> For the complete documentation index, see [llms.txt](https://garychang.gitbook.io/data-structure/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://garychang.gitbook.io/data-structure/lecture2-tree-and-binary-tree/lecture-2.8-advanced-trees/2.8.10-splay-tree.md).

# 2.8.10 - Splay Tree

調整過程較AVL Tree簡單。

Splay Tree是一個Binary Search Tree，其search()/insert()/delete()的運作皆和Binary Search Tree相同，差別在於在做完每一個運算之後必須針對splay起點執行splay運算，將splay起點變成root。

Splay起點:

1. search(x): splay起點為x
2. insert(x): splay起點為x
3. delete(s): splay起點為x的附點

Splay運算:

* 2個節點

![](https://2769815795-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LGckN3OAfinKuVIrkMj%2F-LHvkbf1Unpss3gUwuW1%2F-LHvkoFGFeryVOoPwx-g%2F%E8%9E%A2%E5%B9%95%E5%BF%AB%E7%85%A7%202018-07-21%2015.30.22.jpg?alt=media\&token=15d114ad-d74d-448a-9bec-710b78ec5cf8)

![](https://2769815795-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LGckN3OAfinKuVIrkMj%2F-LHvkbf1Unpss3gUwuW1%2F-LHvkpqLdfXkDUuEn-qr%2F%E8%9E%A2%E5%B9%95%E5%BF%AB%E7%85%A7%202018-07-21%2015.31.35.jpg?alt=media\&token=f418c753-25be-4521-92fe-63a3e854ee9f)

* 3個節點

![](https://2769815795-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LGckN3OAfinKuVIrkMj%2F-LHvlI-SP3hnqNOm4Z7J%2F-LHvlSDqHUa9LUqRHgtt%2F%E8%9E%A2%E5%B9%95%E5%BF%AB%E7%85%A7%202018-07-21%2015.37.33.jpg?alt=media\&token=6ace57f7-712c-4d7f-b9f9-cf8618dc5fa3)

![](https://2769815795-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LGckN3OAfinKuVIrkMj%2F-LHvm1mFXWmMyeICa67b%2F-LHvm2z21sEIQLPNiWyx%2F%E8%9E%A2%E5%B9%95%E5%BF%AB%E7%85%A7%202018-07-21%2015.40.08.jpg?alt=media\&token=7ca054d0-8e70-4c66-a469-ab360957ff18)

![](https://2769815795-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LGckN3OAfinKuVIrkMj%2F-LHvmRkrBKQ_myCJ3H3i%2F-LHvmTaW30uPtAmySSfa%2F%E8%9E%A2%E5%B9%95%E5%BF%AB%E7%85%A7%202018-07-21%2015.41.55.jpg?alt=media\&token=77668751-7873-495d-b0c3-0b073dcdb5aa)

![](https://2769815795-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LGckN3OAfinKuVIrkMj%2F-LHvmRkrBKQ_myCJ3H3i%2F-LHvmmbd71uebi8LXChj%2F%E8%9E%A2%E5%B9%95%E5%BF%AB%E7%85%A7%202018-07-21%2015.43.24.jpg?alt=media\&token=b336abea-2d86-4318-96f3-aaa56666de76)