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39 lines
1.1 KiB
Markdown
39 lines
1.1 KiB
Markdown
---
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title: "binary-search-tree"
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aliases: binary search tree, BST
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tags:
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- cosc201
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- datastructure
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---
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[code](https://blackboard.otago.ac.nz/bbcswebdav/pid-2890167-dt-content-rid-18354839_1/courses/COSC201_S1DNIE_2022/BST.java)
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[bst-operations](notes/bst-operations.md)
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a collection of *nodes* with one distinguished node called the root
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rules:
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- the node data contains a key which comes from some ordered type e.g., `string`
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- each node can have at most who children - there are two fixed slots called left child and right child
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- the left child node and it descendents are called the left subtree
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- the key value at a nodes *left child* (and all its descendants) must be *less* than the key of the node
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- the key value at a nodes *right child* (and all its descendants) must be *greater* than the key of the node
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- we do not allow duplicate keys
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Notation
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- n.key for key
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- n.l and n.r for left and right children
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- n.p for its parent
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- nil for a "not here" marker. e.g., n.r = nil means "n has no right child"
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e.g.,
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In this example:
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- root.p = nil
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- root.r = n
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- n.p = root
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- n.key = emu
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- n.l = nil
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- n.r.key = rat
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