�??xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:trackback="http://madskills.com/public/xml/rss/module/trackback/" xmlns:wfw="http://wellformedweb.org/CommentAPI/" xmlns:slash="http://purl.org/rss/1.0/modules/slash/"><channel><title>&#20122;&#27954;&#27431;&#27954;&#35270;&#39057;&#22312;&#32447;&#44;&#57;&#49;&#20037;&#20037;&#20037;&#20037;&#44;&#26085;&#26412;&#20122;&#27954;&#19981;&#21345;</title><link>http://www.aygfsteel.com/zzzlyr/category/55295.html</link><description /><language>zh-cn</language><lastBuildDate>Thu, 25 Jan 2018 06:05:24 GMT</lastBuildDate><pubDate>Thu, 25 Jan 2018 06:05:24 GMT</pubDate><ttl>60</ttl><item><title>btree/b+tree�l�构原理和应�?/title><link>http://www.aygfsteel.com/zzzlyr/archive/2018/01/25/433028.html</link><dc:creator>张钊�?/dc:creator><author>张钊�?/author><pubDate>Thu, 25 Jan 2018 05:44:00 GMT</pubDate><guid>http://www.aygfsteel.com/zzzlyr/archive/2018/01/25/433028.html</guid><wfw:comment>http://www.aygfsteel.com/zzzlyr/comments/433028.html</wfw:comment><comments>http://www.aygfsteel.com/zzzlyr/archive/2018/01/25/433028.html#Feedback</comments><slash:comments>0</slash:comments><wfw:commentRss>http://www.aygfsteel.com/zzzlyr/comments/commentRss/433028.html</wfw:commentRss><trackback:ping>http://www.aygfsteel.com/zzzlyr/services/trackbacks/433028.html</trackback:ping><description><![CDATA[最�q�在公司有点旉���所以深入研�I�了下数据库索引btree/b+tree数据�l�构和原理，由此牵引��Z��好多问题�Q�请看如下带着问题研究�?br /><br />1�Q��ؓ什�?btree/b+tree 数据�l�构适合数据库烦引，它到底是怎么样一个原理和�l�构�Q?br /><br />btree/b+tree 数据�l�构�Q?br /><br /><span style="color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;">在之前的文章中我们介�l�过AVL树，�U�黑树，它们都属于二叉树�Q�即每个节点最多只能拥�?个子节点�Q�而B-tree�Q�B树）的每个节点可以拥�?个以上的子节点，所以我们简单概括一下：B-tree���是一颗多路��^衡查找树�Q�它�q�泛应用于数据库索引和文件系�l�中�?/span><p style="box-sizing: inherit; margin: 0px 0px 20px; color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;">首先我们介绍一下一�?m 阶B-tree的特性，那么�q�个 m 阶是怎么定义的呢�Q�这里我们以一个节点能拥有的最大子节点数来表示�q�颗树的阶数。�D个例子，如果一个节�Ҏ��多有 n 个key�Q�那么这个节�Ҏ��多就会有 n+1 个子节点�Q�这���|�����叫�?n+1�Q�m=n+1�Q�阶树。一�?m 阶B-tree包括以下5条特性：</p><ol style="box-sizing: inherit; margin: 20px 0px; padding: 0px 0px 0px 40px; color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;"><li style="box-sizing: inherit; list-style-type: decimal; margin-top: 10px; list-style-position: outside;">每个节点最多有 m 个子节点</li><li style="box-sizing: inherit; list-style-type: decimal; margin-top: 10px; list-style-position: outside;">除根节点和叶子节点，其它每个节点臛_���?[m/2] �Q�向上取整的意思）个子节点</li><li style="box-sizing: inherit; list-style-type: decimal; margin-top: 10px; list-style-position: outside;">若根节点不是叶子节点�Q�则其至���有2个子节点</li><li style="box-sizing: inherit; list-style-type: decimal; margin-top: 10px; list-style-position: outside;">所有NULL节点到根节点的高度都一�?/li><li style="box-sizing: inherit; list-style-type: decimal; margin-top: 10px; list-style-position: outside;">除根节点外，其它节点都包�?n 个key�Q�其�?