萬字長文聊哈希

{"type":"doc","content":[{"type":"heading","attrs":{"align":null,"level":1},"content":[{"type":"text","text":"散列（哈希）表總結","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"之前給大家介紹了","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"鏈表","attrs":{}},{"type":"text","text":"，","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"棧和隊列","attrs":{}},{"type":"text","text":"今天我們來說一種新的數據結構散列（哈希）表，散列是應用非常廣泛的數據結構，在我們的刷題過程中，散列表的出場率特別高。所以我們快來一起把散列表的內些事給整明白吧。文章框架如下","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/75/7502d258cc8d7dd38a5980d2d43b7f48.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}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"說散列表之前，我們先設想以下場景。","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}},{"type":"blockquote","content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"袁廚穿越回了古代，憑藉從現代學習的做飯手藝，開了一個袁記菜館，正值開業初期，店裏生意十分火爆，但是顧客結賬時就犯難了，每當結賬的時候，老闆娘總是按照菜單一個一個找價格（遍歷查找），每次都要找半天，所以結賬的地方總是排起長隊，顧客們表示用戶體驗不咋滴。","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":"袁廚一想這不是辦法啊，讓顧客老是等着，太影響客戶體驗啦。所以袁廚就先把菜單按照首字母排序（二分查找），然後查找的時候根據首字母查找，這樣結賬的時候就能大大提高檢索效率啦！但是呢？工作日顧客不多，老闆娘完全應付的過來，但是每逢節假日，還是會排起長隊。","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":"那麼有沒有什麼更好的辦法呢？對呀！我們把所有的價格都背下來不就可以了嗎？每個菜的價格我們都瞭如指掌，結賬的時候我們只需簡單相加即可。所以袁廚和老闆娘加班加點的進行背誦。","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":"下次再結賬的時候一說吃了什麼菜，我們立馬就知道價格啦。自此以後收銀臺再也沒有出現過長隊啦，袁記菜館開着開着一不小心就成了天下第一飯店了。","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":"下面我們來看一下袁記菜館老闆娘進化史。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/17/17cc3bc6e52748909d66371ec5dece92.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}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上面的後期結賬的過程則模擬了我們的散列表查找，那麼在計算機中是如何使用進行查找的呢？","attrs":{}}]},{"type":"heading","attrs":{"align":null,"level":3},"content":[{"type":"text","text":"散列表查找步驟","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"散列表-------最有用的基本數據結構之一。是根據關鍵碼的值兒直接進行訪問的數據結構，散列表的實現常常叫做","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"散列（hasing）","attrs":{}},{"type":"text","text":"。散列是一種用於以","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"常數平均時間","attrs":{}},{"type":"text","text":"執行插入、刪除和查找的技術，下面我們來看一下散列過程。","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":"我們的整個散列過程主要分爲兩步","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":"（1）通過","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"散列函數","attrs":{}},{"type":"text","text":"計算記錄的散列地址，並按此","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"散列地址","attrs":{}},{"type":"text","text":"存儲該記錄。就好比麻辣魚我們就讓它在川菜區，糖醋魚，我們就讓它在魯菜區。但是我們需要注意的是，無論什麼記錄我們都需要用","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"同一個散列函數","attrs":{}},{"type":"text","text":"計算地址，再存儲。","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":"（2)當我們查找時，我們通過","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"同樣的散列函數","attrs":{}},{"type":"text","text":"計算記錄的散列地址，按此散列地址訪問該記錄。因爲我們存和取得時候用的都是一個散列函數，因此結果肯定相同。","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":"剛纔我們在散列過程中提到了散列函數，那麼散列函數是什麼呢？","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":"我們假設某個函數爲 ","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"f","attrs":{}},{"type":"text","text":"，使得","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":"存儲位置 = f (關鍵字)","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":"輸入：關鍵字","attrs":{}},{"type":"text","text":" ","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"輸出：存儲位置(散列地址)","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":"那樣我們就能通過查找關鍵字","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"不需要比較","attrs":{}},{"type":"text","text":"就可獲得需要的記錄的存儲位置。這種存儲技術被稱爲散列技術。散列技術是在通過記錄的存儲位置和它的關鍵字之間建立一個確定的對應關係 ","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"f","attrs":{}},{"type":"text","text":" ,使得每個關鍵字 ","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"key","attrs":{}},{"type":"text","text":" 都對應一個存儲位置 ","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"f(key)","attrs":{}},{"type":"text","text":"。見下圖","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/d2/d2aec8249902212035029ee63bcd9bd5.