Questions and Answers
树是一种 分层 数据结构，由 节点 组成，其中每个 节点 都有一个 值 和零个或多个 子 节点。
层级
二叉树 是每个 节点 最多有两个 子 节点 的树。
儿
树操作包括 遍历、插入 和 删除。
查找
栈是一种线性数据结构，遵循 _______ 原则。
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栈的操作包括 _______、弹出 和 查看。
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在树中，叶 节点 是没有 子 节点 的 节点。
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树的术语包括 根 节点、子 节点、父 节点 和 _______ 节点。
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栈的属性包括 _______ 和 先进后出。
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Study Notes
Trees
Definition
- A tree is a hierarchical data structure consisting of nodes, where each node has a value and zero or more child nodes.
- The topmost node is called the root node.
- Each node in the tree has a unique key or value.
Types of Trees
- Binary Tree: Each node has at most two child nodes (left child and right child).
- B-Tree: A self-balancing search tree that keeps data sorted and allows search, insert, and delete operations in logarithmic time.
- ** AVL Tree**: A self-balancing binary search tree that ensures the height of the tree remains relatively small.
Tree Terminology
- Root Node: The topmost node in the tree.
- Child Node: A node that has a parent node.
- Parent Node: A node that has one or more child nodes.
- Sibling Node: Nodes that have the same parent node.
- Leaf Node: A node with no child nodes.
- Internal Node: A node that has one or more child nodes.
Tree Operations
- Traversal: Visiting each node in the tree in a specific order (e.g., inorder, preorder, postorder).
- Insertion: Adding a new node to the tree while maintaining the tree's properties.
- Deletion: Removing a node from the tree while maintaining the tree's properties.
- Search: Finding a specific node in the tree.
Stacks
Definition
- A stack is a linear data structure that follows the Last-In-First-Out (LIFO) principle.
- A stack consists of a collection of elements, with two primary operations: push and pop.
Stack Operations
- Push: Adding an element to the top of the stack.
- Pop: Removing the top element from the stack.
- Peek: Viewing the top element of the stack without removing it.
Stack Properties
- LIFO: Last-In-First-Out, meaning the most recently added element is the first to be removed.
- FILO: First-In-Last-Out, meaning the first element added is the last to be removed.
Stack Applications
- Evaluating Postfix Expressions: Stacks are used to evaluate postfix expressions by parsing the expression from left to right.
- Implementing Recursive Algorithms: Stacks are used to implement recursive algorithms, allowing for efficient use of memory.
- Undo/Redo Functionality: Stacks are used to implement undo and redo functionality in applications.
树
定义
- 树是一种以节点为基础的层次结构，其中每个节点都具有值和零个或多个子节点。
- 树的顶部节点称为根节点。
- 树中的每个节点都具有唯一的键或值。
树的类型
- 二叉树：每个节点最多有两个子节点（左子树和右子树）。
- B-树：一种自平衡搜索树，能够在对数时间内进行搜索、插入和删除操作，并保持数据排序。
- AVL树：一种自平衡二叉搜索树，确保树的高度保持相对较小。
树的术语
- 根节点：树的顶部节点。
- 子节点：具有父节点的节点。
- 父节点：具有一个或多个子节点的节点。
- 兄弟节点：具有相同父节点的节点。
- 叶节点：没有子节点的节点。
- 内部节点：具有一个或多个子节点的节点。
树操作
- 遍历：按照特定顺序访问树中的每个节点（例如中序、前序、后序）。
- 插入：在保持树性质的情况下将新节点添加到树中。
- 删除：在保持树性质的情况下从树中删除节点。
- 搜索：在树中查找特定节点。
栈
定义
- 栈是一种以元素为基础的线性结构，遵循后进先出（LIFO）的原则。
- 栈由元素集合组成，具有两个主要操作：push和pop。
栈操作
- push：将元素添加到栈的顶部。
- pop：从栈的顶部删除元素。
- peek：查看栈的顶部元素，但不删除它。
栈属性
- LIFO：后进先出，意味着最recently添加的元素是第一个被删除的。
- FILO：先进后出，意味着最first添加的元素是最后一个被删除的。
栈应用
- 后缀表达式求值：栈用于从左到右解析后缀表达式。
- 递归算法实现：栈用于实现递归算法，使得内存使用更加高效。
- 撤销/重做功能：栈用于实现应用程序中的撤销和重做功能。
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