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個子節點。如圖 3 個子節點的數據分別爲：小於 17， 17 ~ 35 ，大於 35。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"假設，從上圖中查找 10 這個數，步驟如下：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"numberedlist","attrs":{"start":"1","normalizeStart":1},"content":[{"type":"listitem","content":[{"type":"paragraph","attrs":{"indent":0,"number":1,"align":null,"origin":null},"content":[{"type":"text","text":"找到根節點，對比 10 與 17 和 35 的大小，發現 10 < 17 在左子節點，也就是第 2 層節點；","attrs":{}}]}],"attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"numberedlist","attrs":{"start":"2","normalizeStart":"2"},"content":[{"type":"listitem","content":[{"type":"paragraph","attrs":{"indent":0,"number":2,"align":null,"origin":null},"content":[{"type":"text","text":"從根節點的指針，找到左子節點，對比 10 與 8 和 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次。事實證明，多叉樹確實可以再次提高查找性能。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"多叉樹是在二分查找樹的基礎上，增加單個節點的數據存儲數量，同時增加了樹的子節點數，一次計算可以把查找範圍縮小更多。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"優點","attrs":{}},{"type":"text","text":"：二叉平衡樹的基礎上，使加載一次節點，可以加載更多路徑數據，同時把查詢範圍縮減到更小。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"複雜節點","attrs":{}},{"type":"text","text":":","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"至此，我們列舉的數據都是孤零零的單個數字。試想，你手裏已經有一個數據 10，爲什麼還要費力吧唧的再從一堆數據中找到這個 10，自己找自己？這不是有病嗎？","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"單個數字只能活在演示中，現實的世界要複雜的多，我們來看一個接近真實場景的案例。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"現有一個以年齡爲索引的 3 階樹，存儲了一批用戶信息，如下圖：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/2d/2d07ca6574fb73b61df037127ba27b90.jpeg","alt":null,"title":null,"style":null,"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"數字爲用戶的年齡，其它爲與樹排序查找無關的業務數據，像這種索引數據與樹排序查找無關的業務一起維護在節點的平衡多叉（階）樹稱爲 B- 樹（ B 樹）。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"缺點","attrs":{}},{"type":"text","text":"：業務數據的大小可能遠遠超過了索引數據的大小，每次爲了查找對比計算，需要把數據加載到內存以及 CPU 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I/O。磁盤的讀取方式和速度會嚴重影響到整個業務的計算性能。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"下面我們簡單瞭解一下磁盤是如何工作的。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"磁盤大概長這個樣子：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/99/9904e8227ee6d5cf9592a9a35e07567d.jpeg","alt":null,"title":null,"style":null,"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"磁盤主要由磁盤盤片、傳動手臂、讀寫磁頭和馬達組成。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"爲了存儲容量,主軸像穿糖葫蘆一樣把多個磁盤片組成一個陣列。通過馬達驅動主軸轉動以及傳動手臂移動，使讀寫磁頭在磁盤片上讀寫數據。大概如下：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d0/d0e25ca3425f700a6731b238250c329a.jpeg","alt":null,"title":null,"style":null,"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"磁盤片由很多半徑不等的同心圓組成，這些圓被稱爲磁道，數據就是寫在這些磁道上。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/70/70166c6fe7c0be860134c09013e07394.jpeg","alt":null,"title":null,"style":null,"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"每個磁道又劃分成塊稱爲扇區。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b0/b0034acc410834dc32de0e876c6c70e8.jpeg","alt":null,"title":null,"style":null,"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果磁盤是一記事本，那麼一張磁盤片就是本子的一頁紙，而主軸就是本子的裝訂線；磁道就是紙頁的行，而扇區可以看作是很寬的列。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/18/18e2f7d76cf1ec36b61e75d20d853041.jpeg","alt":null,"title":null,"style":null,"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果在磁盤中存儲一首詩,想象中大概這個樣子。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/81/810d9b6958877c0d745a987600d66328.jpeg","alt":null,"title":null,"style":null,"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"磁盤的讀 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索引爲什麼能提供查詢性能...