[m/2] -1 &lt;= n &lt;= m-1</li></ol><p style="box-sizing: inherit; margin: 0px 0px 20px; color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;">�q�些�Ҏ��可能看着不太好理解，下面我们会介�l�B-tree的插入，在插入节点的�q�程中我们就会慢慢理解这些特性了。B-tree的插入比较简单，���是一个节点至下而上的分裂过�E�。下面我们具体以一�?阶树来展�C�B-tree的插入过�E��?/p><p style="box-sizing: inherit; margin: 0px 0px 20px; color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;">首先我们 插入 200�Q?00�Q?00�Q�没有什么问题，直接插入���好�?/p><p style="box-sizing: inherit; margin: 0px 0px 20px; color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;">| 200 | 300 | 400 |<br style="box-sizing: inherit;" /></p><p style="box-sizing: inherit; margin: 0px 0px 20px; color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;">现在我们接着插入500�Q�这个时候我们发现有炚w��题，�Ҏ��定义及特�?我们知道一�?阶B-tree的每个节�Ҏ��多只能有3个key�Q�插�?00后这个节点就�?个key了�?/p><p style="box-sizing: inherit; margin: 0px 0px 20px; color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;">| 200 | 300 | 400 | 500 |<br style="box-sizing: inherit;" /></p><p style="box-sizing: inherit; margin: 0px 0px 20px; color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;">�q�个时候我们就需要分裂，���中间的key上移到父节点�Q�左边的作�ؓ左节点，双���的作为右节点�Q�如下图所�C�：</p><p style="box-sizing: inherit; margin: 0px 0px 20px; color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;"></p><figure style="box-sizing: inherit; margin: 24px 0px; color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;"><img src="https://pic4.zhimg.com/80/v2-d44a37240c1d4226d82480e87321e0a9_hd.jpg" data-rawwidth="428" data-rawheight="172" zh-lightbox-thumb=""  lazy"="" width="428" data-original="https://pic4.zhimg.com/v2-d44a37240c1d4226d82480e87321e0a9_r.jpg" data-actualsrc="https://pic4.zhimg.com/v2-d44a37240c1d4226d82480e87321e0a9_b.jpg" style="box-sizing: inherit; overflow: hidden; display: block; max-width: 100%; margin: 0px auto; cursor: -webkit-zoom-in;" alt="" /></figure><span style="color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;">�q�个时候我们是不是���明白特�?了，如果根节点不是叶子节点，那么它肯定发生了分裂�Q�所以至���会�?个子节点。同��h��们接着插入600�Q?00�Q?00�Q?00插入�q�程如下图所�C�：</span><p style="box-sizing: inherit; margin: 0px 0px 20px; color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;"></p><p style="box-sizing: inherit; margin: 0px 0px 20px; color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;"></p><figure style="box-sizing: inherit; margin: 24px 0px; color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;"><img src="https://pic2.zhimg.com/80/v2-4fc1d75f4904af871324b8dd2399e499_hd.jpg" data-rawwidth="834" data-rawheight="810" zh-lightbox-thumb=""  lazy"="" width="834" data-original="https://pic2.zhimg.com/v2-4fc1d75f4904af871324b8dd2399e499_r.jpg" data-actualsrc="https://pic2.zhimg.com/v2-4fc1d75f4904af871324b8dd2399e499_b.jpg" style="box-sizing: inherit; overflow: hidden; display: block; max-width: 100%; margin: 0px auto; cursor: -webkit-zoom-in;" alt="" /></figure><span style="color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;">现在根节点也已经满了�Q�如果我们���l�插�?10�Q?20�Q�会怎样呢？