[{"data":1,"prerenderedAt":232},["ShallowReactive",2],{"article-二叉树非递归解汉诺塔":3},{"title":4,"article":5,"hot_article":18,"month_arch":81,"cover":229},"二叉树非递归解汉诺塔 - 独孤影的博客",{"id":6,"title":7,"uri":7,"author":8,"tags":9,"created_at":15,"view_count":16,"content":17},15,"二叉树非递归解汉诺塔","duguying",[10,11,12,13,14],"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":19,"list":20},"最热文章",[21,27,33,39,45,51,57,63,69,75],{"id":22,"title":23,"uri":24,"author":8,"created_at":25,"view_count":26},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":28,"title":29,"uri":30,"author":8,"created_at":31,"view_count":32},21,"beego中使用fis","\u002Farticle\u002Fbeego中使用fis","2014-12-03 10:47:56",9250,{"id":34,"title":35,"uri":36,"author":8,"created_at":37,"view_count":38},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":40,"title":41,"uri":42,"author":8,"created_at":43,"view_count":44},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":46,"title":47,"uri":48,"author":8,"created_at":49,"view_count":50},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":52,"title":53,"uri":54,"author":8,"created_at":55,"view_count":56},19,"texlive中文书签乱码","\u002Farticle\u002Ftexlive中文书签乱码","2014-11-15 02:54:01",8461,{"id":58,"title":59,"uri":60,"author":8,"created_at":61,"view_count":62},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":64,"title":65,"uri":66,"author":8,"created_at":67,"view_count":68},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":70,"title":71,"uri":72,"author":8,"created_at":73,"view_count":74},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":76,"title":77,"uri":78,"author":8,"created_at":79,"view_count":80},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 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