From 3ee94ec31b9a7e357d1c8d7d660ce9d7512173fc Mon Sep 17 00:00:00 2001 From: CyC2018 Date: Wed, 28 Oct 2026 03:19:00 +0800 Subject: [PATCH] =?UTF-8?q?Update=20=E7=AE=97=E6=B3=95=20-=20=E5=B9=B6?= =?UTF-8?q?=E6=9F=A5=E9=9B=86.md?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 重新绘制配图,补充路径压缩的示意图和参考资料。 --- notes/pics/uf-intro.png | Bin 0 -> 104635 bytes notes/pics/uf-path-compression.png | Bin 0 -> 124174 bytes notes/pics/uf-quick-find.png | Bin 0 -> 145233 bytes notes/pics/uf-quick-union-tree.png | Bin 0 -> 87376 bytes notes/pics/uf-quick-union.png | Bin 0 -> 131461 bytes notes/pics/uf-weighted.png | Bin 0 -> 164249 bytes notes/算法 - 并查集.md | 22 ++++++++++++++++------ 7 files changed, 16 insertions(+), 6 deletions(-) create mode 100644 notes/pics/uf-intro.png create mode 100644 notes/pics/uf-path-compression.png create mode 100644 notes/pics/uf-quick-find.png create mode 100644 notes/pics/uf-quick-union-tree.png create mode 100644 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[比较](#比较) + * [参考资料](#参考资料) @@ -14,7 +15,9 @@ 用于解决动态连通性问题,能动态连接两个点,并且判断两个点是否连通。 -


+

+ +下文用图中这 6 次 union 操作比较几种实现。 | 方法 | 描述 | | :---: | :---: | @@ -53,7 +56,7 @@ public abstract class UF { 但是 union 操作代价却很高,需要将其中一个连通分量中的所有节点 id 值都修改为另一个节点的 id 值。 -

+

```java public class QuickFindUF extends UF { @@ -93,7 +96,7 @@ public class QuickFindUF extends UF { 但是 find 操作开销很大,因为同一个连通分量的节点 id 值不同,id 值只是用来指向另一个节点。因此需要一直向上查找操作,直到找到最上层的节点。 -

+

```java public class QuickUnionUF extends UF { @@ -124,9 +127,9 @@ public class QuickUnionUF extends UF { } ``` -这种方法可以快速进行 union 操作,但是 find 操作和树高成正比,最坏的情况下树的高度为节点的数目。 +这种方法可以快速进行 union 操作,但是 find 操作和树高成正比,最坏的情况下树会退化成一条链,树高为 N - 1。 -

+

## 加权 Quick Union @@ -134,7 +137,7 @@ public class QuickUnionUF extends UF { 理论研究证明,加权 quick-union 算法构造的树深度最多不超过 logN。 -

+

```java public class WeightedQuickUnionUF extends UF { @@ -184,6 +187,8 @@ public class WeightedQuickUnionUF extends UF { 在检查节点的同时将它们直接链接到根节点,只需要在 find 中添加一个循环即可。 +

+ ## 比较 | 算法 | union | find | @@ -192,3 +197,8 @@ public class WeightedQuickUnionUF extends UF { | Quick Union | 树高 | 树高 | | 加权 Quick Union | logN | logN | | 路径压缩的加权 Quick Union | 非常接近 1 | 非常接近 1 | + +## 参考资料 + +- Sedgewick R, Wayne K. 算法(第 4 版)[M]. 人民邮电出版社, 2012. +- [Algorithms, 4th Edition](https://algs4.cs.princeton.edu/home/)

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