“红黑树”详解丨红黑树的应用场景

{"type":"doc","content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"今天我们要说的红黑树就是就是一棵非严格均衡的二叉树，均衡二叉树又是在二叉搜索树的基础上增加了自动维持平衡的性质，插入、搜索、删除的效率都比较高。红黑树也是实现 TreeMap 存储结构的基石。","attrs":{}}]},{"type":"heading","attrs":{"align":null,"level":2},"content":[{"type":"text","text":"文章相关视频讲解：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"link","attrs":{"href":"https://www.bilibili.com/video/BV1hp4y1B7Uf/","title":null,"type":null},"content":[{"type":"text","text":"红黑树在linux中的3种应用场景，听完受益匪浅","attrs":{}}]}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"link","attrs":{"href":"https://ke.qq.com/course/417774?flowToken=1013189","title":null,"type":null},"content":[{"type":"text","text":"5种红黑树的场景，从Linux内核谈到Nginx源码，听完醍醐灌顶","attrs":{}}]}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"link","attrs":{"href":"https://ke.qq.com/course/417774?flowToken=1013189","title":null,"type":null},"content":[{"type":"text","text":"c/c++Linux后台服务器开发高级架构师视频资料","attrs":{}}]}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"二叉搜索树","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"二叉搜索树又叫二叉查找树、二叉排序树，我们先看一下典型的二叉搜索树，这样的二叉树有何规则特点呢？","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"二叉搜索树有如下几个特点：","attrs":{}}]},{"type":"bulletedlist","content":[{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"节点的左子树小于节点本身","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"节点的右子树大于节点本身","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"左右子树同样为二叉搜索树","attrs":{}}]}]}],"attrs":{}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"下图就是一棵典型的二叉搜索树：","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6a/6a21c5c9366012e660241b9f667b064b.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" 二叉搜索树是均衡二叉树的基础，我们看一下它的搜索步骤如何。我们要从二叉树中找到值为 58 的节点。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"第一步：","attrs":{}},{"type":"text","text":"首先查找到根节点，值为 60 的节点。","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/1f/1fce5ac848924ccb6bd798cb849cf26f.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"第二步：","attrs":{}},{"type":"text","text":"比较我们要找的值 58 与该节点的大小。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果等于，那么恭喜，已经找到；如果小于，继续找左子树；如果大于，那么找右子树。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"很明显 58<60，因此我们找到左子树的节点 56，此时我们已经定位到了节点 56。","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6b/6b14a6cd84992a97b00caf8a563345df.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":" 第三步：","attrs":{}},{"type":"text","text":"按照第二步的规则继续找。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"58>56 我们需要继续找右子树，定位到了右子树节点 58，恭喜，此时我们已经找到了。","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/f4/f4f19ac64268a252a5b319534e8f65c8.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们经过三步就已经找到了，其实就是我们平时所说的二分查找，这种二叉搜索树好像查找效率很高，但同样它也有缺陷，如下面这样的二叉搜索树。","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/2c/2c5acd52e3a3161d590b8b39e0672f8b.jpeg","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"看到这样的二叉搜索树是否很别扭，典型的大长腿瘸子，但它也是二叉搜索树，如果我们要找值为 50 的节点，基本上和单链表查询没多大区别了，性能将大打折扣。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"这个时候我们的均衡二叉树就粉墨登场了，均衡二叉树就是在二叉搜索树的基础上添加了自动维持平衡的性质。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上面的大长腿瘸子二叉搜索树经过自动平衡后，可能就成为了下面这样的二叉树。","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/60/60f3e1f60f6c70191b7f6bd370719e2c.jpeg","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"经过了自动平衡，再去找值为 50 的节点，查找性能将提升很多。红黑树就是非严格均衡的二叉搜索树。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"红黑树规则特点","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"红黑树具体有哪些规则特点呢？","attrs":{}},{"type":"text","text":"具体如下：","attrs":{}}]},{"type":"bulletedlist","content":[{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"节点分为红色或者黑色。","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"根节点必为黑色。","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"叶子节点都为黑色，且为 null。","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"连接红色节点的两个子节点都为黑色（红黑树不会出现相邻的红色节点）。","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"从任意节点出发，到其每个叶子节点的路径中包含相同数量的黑色节点。","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"新加入到红黑树的节点为红色节点。","attrs":{}}]}]}],"attrs":{}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"规则看着好像挺多，没错，因为红黑树也是均衡二叉树，需要具备自动维持平衡的性质，上面的 6 条就是红黑树给出的自动维持平衡所需要具备的规则。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们看一看一个典型的红黑树到底是什么样儿？","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/de/ded708d22e316e5da7a4f3b381de3125.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" 首先解读一下规则，除了字面上看到的意思，还隐藏了哪些意思呢？","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"①从根节点到叶子节点的最长路径不大于最短路径的 2 倍","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"怎么样的路径算最短路径？从规则 5 中，我们知道从根节点到每个叶子节点的黑色节点数量是一样的，那么纯由黑色节点组成的路径就是最短路径。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"什么样的路径算是最长路径？根据规则 4 和规则 3，若有红色节点，则必然有一个连接的黑色节点，当红色节点和黑色节点数量相同时，就是最长路径，也就是黑色节点（或红色节点）*2。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"②为什么说新加入到红黑树中的节点为红色节点","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"从规则 4 中知道，当前红黑树中从根节点到每个叶子节点的黑色节点数量是一样的，此时假如新的是黑色节点的话，必然破坏规则。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"但加入红色节点却不一定，除非其父节点就是红色节点，因此加入红色节点，破坏规则的可能性小一些，下面我们也会举例来说明。