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階樹，存儲了一批用戶信息，如下圖：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/2d/2d07ca6574fb73b61df037127ba27b90.jpeg","alt":null,"title":null,"style":null,"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"數字爲用戶的年齡，其它爲與樹排序查找無關的業務數據，像這種索引數據與樹排序查找無關的業務一起維護在節點的平衡多叉（階）樹稱爲 B- 樹（ B 樹）。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"缺點","attrs":{}},{"type":"text","text":"：業務數據的大小可能遠遠超過了索引數據的大小，每次爲了查找對比計算，需要把數據加載到內存以及 CPU 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I/O。磁盤的讀取方式和速度會嚴重影響到整個業務的計算性能。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"下面我們簡單瞭解一下磁盤是如何工作的。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"磁盤大概長這個樣子：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/99/9904e8227ee6d5cf9592a9a35e07567d.jpeg","alt":null,"title":null,"style":null,"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"磁盤主要由磁盤盤片、傳動手臂、讀寫磁頭和馬達組成。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"爲了存儲容量,主軸像穿糖葫蘆一樣把多個磁盤片組成一個陣列。通過馬達驅動主軸轉動以及傳動手臂移動，使讀寫磁頭在磁盤片上讀寫數據。大概如下：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d0/d0e25ca3425f700a6731b238250c329a.jpeg","alt":null,"title":null,"style":null,"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"磁盤片由很多半徑不等的同心圓組成，這些圓被稱爲磁道，數據就是寫在這些磁道上。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/70/70166c6fe7c0be860134c09013e07394.jpeg","alt":null,"title":null,"style":null,"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"每個磁道又劃分成塊稱爲扇區。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/b0/b0034acc410834dc32de0e876c6c70e8.jpeg","alt":null,"title":null,"style":null,"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果磁盤是一記事本，那麼一張磁盤片就是本子的一頁紙，而主軸就是本子的裝訂線；磁道就是紙頁的行，而扇區可以看作是很寬的列。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/18/18e2f7d76cf1ec36b61e75d20d853041.jpeg","alt":null,"title":null,"style":null,"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果在磁盤中存儲一首詩,想象中大概這個樣子。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/81/810d9b6958877c0d745a987600d66328.jpeg","alt":null,"title":null,"style":null,"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"磁盤的讀 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是通過電信號進行數字運算。粗略的認爲，機械查詢數據，與光速處理數據的性能完全不是在一個量級，總之一句話就是","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"磁盤處理太慢太慢了","attrs":{}},{"type":"text","text":"。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"雖然磁盤處理數據太慢了，但是它是目前相對廉價且穩定的存儲設備，所以又不能捨棄不用，但大致可以通過以下方法進行優化。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"bulletedlist","content":[{"type":"listitem","content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"儘量減少 I/O 次數，比如可以使用緩存；","attrs":{}}]}],"attrs":{}},{"type":"listitem","content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"每次 I/O 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B+tree","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"做爲數據庫的索引，無論用什麼樣的數據結構維護，這些數據最終都會存儲到磁盤中。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"鑑於磁盤 I/O 的性能問題，以及每次 I/O 獲取數據量上限所限，提高索引本身 I/O 的方法最好是，減少 I/O 次數和每次獲取有用的數據。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"B-tree 已經大大改進了樹家族的性能，它把多個數據集中存儲在一個節點中，本身就可能減少了 I/O 次數或者尋道次數。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"但是仍然有一個致命的缺陷，那就是它的索引數據與業務綁定在一塊，而業務數據的大小很有可能遠遠超過了索引數據，這會大大減小一次 I/O 有用數據的獲取，間接的增加 I/O 次數去獲取有用的索引數據。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"因爲業務數據纔是我們查詢最終的目的，但是它又是在「二分」查找中途過程無用的數據，因此，如果只把業務數據存儲在最終查詢到的那個節點是不是就可以了？","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"理想很豐滿，現實很骨瘦如柴，誰知道哪個節點就是最終要查詢的節點呢？","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"B+tree 橫空出世，","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"B+ 樹就是爲了拆分索引數據與業務數據的平衡多叉樹","attrs":{}},{"type":"text","text":"。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/18/189890c17c5647c772d5c3db5a57ea05.jpeg","alt":null,"title":null,"style":null,"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"B+ 樹中，非葉子節點只保存索引數據，葉子節點保存索引數據與業務數據。這樣即保證了葉子節點的簡約乾淨，數據量大大減小，又保證了最終能查到對應的業務數。既提高了單次 I/O 數據的有效性，又減少了 I/O 次數，還實現了業務。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"但是，在數據中索引與數據是分離的，不像示例那樣的？","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如圖：我們只需要把真實的業務數據，換成數據所在地址就可以了，此時，業務數據所在的地址在 B+ 樹中充當業務數據。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7d/7da9ecb313f7e6fcbfb139ad073484d2.jpeg","alt":null,"title":null,"style":null,"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"----","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"heading","attrs":{"align":null,"level":3},"content":[{"type":"text","text":"總結","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"bulletedlist","content":[{"type":"listitem","content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"數據存儲在磁盤（ SSD 跟 CPU 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中的數據衝突時，鏈表轉化成紅黑樹；","attrs":{}}]}],"attrs":{}},{"type":"listitem","content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"數據庫索引使用的 B+ 樹；","attrs":{}}]}],"attrs":{}},{"type":"listitem","content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"搜索引擎倒排索引使用的字典樹；","attrs":{}}]}],"attrs":{}}],"attrs":{}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"以上只是淺嘗輒止、點到爲止的描述了數據庫使用 B+ 樹索引爲什麼能提高查詢性能原因及簡單過程。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"並沒有深入各種數據結構的細節，也未提及其它索引類型和索引的具體存儲格式，目的僅僅是，爲了讓大家對索引有一個感性的認識。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}}]}
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