根节点就会���l�分裂，树���l�向上生�ѝ��看下图�Q?/span><p style="box-sizing: inherit; margin: 0px 0px 20px; color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;"></p><figure style="box-sizing: inherit; margin: 24px 0px; color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;"><img src="https://pic1.zhimg.com/80/v2-19c2afb9282e50971e44d6dca939f8f8_hd.jpg" data-rawwidth="736" data-rawheight="674" zh-lightbox-thumb=""  lazy"="" width="736" data-original="https://pic1.zhimg.com/v2-19c2afb9282e50971e44d6dca939f8f8_r.jpg" data-actualsrc="https://pic1.zhimg.com/v2-19c2afb9282e50971e44d6dca939f8f8_b.jpg" style="box-sizing: inherit; overflow: hidden; display: block; max-width: 100%; margin: 0px auto; cursor: -webkit-zoom-in;" alt="" /></figure><p style="box-sizing: inherit; margin: 0px 0px 20px; color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;">通过整个的插入过�E�我们也会发玎ͼ�B-tree和二叉树的一个显著的区别���是�Q�B-tree是从下往上生长，而二叉树是从上往下生长的。现在我们想想特�?和特�?是�ؓ什么？首先我们知道子节点的个数是等于key的数�?1�Q�然后一个节点达到m个key后就会分裂，所以分裂后的节�Ҏ�����能得到 m/2 - 1个key 。�ؓ啥还要减一呢？因�ؓ�q�要拿一个作为父节点。所以这个节�Ҏ�����回拥有 m/2 - 1 + 1 = m/2 个子节点。同样得到特�?�Q�因为最���有m/2个子节点�Q�所以最���就含有m/2-1个key�Q�m 阶树�Q�每个节点存��C��m个key��׃��分裂�Q�所以最多就�?m-1个key�?/p><p style="box-sizing: inherit; margin: 0px 0px 20px; color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;">�Ҏ��以上�Ҏ��我们能推出一���含有N个��d��键字数的m阶的B-tree树的最大高度h的�?</p><p style="box-sizing: inherit; margin: 0px 0px 20px; color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;"><span style="box-sizing: inherit; font-weight: 600;">树的高度h: 1�Q?2�Q?3 �Q?4 �Q?......... �Q?h</span></p><p style="box-sizing: inherit; margin: 0px 0px 20px; color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;"><span style="box-sizing: inherit; font-weight: 600;">节点个数s: 1�Q?2�Q?2*(m/2)�Q?2*(m/2)(m/2)�Q?........ �Q?*(m/2)的h-2�ơ方</span></p><p style="box-sizing: inherit; margin: 0px 0px 20px; color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;"><span style="box-sizing: inherit; font-weight: 600;">s = 1 + 2(1 -&nbsp;<img src="http://www.zhihu.com/equation?tex=%28m%2F2%29%5E%7Bh-1%7D+" alt="(m/2)^{h-1} " eeimg="1" style="box-sizing: inherit; overflow: hidden; display: inline-block; max-width: 100%; margin: 0px 3px; vertical-align: middle;" />)/(1- (m/2))</span></p><p style="box-sizing: inherit; margin: 0px 0px 20px; color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;"><span style="box-sizing: inherit; font-weight: 600;">N = 1 + s * ((m/2) - 1) = 2 * (<img src="http://www.zhihu.com/equation?tex=%28m%2F2%29%5E%7Bh-1%7D+" alt="(m/2)^{h-1} " eeimg="1" style="box-sizing: inherit; overflow: hidden; display: inline-block; max-width: 100%; margin: 0px 3px; vertical-align: middle;" />) - 1</span></p><p style="box-sizing: inherit; margin: 0px 0px 20px; color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;"><span style="box-sizing: inherit; font-weight: 600;">h = log&#9484;m/2&#9488;((N+1)/2 )+1</span></p><p style="box-sizing: inherit; margin: 0px 0px 20px; color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;">2�Q��ؓ什么btree/b+tree 为常用数据库索引�l�构�Q?br /></p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">上文说过�Q�红黑树�{�数据结构也可以用来实现索引�Q�但是文件系�l�及数据库系�l�普遍采用B-/+Tree作�ؓ索引�l�构�Q�这一节将�l�合计算机组成原理相关知识讨论B-/+Tree作�ؓ索引的理论基����?