“紅黑樹”詳解丨紅黑樹的應用場景

{"type":"doc","content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"今天我們要說的紅黑樹就是就是一棵非嚴格均衡的二叉樹，均衡二叉樹又是在二叉搜索樹的基礎上增加了自動維持平衡的性質，插入、搜索、刪除的效率都比較高。紅黑樹也是實現 TreeMap 存儲結構的基石。","attrs":{}}]},{"type":"heading","attrs":{"align":null,"level":2},"content":[{"type":"text","text":"文章相關視頻講解：","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":"紅黑樹在linux中的3種應用場景，聽完受益匪淺","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種紅黑樹的場景，從Linux內核談到Nginx源碼，聽完醍醐灌頂","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後臺服務器開發高級架構師視頻資料","attrs":{}}]}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"二叉搜索樹","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"二叉搜索樹又叫二叉查找樹、二叉排序樹，我們先看一下典型的二叉搜索樹，這樣的二叉樹有何規則特點呢？","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"二叉搜索樹有如下幾個特點：","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":"節點的左子樹小於節點本身","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"節點的右子樹大於節點本身","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"左右子樹同樣爲二叉搜索樹","attrs":{}}]}]}],"attrs":{}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"下圖就是一棵典型的二叉搜索樹：","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":" 二叉搜索樹是均衡二叉樹的基礎，我們看一下它的搜索步驟如何。我們要從二叉樹中找到值爲 58 的節點。","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":"首先查找到根節點，值爲 60 的節點。","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":"比較我們要找的值 58 與該節點的大小。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果等於，那麼恭喜，已經找到；如果小於，繼續找左子樹；如果大於，那麼找右子樹。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"很明顯 58<60，因此我們找到左子樹的節點 56，此時我們已經定位到了節點 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":"按照第二步的規則繼續找。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"58>56 我們需要繼續找右子樹，定位到了右子樹節點 58，恭喜，此時我們已經找到了。","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":"我們經過三步就已經找到了，其實就是我們平時所說的二分查找，這種二叉搜索樹好像查找效率很高，但同樣它也有缺陷，如下面這樣的二叉搜索樹。","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":"看到這樣的二叉搜索樹是否很彆扭，典型的大長腿瘸子，但它也是二叉搜索樹，如果我們要找值爲 50 的節點，基本上和單鏈表查詢沒多大區別了，性能將大打折扣。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"這個時候我們的均衡二叉樹就粉墨登場了，均衡二叉樹就是在二叉搜索樹的基礎上添加了自動維持平衡的性質。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上面的大長腿瘸子二叉搜索樹經過自動平衡後，可能就成爲了下面這樣的二叉樹。","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":"經過了自動平衡，再去找值爲 50 的節點，查找性能將提升很多。紅黑樹就是非嚴格均衡的二叉搜索樹。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"紅黑樹規則特點","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"紅黑樹具體有哪些規則特點呢？","attrs":{}},{"type":"text","text":"具體如下：","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":"節點分爲紅色或者黑色。","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"根節點必爲黑色。","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"葉子節點都爲黑色，且爲 null。","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"連接紅色節點的兩個子節點都爲黑色（紅黑樹不會出現相鄰的紅色節點）。","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"從任意節點出發，到其每個葉子節點的路徑中包含相同數量的黑色節點。","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"新加入到紅黑樹的節點爲紅色節點。","attrs":{}}]}]}],"attrs":{}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"規則看着好像挺多，沒錯，因爲紅黑樹也是均衡二叉樹，需要具備自動維持平衡的性質，上面的 6 條就是紅黑樹給出的自動維持平衡所需要具備的規則。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我們看一看一個典型的紅黑樹到底是什麼樣兒？","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":" 首先解讀一下規則，除了字面上看到的意思，還隱藏了哪些意思呢？","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"①從根節點到葉子節點的最長路徑不大於最短路徑的 2 倍","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"怎麼樣的路徑算最短路徑？從規則 5 中，我們知道從根節點到每個葉子節點的黑色節點數量是一樣的，那麼純由黑色節點組成的路徑就是最短路徑。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"什麼樣的路徑算是最長路徑？根據規則 4 和規則 3，若有紅色節點，則必然有一個連接的黑色節點，當紅色節點和黑色節點數量相同時，就是最長路徑，也就是黑色節點（或紅色節點）*2。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"②爲什麼說新加入到紅黑樹中的節點爲紅色節點","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"從規則 4 中知道，當前紅黑樹中從根節點到每個葉子節點的黑色節點數量是一樣的，此時假如新的是黑色節點的話，必然破壞規則。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"但加入紅色節點卻不一定，除非其父節點就是紅色節點，因此加入紅色節點，破壞規則的可能性小一些，下面我們也會舉例來說明。