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}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"這裏的 ","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"f","attrs":{}},{"type":"text","text":" 就是我們所說的散列函數（哈希）函數。我們利用散列技術將記錄存儲在一塊連續的存儲空間中，這塊連續存儲空間就是我們本文的主人公------","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"散列(哈希)表","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":"上圖爲我們描述了用散列函數將關鍵字映射到散列表，但是大家有沒有考慮到這種情況，那就是將關鍵字映射到同一個槽中的情況，即 ","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"f(k4) = f(k3)","attrs":{}},{"type":"text","text":" 時。這種情況我們將其稱之爲","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"衝突","attrs":{}},{"type":"text","text":"，","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"k3","attrs":{}},{"type":"text","text":" 和 ","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"k4","attrs":{}},{"type":"text","text":"則被稱之爲散列函數 ","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"f","attrs":{}},{"type":"text","text":" 的","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"同義詞","attrs":{}},{"type":"text","text":"，如果產生這種情況，則會讓我們查找錯誤。幸運的是我們能找到有效的方法解決衝突。","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":"首先我們可以對哈希函數下手，我們可以精心設計哈希函數，讓其儘可能少的產生衝突，所以我們創建哈希函數時應遵循以下規則","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":"（1）","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"必須是一致的","attrs":{}},{"type":"text","text":"，假設你輸入辣子雞丁時得到的是","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"在看","attrs":{}},{"type":"text","text":"，那麼每次輸入辣子雞丁時，得到的也必須爲","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"在看","attrs":{}},{"type":"text","text":"。如果不是這樣，散列表將毫無用處。","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":"（2）","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"計算簡單","attrs":{}},{"type":"text","text":"，假設我們設計了一個算法，可以保證所有關鍵字都不會衝突，但是這個算法計算複雜，會耗費很多時間，這樣的話就大大降低了查找效率，反而得不償失。所以咱們","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"散列函數的計算時間不應該超過其他查找技術與關鍵字的比較時間","attrs":{}},{"type":"text","text":"，不然的話我們幹嘛不使用其他查找技術呢?","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":"（3）","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"散列地址分佈均勻","attrs":{}},{"type":"text","text":"我們剛纔說了衝突的帶來的問題，所以我們最好的辦法就是讓","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"散列地址儘量均勻分佈在存儲空間中","attrs":{}},{"type":"text","text":"，這樣即保證空間的有效利用，又減少了處理衝突而消耗的時間。","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":"現在我們已經對散列表，散列函數等知識有所瞭解啦，那麼我們來看幾種常用的散列函數構造規則。這些方法的共同點爲都是將原來的數字按某種規律變成了另一個數字。","attrs":{}}]},{"type":"heading","attrs":{"align":null,"level":3},"content":[{"type":"text","text":"散列函數構造方法","attrs":{}}]},{"type":"heading","attrs":{"align":null,"level":4},"content":[{"type":"text","text":"直接定址法","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果我們對盈利爲 0-9 的菜品設計哈希表，我們則直接可以根據作爲地址，則 ","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"f(key) = key","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":"即下面這種情況。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/76/76390ff5c2c2a295fae167fd99e9fd38.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}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有沒有感覺上面的圖很熟悉，沒錯我們經常用的數組其實就是一張哈希表，關鍵碼就是數組的索引下標，然後我們通過下標直接訪問數組中的元素。","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":"另外我們假設每道菜的成本爲 50 塊，那我們還可以根據盈利+成本來作爲地址，那麼則 f(key) = key + 50。也就是說我們可以根據線性函數值作爲散列地址。","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":"f(key) = a * key + b","attrs":{}},{"type":"text","text":" ","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"a,b 均爲常數","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":"優點：簡單、均勻、無衝突。","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":"應用場景：需要事先知道關鍵字的分佈情況，適合查找表較小且連續的情況","attrs":{}}]},{"type":"heading","attrs":{"align":null,"level":4},"content":[{"type":"text","text":"數字分析法","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"該方法也是十分簡單的方法，就是分析我們的關鍵字，取其中一段，或對其位移，疊加，用作地址。比如我們的學號，前 6 位都是一樣的，但是後面 3 位都不相同，我們則可以用學號作爲鍵，後面的 3 位做爲我們的散列地址。如果我們這樣還是容易產生衝突，則可以對抽取數字再進行處理。我們的目的只有一個，提供一個散列函數將關鍵字合理的分配到散列表的各位置。這裏我們提到了一種新的方式，抽取，這也是在散列函數中經常用到的手段。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/e2/e2e2e6fb20e2d44e4cac7a885411c147.