/p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">一般来��_��索引本��n也很大，不可能全部存储在内存中，因此索引往往以烦引文件的形式存储的磁盘上。这��L��话，索引查找�q�程中就要��生磁盘I/O消耗，相对于内存存取，I/O存取的消耗要高几个数量���Q�所以评价一个数据结构作为烦引的优劣最重要的指标就是在查找�q�程中磁盘I/O操作�ơ数的渐�q�复杂度。换句话��_��索引的结构组�l�要���量减少查找�q�程中磁盘I/O的存取次数。下面先介绍内存和磁盘存取原理，然后再结合这些原理分析B-/+Tree作�ؓ索引的效率�?/p><h3><a name="t8" style="box-sizing: border-box; background: transparent; color: rgb(66, 139, 202); margin: 0px; padding: 0px; outline: 0px;"></a>��d��存取原理</h3><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">目前计算��Z��用的��d��基本都是随机��d��存储器（RAM�Q�，��C��RAM的结构和存取原理比较复杂�Q�这里本文抛却具体差别，抽象��Z��个十分简单的存取模型来说明RAM的工作原理�?/p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;"><a  target="_blank" style="box-sizing: border-box; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; color: #ca0c16; text-decoration-line: none; margin: 0px; padding: 0px; outline: 0px;"></a></p><p align="center" style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;"><strong style="box-sizing: border-box;">�?</strong></p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">从抽象角度看�Q�主存是一�p�d��的存储单元组成的矩阵�Q�每个存储单元存储固定大���的数据。每个存储单元有唯一的地址�Q�现代主存的�~�址规则比较复杂�Q�这里将其简化成一个二�l�地址�Q�通过一个行地址和一个列地址可以唯一定位��C��个存储单元。图5展示了一�? x 4的主存模型�?/p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">��d��的存取过�E�如下：</p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">当系�l�需要读取主存时�Q�则���地址信号攑ֈ�地址�ȝ��上传�l�主存，��d����d��地址信号后，解析信号�q�定位到指定存储单元�Q�然后将此存储单元数据放到数据�ȝ��上，供其它部件读取�?/p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">写主存的�q�程�c�M���Q�系�l�将要写入单元地址和数据分别放在地址�ȝ��和数据�ȝ��上，��d����d��两个�ȝ��的内容，做相应的写操作�?/p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">�q�里可以看出�Q�主存存取的旉���仅与存取�ơ数呈线性关�p�，因�ؓ不存在机械操作，两次存取的数据的&#8220;距离&#8221;不会�Ҏ��间有��M��影响�Q�例如，先取A0再取A1和先取A0再取D3的时间消耗是一��L���?/p><h3><a name="t9" style="box-sizing: border-box; background: transparent; color: rgb(66, 139, 202); margin: 0px; padding: 0px; outline: 0px;"></a>���盘存取原理</h3><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">上文说过�Q�烦引一般以文�g形式存储在磁盘上�Q�烦引检索需要磁盘I/O操作。与��d��不同�Q�磁盘I/O存在机械�q�动耗费�Q�因此磁盘I/O的时间消耗是巨大的�?/p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">�?是磁盘的整体�l�构�C�意图�?/p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;"></p><p align="center" style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;"><strong style="box-sizing: border-box;">�?</strong></p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">一个磁盘由大小相同且同轴的圆�Ş盘片�l�成�Q�磁盘可以�{动（各个���盘必须同步转动�Q�。在���盘的一侧有���头支架�Q�磁头支架固定了一�l�磁��_��每个���头负责存取一个磁盘的内容。