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理想情况下,哈希函数应该为每个输入产生唯一的输出,使得 key 和 value 一一对应。而实际上,往往存在向哈希函数输入不同的 key 而产生相同输出的情况,这种情况被称为「哈希冲突 Hash Collision」。哈希冲突会导致查询结果错误,从而严重影响哈希表的可用性。 -那么,为什么会出现哈希冲突呢?本质上看,**由于哈希函数的输入空间往往远大于输出空间**,因此不可避免地会出现多个输入产生相同输出的情况,即为哈希冲突。比如,输入空间是全体整数,输出空间是一个固定大小的桶(数组)的索引范围,那么必定会有多个整数同时映射到一个桶索引。 +那么,为什么会出现哈希冲突呢?本质上看,**由于哈希函数的输入空间往往远大于输出空间**,因此不可避免地会出现多个输入产生相同输出的情况,即为哈希冲突。比如,输入空间是全体整数,输出空间是一个固定大小的数组,那么必定会有多个整数映射到同一个数组索引。 -为了缓解哈希冲突,一方面,**我们可以通过哈希表扩容来减小冲突概率**。极端情况下,当输入空间和输出空间大小相等时,哈希表就等价于数组了,可谓“大力出奇迹”。 +为了缓解哈希冲突,一方面,**我们可以通过哈希表扩容来减小冲突概率**。极端情况下,当输入空间和输出空间大小相等时,哈希表就等价于数组了,每个 key 都对应唯一的数组索引,可谓“大力出奇迹”。 -另一方面,**考虑通过优化哈希表的表示方式以缓解哈希冲突**,常见的方法有「链式地址」和「开放寻址」。 +另一方面,**考虑通过优化哈希表的来缓解哈希冲突**,常见的方法有「链式地址」和「开放寻址」。 ## 哈希表扩容 -「负载因子 Load Factor」定义为 **哈希表中元素数量除以桶槽数量(即数组大小)**,代表哈希冲突的严重程度。 +「负载因子 Load Factor」定义为 **哈希表中元素数量除以桶数量(即数组大小)**,代表哈希冲突的严重程度。 **负载因子常用作哈希表扩容的触发条件**。比如在 Java 中,当负载因子 $> 0.75$ 时则触发扩容,将 HashMap 大小扩充至原先的 $2$ 倍。 @@ -18,13 +18,13 @@ ## 链式地址 -在原始哈希表中,桶内的每个地址只能存储一个元素(即键值对)。**考虑将单个元素转化成一个链表,将所有冲突元素都存储在一个链表中**。 +在原始哈希表中,每个桶只能存储一个元素(即键值对)。**考虑将单个元素转化成一个链表,将所有冲突元素都存储在一个链表中**。 ![链式地址](hash_collision.assets/hash_collision_chaining.png) 链式地址下,哈希表操作方法为: -- **查询元素**:先将 key 输入到哈希函数得到桶内索引,即可访问链表头结点,再通过遍历链表查找对应 value 。 +- **查询元素**:输入 key ,经过哈希函数得到数组索引,即可访问链表头结点,再通过遍历链表并对比 key 来查找键值对。 - **添加元素**:先通过哈希函数访问链表头部,再将结点(即键值对)添加到链表头部即可。 - **删除元素**:同样先根据哈希函数结果访问链表头部,再遍历链表查找对应结点,删除之即可。 @@ -54,8 +54,8 @@ 线性探测存在以下缺陷: -- **不能直接删除元素**。删除元素会导致桶内出现一个空位,在查找其他元素时,该空位有可能导致程序认为元素不存在(即上述第 `2.` 种情况)。因此需要借助一个标志位来标记删除元素。 -- **容易产生聚集**。桶内被占用的连续位置越长,这些连续位置发生哈希冲突的可能性越大,从而进一步促进这一位置的“聚堆生长”,最终导致增删查改操作效率的劣化。 +- **不能直接删除元素**。删除元素会导致数组内出现一个空位,在查找其他元素时,该空位有可能导致程序认为元素不存在(即上述第 `2.` 种情况)。因此需要借助一个标志位来标记删除元素。 +- **容易产生聚集**。数组内被占用的连续位置越长,这些连续位置发生哈希冲突的可能性越大,从而进一步促进这一位置的“聚堆生长”,最终导致增删查改操作效率的劣化。 ### 多次哈希 diff --git a/docs/chapter_hashing/hash_map.assets/hash_collision.png b/docs/chapter_hashing/hash_map.assets/hash_collision.png index f4de6de961666337b4b371cf9eb7d664d1319f17..91d7ff3a2d1d6e5cbd76b6266f1a58384dc340a4 100644 GIT binary patch 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z{stt8)y^x7{hz&Zjbvb8JPNwa)|lb*UEn6fI^bP)^&4%A@?Gw?3hV){Sx^;W^!pAxnE1)Dt&=~zCQ;CyXOw(?HW56p+X7l*$Q~h|X zyJ*jf!$M|~@{0w2ADNVKw;Wbf!3r%kffFS&6OFl+#6&HYS?{yIX36{Mk?VK7pZ>ej zdb@=IgM0VwZMnO@UW?Y8oGHy{5tOI=`qRX1?CJljyL1ruRRU7%sow zUG_F=(fbP#RyGXJ^*(hxum&zKUAOyPQi;j>8*w=c?)XewIpK8_db#PFAkug)K$3BC zIdBiULV6r%4sUPO*Dg_Qx6El)$t({9qql(9{=ri>uvpx^@W6jY-gn~L-{~1WW&i?D LS3j3^P6 value 姓名` 为例,我们可以将「哈希函数」设计为 @@ -405,6 +407,8 @@ $$ f(x) = x \% 100 $$ +如下图所示,输入一个学号 key ,经过哈希函数计算就能访问到对应的姓名 value 。 + ![简单哈希函数示例](hash_map.assets/hash_function.png) === "Java"