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}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"優點：簡單、均勻、適用於關鍵字位數較大的情況","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":"應用場景：關鍵字位數較大，知道關鍵字分佈情況且關鍵字的若干位較均勻","attrs":{}}]},{"type":"heading","attrs":{"align":null,"level":4},"content":[{"type":"text","text":"摺疊法","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"其實這個方法也很簡單，也是處理我們的關鍵字然後用作我們的散列地址，主要思路是將關鍵字從左到右分割成位數相等的幾部分，然後疊加求和，並按散列表表長，取後幾位作爲散列地址。","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":"比如我們的關鍵字是 123456789，則我們分爲三部分 123 ，456 ，789 然後將其相加得 1368 然後我們再取其後三位 368 作爲我們的散列地址。","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":"優點：事先不需要知道關鍵字情況","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":"應用場景：適合關鍵字位數較多的情況","attrs":{}}]},{"type":"heading","attrs":{"align":null,"level":4},"content":[{"type":"text","text":"除法散列法","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在用來設計散列函數的除法散列法中，通過取 key 除以 p 的餘數，將關鍵字映射到 p 個槽中的某一個上，對於散列表長度爲 m 的散列函數公式爲","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":"f(k) = k mod p (p <= m)","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":"例如，如果散列表長度爲 12，即 m = 12 ，我們的參數 p 也設爲 12，","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"那 k = 100 時 f(k) = 100 % 12 = 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時會有什麼事情發生呢？","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/0a/0af95e63a838238f5cccd40f30acfc8d.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}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"此時他第一次會落在下標爲 10 的位置，那麼如果繼續使用線性探測的話，則需要通過不斷取餘後得到結果，數據量小還好，要是很大的話那也太慢了吧，但是明明他的前面就有一個空房間呀，如果向前移動只需移動一次即可。不要着急，前輩們已經幫我們想好了解決方法","attrs":{}}]},{"type":"heading","attrs":{"align":null,"level":5},"content":[{"type":"text","text":"二次探測法","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"其實理解了我們的上個例子之後，這個一下就能整明白了，根本不用費腦子，這個方法就是更改了一下 di 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key 轉成數組下標","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":"（2）通過數組下標找到 key 值，如果 key 一致，則查找成功，否則利用線性探測法繼續查找。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/4b/4b6dc5bfa027622403927e19a182f7bd.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}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"下面我們來看一下完整代碼","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/6e/6e2c1182e016321bcbf548e83bc82d3a.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"heading","attrs":{"align":null,"level":3},"content":[{"type":"text","text":"散列表性能分析","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果沒有衝突的話，散列查找是我們查找中效率最高的，時間複雜度爲 O(1),但是沒有衝突的情況是一種理想情況，那麼散列查找的平均查找長度取決於哪些方面呢？","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","marks":[{"type":"strong","attrs":{}}],"text":"1.散列函數是否均勻","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":"我們在上文說到，可以通過設計散列函數減少衝突，但是由於不同的散列函數對一組關鍵字產生衝突可能性是相同的，因此我們可以不考慮它對平均查找長度的影響。","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":"2.處理衝突的方法","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":"相同關鍵字，相同散列函數，不同處理衝突方式，會使平均查找長度不同，比如我們線性探測有時會堆積，則不如二次探測法好，因爲鏈地址法處理衝突時不會產生任何堆積，因而具有最佳的平均查找性能","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","marks":[{"type":"strong","attrs":{}}],"text":"3.散列表的裝填因子","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":"本來想在上文中提到裝填因子的，但是後來發現即使沒有說明也不影響我們對哈希表的理解，下面我們來看一下裝填因子的總結","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"blockquote","content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"裝填因子 α = 填入表中的記錄數 / 散列表長度","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":"散列因子則代表着散列表的裝滿程度，表中記錄越多，α 就越大，產生衝突的概率就越大。我們上面提到的例子中 表的長度爲 12，填入記錄數爲 6，那麼此時的 α = 6 / 12 = 0.5 所以說當我們的 α 比較大時再填入元素那麼產生衝突的可能性就非常大了。所以說散列表的平均查找長度取決於裝填因子，而不是取決於記錄數。所以說我們需要做的就是選擇一個合適的裝填因子以便將平均查找長度限定在一個範圍之內。","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":"原文地址：","attrs":{}},{"type":"link","attrs":{"href":"http://www.chengxuchu.com/#/%E7%AE%97%E6%B3%95%E5%9F%BA%E5%9C%B0/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84%E5%92%8C%E7%AE%97%E6%B3%95/Hash%E8%A1%A8%E7%9A%84%E9%82%A3%E4%BA%9B%E4%BA%8B","title":"","type":null},"content":[{"type":"text","text":"http://www.chengxuchu.com/#/","attrs":{}}]}]}]}