diff --git a/notes/算法.md b/notes/算法.md index 08f66a3d..1830732f 100644 --- a/notes/算法.md +++ b/notes/算法.md @@ -1195,7 +1195,7 @@ private void keys(Node x, Queue queue, Key lo, Key hi) {

-2-3 查找树引入了 2- 节点和 3- 节点，目的是为了让树更平衡。一颗完美平衡的 2-3 查找树的所有空链接到根节点的距离应该是相同的。 +2-3 查找树引入了 2- 节点和 3- 节点，目的是为了让树平衡。一颗完美平衡的 2-3 查找树的所有空链接到根节点的距离应该是相同的。 ### 1. 插入操作 @@ -1217,8 +1217,6 @@ private void keys(Node x, Queue queue, Key lo, Key hi) { 2-3 查找树的查找和插入操作复杂度和插入顺序无关，在最坏的情况下查找和插入操作访问的节点必然不超过 logN 个，含有 10 亿个节点的 2-3 查找树最多只需要访问 30 个节点就能进行任意的查找和插入操作。 -

- ## 红黑二叉查找树 2-3 查找树需要用到 2- 节点和 3- 节点，红黑树使用红链接来实现 3- 节点。指向一个节点的链接颜色如果为红色，那么这个节点和上层节点表示的是一个 3- 节点，而黑色则是普通链接。 @@ -1232,7 +1230,7 @@ private void keys(Node x, Queue queue, Key lo, Key hi) { 画红黑树时可以将红链接画平。 -

+

```java public class RedBlackBST, Value> { @@ -1423,7 +1421,7 @@ public class Transaction{ 拉链法使用链表来存储 hash 值相同的键，从而解决冲突。此时查找需要分两步，首先查找 Key 所在的链表，然后在链表中顺序查找。 -

+

对于 N 个键，M 条链表 (N>M)，如果哈希函数能够满足均匀性的条件，每条链表的大小趋向于 N/M，因此未命中的查找和插入操作所需要的比较次数为 \~N/M。 @@ -1521,12 +1519,12 @@ public void delete(Key key) { **（四）调整数组大小** -线性探测法的成本取决于连续条目的长度，连续条目也叫聚簇。当聚簇很长时，在查找和插入时也需要进行很多次探测。 +线性探测法的成本取决于连续条目的长度，连续条目也叫聚簇。当聚簇很长时，在查找和插入时也需要进行很多次探测。例如下图中 2\~5 位置就是一个聚簇。 + +

α = N/M，把 α 称为利用率。理论证明，当 α 小于 1/2 时探测的预计次数只在 1.5 到 2.5 之间。 -

- 为了保证散列表的性能，应当调整数组的大小，使得 α 在 [1/4, 1/2] 之间。 ```java @@ -1550,8 +1548,6 @@ private void resize(int cap) { 虽然每次重新调整数组都需要重新把每个键值对插入到散列表，但是从摊还分析的角度来看，所需要的代价却是很小的。从下图可以看出，每次数组长度加倍后，累计平均值都会增加 1，这是因为散列表中每个键都需要重新计算散列值。随后平均值会下降。 -

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