From baf315e449b21d5c94cf05192f214b704ed03ea5 Mon Sep 17 00:00:00 2001 From: yuteng lin <76236579+swaggyp7@users.noreply.github.com> Date: Fri, 26 Aug 2022 10:47:49 +0800 Subject: [PATCH] Translation Translation of binary search tree --- src/data-structures/tree/README.zh-CN.md | 20 +- .../tree/binary-search-tree/README.md | 7 +- .../tree/binary-search-tree/README.zh-CN.md | 268 ++++++++++++++++++ 3 files changed, 281 insertions(+), 14 deletions(-) create mode 100644 src/data-structures/tree/binary-search-tree/README.zh-CN.md diff --git a/src/data-structures/tree/README.zh-CN.md b/src/data-structures/tree/README.zh-CN.md index 2f4df983..e4101369 100644 --- a/src/data-structures/tree/README.zh-CN.md +++ b/src/data-structures/tree/README.zh-CN.md @@ -1,26 +1,26 @@ # 树 -* [二叉搜索树](binary-search-tree) -* [AVL树](avl-tree) -* [红黑树](red-black-tree) -* [线段树](segment-tree) - with min/max/sum range queries examples -* [芬威克树/Fenwick Tree](fenwick-tree) (Binary Indexed Tree) +- [二叉搜索树](binary-search-tree/README.zh-CN.md) +- [AVL 树](avl-tree) +- [红黑树](red-black-tree) +- [线段树](segment-tree) - with min/max/sum range queries examples +- [芬威克树/Fenwick Tree](fenwick-tree) (Binary Indexed Tree) -在计算机科学中, **树(tree)** 是一种广泛使用的抽象数据类型(ADT)— 或实现此ADT的数据结构 — 模拟分层树结构, 具有根节点和有父节点的子树,表示为一组链接节点。 +在计算机科学中, **树(tree)** 是一种广泛使用的抽象数据类型(ADT)— 或实现此 ADT 的数据结构 — 模拟分层树结构, 具有根节点和有父节点的子树,表示为一组链接节点。 树可以被(本地地)递归定义为一个(始于一个根节点的)节点集, 每个节点都是一个包含了值的数据结构, 除了值,还有该节点的节点引用列表(子节点)一起。 树的节点之间没有引用重复的约束。 一棵简单的无序树; 在下图中: -标记为7的节点具有两个子节点, 标记为2和6; -一个父节点,标记为2,作为根节点, 在顶部,没有父节点。 +标记为 7 的节点具有两个子节点, 标记为 2 和 6; +一个父节点,标记为 2,作为根节点, 在顶部,没有父节点。 ![Tree](./images/tree.jpeg) -*Made with [okso.app](https://okso.app)* +_Made with [okso.app](https://okso.app)_ ## 参考 -- [Wikipedia](https://en.wikipedia.org/wiki/Tree_(data_structure)) +- [Wikipedia]() - [YouTube](https://www.youtube.com/watch?v=oSWTXtMglKE&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&index=8) diff --git a/src/data-structures/tree/binary-search-tree/README.md b/src/data-structures/tree/binary-search-tree/README.md index d05a8915..9c6c7dc5 100644 --- a/src/data-structures/tree/binary-search-tree/README.md +++ b/src/data-structures/tree/binary-search-tree/README.md @@ -1,7 +1,7 @@ # Binary Search Tree _Read this in other languages:_ -[_Português_](README.pt-BR.md) +[_Português_](README.pt-BR.md),[_简体中文_](README.zh-CN.md) In computer science, **binary search trees** (BST), sometimes called ordered or sorted binary trees, are a particular type of container: @@ -30,7 +30,7 @@ The leaves are not drawn. ![Trie](./images/binary-search-tree.jpg) -*Made with [okso.app](https://okso.app)* +_Made with [okso.app](https://okso.app)_ ## Pseudocode for Basic Operations @@ -87,7 +87,6 @@ contains(root, value) end contains ``` - ### Deletion ```text @@ -265,7 +264,7 @@ end postorder ### Time Complexity -| Access | Search | Insertion | Deletion | +| Access | Search | Insertion | Deletion | | :-------: | :-------: | :-------: | :-------: | | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | diff --git a/src/data-structures/tree/binary-search-tree/README.zh-CN.md b/src/data-structures/tree/binary-search-tree/README.zh-CN.md new file mode 100644 index 00000000..12284487 --- /dev/null +++ b/src/data-structures/tree/binary-search-tree/README.zh-CN.md @@ -0,0 +1,268 @@ +# 二叉搜索树 + +_Read this in other languages:_ +[_Português_](README.pt-BR.md) + +在计算机科学中, **二叉搜索树** (BST), 也称为有序二叉树或排序二叉树, 是一种特殊的容器: +在内存中存储“元素”的数据结构（如数字，名称等）。二叉搜索树可以快速查找，添加和删除元素，也可用于 +构建动态元素集或在表中根据键查找元素值 （例：通过某人姓名找到某人的手机号）。 + +二叉搜索树为有序序列，所以在进行查找或其他操作时可以使用二分查找原理： +在树中寻找键（或插入新键的位置）时，查找过程为: 从根到叶遍历树，通过比较 +存储在树的节点中的键来判断继续向左或向右搜索子树。 平均而言，这意味着每次 +比较都允许跳过大约一半的操作，这样每个查找、插入或删除所花费的时间为 +树中存储的项目数的对数。 这是比按键在（未排序的）数组中查找元素所需的 +线性时间要好得多，但比在哈希表中相应的操作慢。 + +下图为一个大小为 9，深度为 3，8 为根结点的二叉搜索树。 +叶子节点没有被绘制。 + +![Trie](./images/binary-search-tree.jpg) + +_Made with [okso.app](https://okso.app)_ + +## 基础操作的伪代码 + +### 插入 + +```text +insert(value) + Pre: value has passed custom type checks for type T + Post: value has been placed in the correct location in the tree + if root = ø + root ← node(value) + else + insertNode(root, value) + end if +end insert +``` + +```text +insertNode(current, value) + Pre: current is the node to start from + Post: value has been placed in the correct location in the tree + if value < current.value + if current.left = ø + current.left ← node(value) + else + InsertNode(current.left, value) + end if + else + if current.right = ø + current.right ← node(value) + else + InsertNode(current.right, value) + end if + end if +end insertNode +``` + +### 查找 + +```text +contains(root, value) + Pre: root is the root node of the tree, value is what we would like to locate + Post: value is either located or not + if root = ø + return false + end if + if root.value = value + return true + else if value < root.value + return contains(root.left, value) + else + return contains(root.right, value) + end if +end contains +``` + +### 删除 + +```text +remove(value) + Pre: value is the value of the node to remove, root is the node of the BST + count is the number of items in the BST + Post: node with value is removed if found in which case yields true, otherwise false + nodeToRemove ← findNode(value) + if nodeToRemove = ø + return false + end if + parent ← findParent(value) + if count = 1 + root ← ø + else if nodeToRemove.left = ø and nodeToRemove.right = ø + if nodeToRemove.value < parent.value + parent.left ← nodeToRemove.right + else + parent.right ← nodeToRemove.right + end if + else if nodeToRemove.left != ø and nodeToRemove.right != ø + next ← nodeToRemove.right + while next.left != ø + next ← next.left + end while + if next != nodeToRemove.right + remove(next.value) + nodeToRemove.value ← next.value + else + nodeToRemove.value ← next.value + nodeToRemove.right ← nodeToRemove.right.right + end if + else + if nodeToRemove.left = ø + next ← nodeToRemove.right + else + next ← nodeToRemove.left + end if + if root = nodeToRemove + root = next + else if parent.left = nodeToRemove + parent.left = next + else if parent.right = nodeToRemove + parent.right = next + end if + end if + count ← count - 1 + return true +end remove +``` + +### 查找某个节点的父节点 + +```text +findParent(value, root) + Pre: value is the value of the node we want to find the parent of + root is the root node of the BST and is != ø + Post: a reference to the prent node of value if found; otherwise ø + if value = root.value + return ø + end if + if value < root.value + if root.left = ø + return ø + else if root.left.value = value + return root + else + return findParent(value, root.left) + end if + else + if root.right = ø + return ø + else if root.right.value = value + return root + else + return findParent(value, root.right) + end if + end if +end findParent +``` + +### 查找节点 + +```text +findNode(root, value) + Pre: value is the value of the node we want to find the parent of + root is the root node of the BST + Post: a reference to the node of value if found; otherwise ø + if root = ø + return ø + end if + if root.value = value + return root + else if value < root.value + return findNode(root.left, value) + else + return findNode(root.right, value) + end if +end findNode +``` + +### 查找最小值 + +```text +findMin(root) + Pre: root is the root node of the BST + root = ø + Post: the smallest value in the BST is located + if root.left = ø + return root.value + end if + findMin(root.left) +end findMin +``` + +### 查找最大值 + +```text +findMax(root) + Pre: root is the root node of the BST + root = ø + Post: the largest value in the BST is located + if root.right = ø + return root.value + end if + findMax(root.right) +end findMax +``` + +### 遍历 + +#### 中序遍历 + +```text +inorder(root) + Pre: root is the root node of the BST + Post: the nodes in the BST have been visited in inorder + if root != ø + inorder(root.left) + yield root.value + inorder(root.right) + end if +end inorder +``` + +#### 前序遍历 + +```text +preorder(root) + Pre: root is the root node of the BST + Post: the nodes in the BST have been visited in preorder + if root != ø + yield root.value + preorder(root.left) + preorder(root.right) + end if +end preorder +``` + +#### 后序遍历 + +```text +postorder(root) + Pre: root is the root node of the BST + Post: the nodes in the BST have been visited in postorder + if root != ø + postorder(root.left) + postorder(root.right) + yield root.value + end if +end postorder +``` + +## 复杂度 + +### 时间复杂度 + +| Access | Search | Insertion | Deletion | +| :-------: | :-------: | :-------: | :-------: | +| O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | + +### 空间复杂度 + +O(n) + +## 参考资料 + +- [Wikipedia](https://en.wikipedia.org/wiki/Binary_search_tree) +- [Inserting to BST on YouTube](https://www.youtube.com/watch?v=wcIRPqTR3Kc&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&index=9&t=0s) +- [BST Interactive Visualisations](https://www.cs.usfca.edu/~galles/visualization/BST.html)