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"什么情况下，红黑树的结构会被破坏呢？","attrs":{}},{"type":"text","text":"破坏后又怎么维持平衡，","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"维持平衡主要通过两种方式【变色】和【旋转】，【旋转】又分【左旋】和【右旋】","attrs":{}},{"type":"text","text":"，两种方式可相互结合。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"下面我们从插入和删除两种场景来举例说明。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"红黑树节点插入：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"当我们插入值为 66 的节点时，红黑树变成了这样：","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/44/44c28950f0bf4ea85712c2edcbbaa917.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"很明显，这个时候结构依然遵循着上述 6 大规则，无需启动自动平衡机制调整节点平衡状态。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果再向里面插入值为 51 的节点，这个时候红黑树变成了这样：","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/9b/9be71971ecdfbfd0c619e36bf48029a2.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"很明显现在的结构不遵循规则 4 了，这个时候就需要启动自动平衡机制调整节点平衡状态。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"关于C/C++ Linux后端开发网络底层原理知识学习提升 点击 ","attrs":{}},{"type":"link","attrs":{"href":"https://ke.qq.com/course/417774?flowToken=1013189","title":null,"type":null},"content":[{"type":"text","text":"学习资料","attrs":{}}]},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":" 获取，内容知识点包括Linux，Nginx，ZeroMQ，MySQL，Redis，线程池，MongoDB，ZK，Linux内核，CDN，P2P，epoll，Docker，TCP/IP，协程，DPDK等等。","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/a2/a279659463c84a48ea38f92d864eae90.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"变色：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们可以通过变色的方式，使结构满足红黑树的规则：","attrs":{}}]},{"type":"bulletedlist","content":[{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"首先解决结构不遵循规则 4 这一点（红色节点相连，节点 49-51），需将节点 49 改为黑色。","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"此时我们发现又违反了规则 5（56-49-51-XX 路径中黑色节点超过了其他路径），那么我们将节点 45 改为红色节点。","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"哈哈，妹的，又违反了规则 4（红色节点相连，节点 56-45-43），那么我们将节点 56 和节点 43 改为黑色节点。","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"但是我们发现此时又违反了规则 5（60-56-XX 路径的黑色节点比 60-68-XX 的黑色节点多），因此我们需要调整节点 68 为黑色。","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"完成！","attrs":{}}]}]}],"attrs":{}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/00/007faee8f95b3ecb2b93bed34aa156da.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"最终调整完成后的树为：","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/4c/4c7a30f1ddcb7bfcd2303d7c9b06b6c4.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"但并不是什么时候都那么幸运，可以直接通过变色就达成目的，大多数时候还需要通过旋转来解决。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如在下面这棵树的基础上，加入节点 65：","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/44/44c28950f0bf4ea85712c2edcbbaa917.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"插入节点 65 后进行以下步骤：","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/cb/cb8b7e866360e8a2d3325bd77f1c4cc2.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"这个时候，你会发现对于节点 64 无论是红色节点还是黑色节点，都会违反规则 5，路径中的黑色节点始终无法达成一致，这个时候仅通过【变色】已经无法达成目的。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们需要通过旋转操作，当然【旋转】操作一般还需要搭配【变色】操作。旋转包括【左旋】和【右旋】。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"左旋：","attrs":{}},{"type":"text","text":"逆时针旋转两个节点，让一个节点被其右子节点取代，而该节点成为右子节点的左子节点。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"左旋操作步骤如下：","attrs":{}},{"type":"text","text":"首先断开节点 PL 与右子节点 G 的关系，同时将其右子节点的引用指向节点 C2；然后断开节点 G 与左子节点 C2 的关系，同时将 G 的左子节点的应用指向节点 PL。","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/94/9466c3102beb3b72a51b8e17a0392b71.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"右旋：","attrs":{}},{"type":"text","text":"顺时针旋转两个节点，让一个节点被其左子节点取代，而该节点成为左子节点的右子节点。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"右旋操作步骤如下：","attrs":{}},{"type":"text","text":"首先断开节点 G 与左子节点 PL 的关系，同时将其左子节点的引用指向节点 C2；然后断开节点 PL 与右子节点 C2 的关系，同时将 PL 的右子节点的应用指向节点 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null）。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"前驱和后继都是值最接近该节点值的节点，类似于该节点.prev=前驱，该节点.next=后继。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"第二步：将前驱或者后继的值复制到该节点中，然后删掉前驱或者后继。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果删除的是左节点，则将前驱的值复制到该节点中，然后删除前驱；如果删除的是右节点，则将后继的值复制到该节点中，然后删除后继。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"这相当于是一种“取巧”的方法，我们删除节点的目的是使该节点的值在红黑树上不存在。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"因此专注于该目的，我们并不关注删除节点时是否真是我们想删除的那个节点，同时我们也不需考虑树结构的变化，因为树的结构本身就会因为自动平衡机制而经常进行调整。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"前面我们已经说了，我们要删除的实际上是前驱或者后继，因此我们就以前驱为主线来讲解。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"后继的学习可参考前驱，包括下面几种情况：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"①前驱为黑色节点，并且有一个非 null 子节点","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/dc/dc34ad67d8c9687eb7e936b7f0f72ab4.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"分析：","attrs":{}},{"type":"text","text":"因为要删除的是左节点 64，找到该节点的前驱 63；然后用前驱的值 63替换待删除节点的值 64，此时两个节点（待删除节点和前驱）的值都为 63；","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"删除前驱 63，此时成为上图过程中间环节，但我们发现其不符合红黑树规则 4，因此需要进行自动平衡调整。这里直接通过【变色】即可完成。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"②前驱为黑色节点，同时子节点都为 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