磁头不能�{动，但是可以沿磁盘半径方向运动（实际是斜切向�q�动�Q�，每个���头同一时刻也必���L��同��u的，即从正上方向下看�Q�所有磁头�Q何时候都是重叠的�Q�不�q�目前已�l�有多磁头独立技术，可不受此限制�Q��?/p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">�?是磁盘结构的�C�意图�?/p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;"></p><p align="center" style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;"><strong style="box-sizing: border-box;">�?</strong></p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">盘片被划分成一�p�d��同心环，圆心是盘片中心，每个同心环叫做一个磁道，所有半径相同的���道�l�成一个柱面。磁道被沿半径线划分成一个个���的�D�，每个�D�叫做一个扇区，每个扇区是磁盘的最���存储单元。�ؓ了简单�v见，我们下面假设���盘只有一个盘片和一个磁头�?/p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">当需要从���盘��d��数据�Ӟ���pȝ��会将数据逻辑地址传给���盘�Q�磁盘的控制电�\按照��d��逻辑���逻辑地址���译成物理地址�Q�即���定要读的数据在哪个���道�Q�哪个扇区。�ؓ了读取这个扇区的数据�Q�需要将���头攑ֈ��q�个扇区上方�Q��ؓ了实现这一点，���头需要移动对准相应磁道，�q�个�q�程叫做寻道�Q�所耗费旉���叫做寻道旉����Q�然后磁盘旋转将目标扇区旋�{到磁头下�Q�这个过�E�耗费的时间叫做旋转时间�?/p><h3><a name="t10" style="box-sizing: border-box; background: transparent; color: rgb(66, 139, 202); margin: 0px; padding: 0px; outline: 0px;"></a>局部性原理与���盘预读</h3><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">�׃��存储介质的特性，���盘本��n存取���比��d��慢很多，再加上机械运动耗费�Q�磁盘的存取速度往往是主存的几百分分之一�Q�因此�ؓ了提高效率，要尽量减���磁盘I/O。�ؓ了达到这个目的，���盘往往不是严格按需��d���Q�而是每次都会预读�Q�即使只需要一个字节，���盘也会从这个位�|�开始，��序向后��d��一定长度的数据攑օ�内存。这样做的理��Z��据是计算机科学中著名的局部性原理：</p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">当一个数据被用到�Ӟ��光����q�的数据也通常会马上被使用�?/p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">�E�序�q�行期间所需要的数据通常比较集中�?/p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">�׃�����盘��序��d��的效率很高（不需要寻道时��_��只需很少的旋转时��_���Q�因此对于具有局部性的�E�序来说�Q�预��d��以提高I/O效率�?/p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">预读的长度一般�ؓ��（page�Q�的整倍数。页是计���机���理存储器的逻辑块，����g及操作系�l�往往���主存和���盘存储区分割�ؓ�q�箋的大���相�{�的块，每个存储块称��Z����（在许多操作系�l�中�Q�页得大���通常�?k�Q�，��d��和磁盘以���ؓ单位交换数据。当�E�序要读取的数据不在��d��中时�Q�会触发一个缺��异常，此时�pȝ��会向���盘发出�ȝ��信号�Q�磁盘会扑ֈ�数据的�v始位�|��ƈ向后�q�箋��d��一��|��几页载入内存中，然后异常�q�回�Q�程序���l�运行�?/p><h3><a name="t11" style="box-sizing: border-box; background: transparent; color: rgb(66, 139, 202); margin: 0px; padding: 0px; outline: 0px;"></a>B-/+Tree索引的性能分析</h3><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">到这里终于可以分析B-/+Tree索引的性能了�?/p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">上文说过一般��用磁盘I/O�ơ数评�h索引�l�构的优劣。先从B-Tree分析�Q�根据B-Tree的定义，可知���索一�ơ最多需要访问h个节炏V��数据库�pȝ��的设计者��y妙利用了���盘预读原理�Q�将一个节点的大小设�ؓ�{�于一个页�Q�这��h��个节点只需要一�ơI/O���可以完全蝲入。�ؓ了达到这个目的，在实际实现B- Tree�q�需要��用如下技巧：</p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">每次新徏节点�Ӟ��直接甌���一个页的空��_���q�样��׃��证一个节点物理上也存储在一个页里，加之计算机存储分配都是按��对齐的�Q�就实现了一个node只需一�ơI/O�?/p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;"><strong style="box-sizing: border-box;">B-Tree中一�ơ检索最多需要h-1�ơI/O�Q�根节点帔R��内存�Q�，渐进复杂度�ؓO(h)=O(log<span style="box-sizing: border-box; position: relative; font-size: 12px; line-height: 0; vertical-align: baseline; bottom: -0.25em;">d</span>N)�?