,"uri":91,"view_count":88},"2026年1月","\u002Farchive\u002F2026\u002F1\u002F1",{"title":93,"uri":94,"view_count":88},"2025年4月","\u002Farchive\u002F2025\u002F4\u002F1",{"title":96,"uri":97,"view_count":88},"2024年6月","\u002Farchive\u002F2024\u002F6\u002F1",{"title":99,"uri":100,"view_count":88},"2024年5月","\u002Farchive\u002F2024\u002F5\u002F1",{"title":102,"uri":103,"view_count":88},"2024年4月","\u002Farchive\u002F2024\u002F4\u002F1",{"title":105,"uri":106,"view_count":107},"2023年12月","\u002Farchive\u002F2023\u002F12\u002F1","[6]",{"title":109,"uri":110,"view_count":111},"2023年11月","\u002Farchive\u002F2023\u002F11\u002F1","[2]",{"title":113,"uri":114,"view_count":88},"2023年10月","\u002Farchive\u002F2023\u002F10\u002F1",{"title":116,"uri":117,"view_count":88},"2023年7月","\u002Farchive\u002F2023\u002F7\u002F1",{"title":119,"uri":120,"view_count":111},"2023年6月","\u002Farchive\u002F2023\u002F6\u002F1",{"title":122,"uri":123,"view_count":124},"2023年5月","\u002Farchive\u002F2023\u002F5\u002F1","[3]",{"title":126,"uri":127,"view_count":111},"2023年4月","\u002Farchive\u002F2023\u002F4\u002F1",{"title":129,"uri":130,"view_count":111},"2023年3月","\u002Farchive\u002F2023\u002F3\u002F1",{"title":132,"uri":133,"view_count":134},"2023年2月","\u002Farchive\u002F2023\u002F2\u002F1","[5]",{"title":136,"uri":137,"view_count":88},"2023年1月","\u002Farchive\u002F2023\u002F1\u002F1",{"title":139,"uri":140,"view_count":111},"2022年12月","\u002Farchive\u002F2022\u002F12\u002F1",{"title":142,"uri":143,"view_count":134},"2022年11月","\u002Farchive\u002F2022\u002F11\u002F1",{"title":145,"uri":146,"view_count":147},"2022年10月","\u002Farchive\u002F2022\u002F10\u002F1","[4]",{"title":149,"uri":150,"view_count":107},"2022年9月","\u002Farchive\u002F2022\u002F9\u002F1",{"title":152,"uri":153,"view_count":134},"2022年8月","\u002Farchive\u002F2022\u002F8\u002F1",{"title":155,"uri":156,"view_count":88},"2019年7月","\u002Farchive\u002F2019\u002F7\u002F1",{"title":158,"uri":159,"view_count":88},"2019年2月","\u002Farchive\u002F2019\u002F2\u002F1",{"title":161,"uri":162,"view_count":88},"2018年9月","\u002Farchive\u002F2018\u002F9\u002F1",{"title":164,"uri":165,"view_count":88},"2018年8月","\u002Farchive\u002F2018\u002F8\u002F1",{"title":167,"uri":168,"view_count":88},"2017年11月","\u002Farchive\u002F2017\u002F11\u002F1",{"title":170,"uri":171,"view_count":88},"2017年8月","\u002Farchive\u002F2017\u002F8\u002F1",{"title":173,"uri":174,"view_count":88},"2017年5月","\u002Farchive\u002F2017\u002F5\u002F1",{"title":176,"uri":177,"view_count":88},"2017年4月","\u002Farchive\u002F2017\u002F4\u002F1",{"title":179,"uri":180,"view_count":88},"2016年11月","\u002Farchive\u002F2016\u002F11\u002F1",{"title":182,"uri":183,"view_count":88},"2016年10月","\u002Farchive\u002F2016\u002F10\u002F1",{"title":185,"uri":186,"view_count":111},"2016年9月","\u002Farchive\u002F2016\u002F9\u002F1",{"title":188,"uri":189,"view_count":88},"2016年8月","\u002Farchive\u002F2016\u002F8\u002F1",{"title":191,"uri":192,"view_count":111},"2016年7月","\u002Farchive\u002F2016\u002F7\u002F1",{"title":194,"uri":195,"view_count":134},"2016年6月","\u002Farchive\u002F2016\u002F6\u002F1",{"title":197,"uri":198,"view_count":88},"2015年12月","\u002Farchive\u002F2015\u002F12\u002F1",{"title":200,"uri":201,"view_count":88},"2015年10月","\u002Farchive\u002F2015\u002F10\u002F1",{"title":203,"uri":204,"view_count":111},"2015年2月","\u002Farchive\u002F2015\u002F2\u002F1",{"title":206,"uri":207,"view_count":88},"2015年1月","\u002Farchive\u002F2015\u002F1\u002F1",{"title":209,"uri":210,"view_count":211},"2014年12月","\u002Farchive\u002F2014\u002F12\u002F1","[8]",{"title":213,"uri":214,"view_count":111},"2014年11月","\u002Farchive\u002F2014\u002F11\u002F1",{"title":216,"uri":217,"view_count":134},"2014年10月","\u002Farchive\u002F2014\u002F10\u002F1",{"title":219,"uri":220,"view_count":124},"2014年9月","\u002Farchive\u002F2014\u002F9\u002F1",{"title":222,"uri":223,"view_count":124},"2014年8月","\u002Farchive\u002F2014\u002F8\u002F1",{"title":225,"uri":226,"view_count":124},"2014年7月","\u002Farchive\u002F2014\u002F7\u002F1",{"title":228,"uri":229,"view_count":111},"2013年9月","\u002Farchive\u002F2013\u002F9\u002F1",1,{"url":232,"title":233},"https:\u002F\u002Fimage.duguying.net\u002F2022\u002F09\u002Fij6x8o4s.webp","老家 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