数据结构可视化工具usfca

https://www.cs.usfca.edu/~galles/visualization/Algorithms.html

这里介绍一个可以可视化学习数据结构和算法的网站

目前支持以下数据结构和算法的可视化：

Currently, we have visualizations for the following data structures and algorithms:

• Basics

• Stack: Array Implementation

• Stack: Linked List Implementation

• Queues: Array Implementation

• Queues: Linked List Implementation

• Lists: Array Implementation (available in java version)

• Lists: Linked List Implementation (available in java version)

• Recursion

• Factorial

• Reversing a String

• N-Queens Problem

• Indexing

• Binary and Linear Search (of sorted list)

• Binary Search Trees

• AVL Trees (Balanced binary search trees)

• Red-Black Trees

• Splay Trees

• Open Hash Tables (Closed Addressing)

• Closed Hash Tables (Open Addressing)

• Closed Hash Tables, using buckets

• Trie (Prefix Tree, 26-ary Tree)

• Radix Tree (Compact Trie)

• Ternary Search Tree (Trie with BST of children)

• B Trees

• B+ Trees

• Sorting

• Comparison Sorting

• Bubble Sort

• Selection Sort

• Insertion Sort

• Shell Sort

• Merge Sort

• Quck Sort

• Bucket Sort

• Counting Sort

• Radix Sort

• Heap Sort

• Heap-like Data Structures

• Heaps

• Binomial Queues

• Fibonacci Heaps

• Leftist Heaps

• Skew Heaps

• Graph Algorithms

• Breadth-First Search

• Depth-First Search

• Connected Components

• Dijkstra's Shortest Path

• Prim's Minimum Cost Spanning Tree

• Topological Sort (Using Indegree array)

• Topological Sort (Using DFS)

• Floyd-Warshall (all pairs shortest paths)

• Kruskal Minimum Cost Spanning Tree Algorithm

• Dynamic Programming

• Calculating nth Fibonacci number

• Making Change

• Longest Common Subsequence

• Geometric Algorithms

• 2D Rotation and Scale Matrices

• 2D Rotation and Translation Matrices

• 2D Changing Coordinate Systems

• 3D Rotation and Scale Matrices

• 3D Changing Coordinate Systems

• Others ...

• Disjoint Sets

• Huffman Coding (available in java version)

以B+树为例进行演示：

https://www.cs.usfca.edu/~galles/visualization/BPlusTree.html

空树中插入5

依次插入8，10，15

插入16

插入16后超过了关键字的个数限制，所以要进行分裂。在叶子结点分裂时，分裂出来的左结点2个记录，右边3个记录，中间key成为索引结点中的key，分裂后当前结点指向了父结点（根结点）。

插入17

插入18

插入20 21 22 20之后

继续插入7 6 9，继续分裂，高度变成3

还有删除、查找，其他数据结构都可以照此演示

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