/strong>一般实际应用中�Q�出度d是非常大的数字，通常���过100�Q�因此h非常���（通常不超�q?�Q��?/p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">�l�g��所�q�ͼ�用B-Tree作�ؓ索引�l�构效率是非帔R��的�?/p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">而红黑树�q�种�l�构�Q�h明显要深的多。由于逻辑上很�q�的节点�Q�父子）物理上可能很�q�，无法利用局部性，所以红黑树的I/O渐进复杂度也为O(h)�Q�效率明显比B-Tree差很多�?/p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">上文�q�说�q�，B+Tree更适合外存索引�Q�原因和内节点出度d有关。从上面分析可以看到�Q�d���大索引的性能���好�Q�而出度的上限取决于节点内key和data的大���：</p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">d<span style="box-sizing: border-box; position: relative; font-size: 12px; line-height: 0; vertical-align: baseline; bottom: -0.25em;">max</span>&nbsp;=&nbsp;<span style="box-sizing: border-box;"><strong style="box-sizing: border-box;">floor</strong></span>(pagesize / (keysize + datasize + pointsize))&nbsp;&nbsp;<span style="box-sizing: border-box;"><span style="box-sizing: border-box; margin: 0px; padding: 0px; color: #a5a5a5;">(pagesize &#8211; dmax &gt;= pointsize)</span></span></p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">�?/p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">d<span style="box-sizing: border-box; position: relative; font-size: 12px; line-height: 0; vertical-align: baseline; bottom: -0.25em;">max</span>&nbsp;=&nbsp;<span style="box-sizing: border-box;"><strong style="box-sizing: border-box;">floor</strong></span>(pagesize / (keysize + datasize + pointsize)) - 1&nbsp;&nbsp;<span style="box-sizing: border-box;"><span style="box-sizing: border-box; margin: 0px; padding: 0px; color: #a5a5a5;">(pagesize &#8211; dmax &lt; pointsize)</span></span></p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">floor表示向下取整。由于B+Tree内节点去掉了data域，因此可以拥有更大的出度，拥有更好的性能�?/p><p style="box-sizing: border-box; margin: 0px; padding: 0px; color: #454545; font-family: &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, SimHei, Arial, SimSun; font-size: 16px;">�q�一章从理论角度讨论了与索引相关的数据结构与���法问题�Q�下一章将讨论B+Tree是如何具体实��CؓMySQL中烦引，同时���结合MyISAM和InnDB存储引擎介绍非聚集烦引和聚集索引两种不同的烦引实现�Ş式�?/p><p style="box-sizing: inherit; margin: 0px 0px 20px; color: #333333; font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Microsoft YaHei&quot;, &quot;Source Han Sans SC&quot;, &quot;Noto Sans CJK SC&quot;, &quot;WenQuanYi Micro Hei&quot;, sans-serif; font-size: medium;"><br /><br /></p><img src ="http://www.aygfsteel.com/zzzlyr/aggbug/433028.html" width = "1" height = "1" /><br><br><div align=right><a style="text-decoration:none;" href="http://www.aygfsteel.com/zzzlyr/" target="_blank">张钊�?/a> 2018-01-25 13:44 <a href="http://www.aygfsteel.com/zzzlyr/archive/2018/01/25/433028.html#Feedback" target="_blank" style="text-decoration:none;">发表评论</a></div>]]></description></item></channel></rss>                                                                                          <footer>
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