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"什麼情況下，紅黑樹的結構會被破壞呢？","attrs":{}},{"type":"text","text":"破壞後又怎麼維持平衡，","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"維持平衡主要通過兩種方式【變色】和【旋轉】，【旋轉】又分【左旋】和【右旋】","attrs":{}},{"type":"text","text":"，兩種方式可相互結合。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"下面我們從插入和刪除兩種場景來舉例說明。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"紅黑樹節點插入：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"當我們插入值爲 66 的節點時，紅黑樹變成了這樣：","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":"很明顯，這個時候結構依然遵循着上述 6 大規則，無需啓動自動平衡機制調整節點平衡狀態。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果再向裏面插入值爲 51 的節點，這個時候紅黑樹變成了這樣：","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":"很明顯現在的結構不遵循規則 4 了，這個時候就需要啓動自動平衡機制調整節點平衡狀態。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"關於C/C++ Linux後端開發網絡底層原理知識學習提升 點擊 ","attrs":{}},{"type":"link","attrs":{"href":"https://ke.qq.com/course/417774?flowToken=1013189","title":null,"type":null},"content":[{"type":"text","text":"學習資料","attrs":{}}]},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":" 獲取，內容知識點包括Linux，Nginx，ZeroMQ，MySQL，Redis，線程池，MongoDB，ZK，Linux內核，CDN，P2P，epoll，Docker，TCP/IP，協程，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":"變色：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我們可以通過變色的方式，使結構滿足紅黑樹的規則：","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":"首先解決結構不遵循規則 4 這一點（紅色節點相連，節點 49-51），需將節點 49 改爲黑色。","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"此時我們發現又違反了規則 5（56-49-51-XX 路徑中黑色節點超過了其他路徑），那麼我們將節點 45 改爲紅色節點。","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，又違反了規則 4（紅色節點相連，節點 56-45-43），那麼我們將節點 56 和節點 43 改爲黑色節點。","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"但是我們發現此時又違反了規則 5（60-56-XX 路徑的黑色節點比 60-68-XX 的黑色節點多），因此我們需要調整節點 68 爲黑色。","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":"最終調整完成後的樹爲：","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":"但並不是什麼時候都那麼幸運，可以直接通過變色就達成目的，大多數時候還需要通過旋轉來解決。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如在下面這棵樹的基礎上，加入節點 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":"插入節點 65 後進行以下步驟：","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":"這個時候，你會發現對於節點 64 無論是紅色節點還是黑色節點，都會違反規則 5，路徑中的黑色節點始終無法達成一致，這個時候僅通過【變色】已經無法達成目的。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我們需要通過旋轉操作，當然【旋轉】操作一般還需要搭配【變色】操作。旋轉包括【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":"逆時針旋轉兩個節點，讓一個節點被其右子節點取代，而該節點成爲右子節點的左子節點。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"左旋操作步驟如下：","attrs":{}},{"type":"text","text":"首先斷開節點 PL 與右子節點 G 的關係，同時將其右子節點的引用指向節點 C2；然後斷開節點 G 與左子節點 C2 的關係，同時將 G 的左子節點的應用指向節點 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":"順時針旋轉兩個節點，讓一個節點被其左子節點取代，而該節點成爲左子節點的右子節點。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"右旋操作步驟如下：","attrs":{}},{"type":"text","text":"首先斷開節點 G 與左子節點 PL 的關係，同時將其左子節點的引用指向節點 C2；然後斷開節點 PL 與右子節點 C2 的關係，同時將 PL 的右子節點的應用指向節點 G。","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/bb/bb92f1ed37672dc3e55375665aedd46e.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":"無法通過變色而進行旋轉的場景分爲以下四種：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"第一種：左左節點旋轉","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"這種情況下，父節點和插入的節點都是左節點，如下圖(旋轉原始圖1)這種情況下，我們要插入節點 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1 中，我們要插入節點 67。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"規則如下：","attrs":{}},{"type":"text","text":"先父節點【左旋】，然後祖父節點【右旋】，搭配【變色】。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"按照規則，步驟如下：","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/73/737f7dd24ae931bdc3ee754c7954034e.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":"第三種：右左節點旋轉","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"這種情況下，父節點是右節點，插入的節點是左節點，如下圖（旋轉原始圖 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2 中，我們要插入節點 70。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"規則如下：以祖父節點【左旋】，搭配【變色】。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"按照規則，步驟如下：","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/4d/4da572cb787cbdf41108b48230ebf21d.