From 5394ba5657e59a12960132edf099dceeb9616fd0 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E7=BB=93=E5=8F=91=E5=8F=97=E9=95=BF=E7=94=9F?= Date: Tue, 16 Jul 2019 22:38:51 +0800 Subject: [PATCH] =?UTF-8?q?=E6=95=B0=E6=8D=AE=E5=BA=93=E7=B4=A2=E5=BC=95?= =?UTF-8?q?=E5=8E=9F=E7=90=86=E6=B5=85=E6=9E=90?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- images/算法/B+树.png | Bin 0 -> 368363 bytes images/算法/二叉查找树.png | Bin 0 -> 110901 bytes images/算法/二维阵列.png | Bin 0 -> 94092 bytes images/算法/等比数列求和.png | Bin 0 -> 3838 bytes source/_posts/算法/数据库索引原理浅析.md | 93 +++++++++++++++++++++++ 5 files changed, 93 insertions(+) create mode 100644 images/算法/B+树.png create mode 100644 images/算法/二叉查找树.png create mode 100644 images/算法/二维阵列.png create mode 100644 images/算法/等比数列求和.png create mode 100644 source/_posts/算法/数据库索引原理浅析.md diff --git a/images/算法/B+树.png b/images/算法/B+树.png new file mode 100644 index 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列用来描述主体的特征 ++ 每个列保存的是某一种类型的数据 ( 整数/字符串/日期时间… ) + +如果采用这种方法保存数据 , 如果要一次性获得所有的数据十分方便 , 但是如果要查找特定的值 +就要逐条记录进行遍历 +在最不利的情况下 , 需要执行n次运算 +时间复杂度1是O(n) +> `时间复杂度`是一个函数,它定量描述了该算法的运行时间。这是一个关于代表算法输入值的字符串的长度的函数。时间复杂度常用大O符号表述,不包括这个函数的低阶项和首项系数。使用这种方式时,时间复杂度可被称为是渐近的,它考察当输入值大小趋近无穷时的情况。 + +如果想要检索的速度更快一些 , 就需要用到`二叉树`结构 + +### 树与数据库索引 +`二叉查找树`是具有特殊属性的二叉树 , 其中的每个节点都代表了一条记录的数据 , 并且要满足如下要求 ++ 比保存在其左子树的任何键值都要大 ++ 比保存在其右子树的任何键值都要小 + +![二叉查找树](/images/算法/二叉查找树.png) + +如果要在二叉查找树中搜索一个值, 首先与根节点比较, 如果值比根节点的值小, 那么就去找左子树, 反之去找右子树 +再与子树的根节点比较, 依次进行下去 +最终结果可能是在某个节点找到了这个值 +或者需要进入下一个子树时, 已经没有子树 +那么就代表这个值在树当中不存在 + +比如说我要找208 , 步骤如下: +1. 从键值为 136 的根开始,因为 136<208,我去找节点136的右子树。 +2. 398>208,所以我去找节点398的左子树 +3. 250>208,所以我去找节点250的左子树 +4. 200<208,所以我去找节点200的右子树。但是 200 没有右子树,值不存在(因为如果存在,它会在 200 的右子树) + +如果有n个数据 , 那么二叉树的深度就是log2(n) +所以这个查询的时间复杂度就是O(log2(n)) + +> 相当于一个等比数列求和, 首项是1, 公比是2, 总共有n项 +根据等比数列的求和公式 +![等比数列求和公式](/images/算法/等比数列求和.png) +代入可知 S = 2n-1 +当n趋向于正无穷 , S = 2n , 所以 n = log2(S) +这里的S就表示集合当中的数据总数, n就表示进行一次查询的节点访问次数 + +这种二叉查找树就是一个数据库索引的模型 +当然, 如果直接套用上述的方式, 只能解决快速的精确查询(针对某个特定值的), 如果要查找某个范围内的值, 仍然需要遍历整个树 + +#### B+树索引 +为了解决查找某个范围内的值的问题, 需要找到高效的范围查询的方法, 现代数据库使用了一种修订版的二叉查找树, 称为`B+树` +这种树结构有如下特点 ++ 只有叶子节点才保存信息(根据其中的信息可以直接找到表中对应的行) ++ 其他节点只是在搜索中用来指引到正确节点的 ++ 临近的叶子节点是相连的, 构成链表结构 + +![B+树](/images/算法/B+树.png) + +当然会造成节点的数量更多, 但是这个树的深度只是增加了1, 即使是从中搜索某个特定的值, 时间复杂度仍然是O(log2(n)) + +使用这个树 , 比如要查找\[40,100\]之间的数据 +那么首先找40即可(如果没有40, 就找40之后最接近的一个, 然后沿着叶子节点的链表结构依次向后遍历, 直到遇到一个比100大的数) + +**数据的增加与删除** +解决了数据查询的问题, 但是一定会给数据的增加和删除带来额外的负担, 因为必须要维护B+树的结构, 否则查询的复杂度就会增加, 甚至会失败 +也就是说这棵二叉树的子树必须尽可能匀称, 才能保证最佳的查询效率 +如果一边偏重, 复杂度就会增加, 甚至极端的情况, 它整体成为了一个链表, 也就是对于每个节点, 它下方的所有节点均在其一棵子树上 +那么就会彻底失去意义 + +B+树本身内置了自我整理和自我平衡的相关算法, 在这里暂且不做详细介绍 +插入和删除对B+树的维护都是O(log2(n))的复杂度 +所以对于一个表, 不宜创建太多的索引 + +### 哈希表 +这种数据结构与Java当中的HashMap实现原理基本相同 +只不过作为一个对象是在内存当中的 +数据库存储和管理数据, 可以将硬盘存储于内存存储相结合 +如果有了好的哈希函数(尽最大可能减少哈希冲突), 哈希表查找的时间复杂度是 O(1) + ++ 一个哈希表可以只装载一半到内存, 剩下的哈希桶可以留在硬盘上 ++ 如果要使用阵列, 则基于数组的结构需要连续的内存空间 , 如果数据量庞大 , 则很难分配到足够的内存空间 ++ 使用哈希表可以根据需要选择关键字