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":"紅黑樹插入總結","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"紅黑樹插入總結如下圖：","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d2/d22d8241c38823a6e0dcdaae8ce6aa3e.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":"紅黑樹節點刪除:","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"相比較於紅黑樹的節點插入，刪除節點更爲複雜，我們從子節點是否爲 null 和紅色爲思考維度來討論。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"子節點至少有一個爲 null","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"當待刪除的節點的子節點至少有一個爲 null 節點時，刪除了該節點後，將其有值的節點取代當前節點即可。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"若都爲 null，則將當前節點設置爲 null，當然如果違反規則了，則按需調整，如【變色】以及【旋轉】。","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/82/8228d55d38368a6f556dfbd851b1f0e1.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":"子節點都是非 null 節點","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"這種情況下：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"第一步：找到該節點的前驅或者後繼。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"前驅：","attrs":{}},{"type":"text","text":"左子樹中值最大的節點（可得出其最多隻有一個非 null 子節點，可能都爲 null）。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"後繼：","attrs":{}},{"type":"text","text":"右子樹中值最小的節點（可得出其最多隻有一個非 null 子節點，可能都爲 null）。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"前驅和後繼都是值最接近該節點值的節點，類似於該節點.prev=前驅，該節點.next=後繼。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"第二步：將前驅或者後繼的值複製到該節點中，然後刪掉前驅或者後繼。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果刪除的是左節點，則將前驅的值複製到該節點中，然後刪除前驅；如果刪除的是右節點，則將後繼的值複製到該節點中，然後刪除後繼。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"這相當於是一種“取巧”的方法，我們刪除節點的目的是使該節點的值在紅黑樹上不存在。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"因此專注於該目的，我們並不關注刪除節點時是否真是我們想刪除的那個節點，同時我們也不需考慮樹結構的變化，因爲樹的結構本身就會因爲自動平衡機制而經常進行調整。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"前面我們已經說了，我們要刪除的實際上是前驅或者後繼，因此我們就以前驅爲主線來講解。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"後繼的學習可參考前驅，包括下面幾種情況：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"①前驅爲黑色節點，並且有一個非 null 子節點","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":"因爲要刪除的是左節點 64，找到該節點的前驅 63；然後用前驅的值 63替換待刪除節點的值 64，此時兩個節點（待刪除節點和前驅）的值都爲 63；","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"刪除前驅 63，此時成爲上圖過程中間環節，但我們發現其不符合紅黑樹規則 4，因此需要進行自動平衡調整。這裏直接通過【變色】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前驅爲黑色節點，同時子節點都爲 null","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/64/64230d0413adc3a74b5e79222b84502b.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":"因爲要刪除的是左節點 64，找到該節點的前驅 63；然後用前驅的值 63 替換待刪除節點的值 64，此時兩個節點（待刪除節點和前驅）的值都爲 63。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"刪除前驅 63，此時成爲上圖過程中間環節，但我們發現其不符合紅黑樹規則 5，因此需要進行自動平衡調整。這裏直接通過【變色】即可完成。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"③前驅爲紅色節點，同時子節點都爲 null","attrs":{}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/5a/5af1940c92d55b43f0180fed72fe8f3f.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":"因爲要刪除的是左節點 64，找到該節點的前驅 63；然後用前驅的值 63替換待刪除節點的值 64，此時兩個節點（待刪除節點和前驅）的值都爲 63；刪除前驅 63，樹的結構並沒有打破規則。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"紅黑樹刪除總結","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"紅黑樹刪除的情況比較多，但也就存在以下情況：","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":"刪除的是根節點，則直接將根節點置爲 null。","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"待刪除節點的左右子節點都爲 null，刪除時將該節點置爲 null。","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"待刪除節點的左右子節點有一個有值，則用有值的節點替換該節點即可。","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"待刪除節點的左右子節點都不爲 null，則找前驅或者後繼，將前驅或者後繼的值複製到該節點中，然後刪除前驅或者後繼。","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"節點刪除後可能會造成紅黑樹的不平衡，這時我們需通過【變色】+【旋轉】的方式來調整，使之平衡，上面也給出了例子，建議大家多多練習，而不必背下來。","attrs":{}}]}]}],"attrs":{}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"總結","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"本文主要介紹了紅黑樹的相關原理，首先紅黑樹的基礎二叉搜索樹，我們先簡單說了一下二叉搜索樹，並且講了一下搜索的流程。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"然後就針對紅黑樹的六大規則特點，紅黑樹的插入操作，刪除操作，都使用了大量的圖形來加以說明。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"紅黑樹的使用非常廣泛，如 TreeMap 和 TreeSet 都是基於紅黑樹實現的，而 JDK8 中 HashMap 當鏈表長度大於 8 時也會轉化爲紅黑樹。","attrs":{}}]}]}