MeandNi / Algorithms4 Common
🔥Algorithms, 4th Edition 算法4精华笔记，通俗理解，算法收集与强化。
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JVM 是 java 程序员永远的考题，算法是所有程序员永久的考题。这应该是很多人的共识，不管是谁，学习的路上我们时常遇到迷茫阶段，抓住最根本的东西你永远不会觉得迷失。
年假之前，我就规定自己要完成多少多少的任务，要做一些些有意义的事情，读书，练习，输出一些有价值的文字和笔记正是这一理念的实现，这样不仅让自己的经历更漂亮一点，也能帮助很多其他人！
《算法（第4版）》是一本晦涩的书，特别是中文版！我要强烈吐槽一下中文版的翻译，因为这本书业内评价都极高，当我兴致勃勃准备开始复习时，却被绕口的中文读的喘不过气，导致我推迟好久终于在今年年假期间才又拿出来慢慢对着英文原版啃起来！
除去基础数据结构的介绍，从大的方面讲，全书共有 4 大块，分别是排序、搜索、图、字符串，每大块基本都有 5 节的内容，每节又会有 4～5 种算法的实现与讲解，总共超过 80 道算法类型，图文并茂，确实是本好书（除了翻译）。
我希望能用这种方式激励我自己把这本书啃完，也希望帮助到一些正在准备面试和同样准备复习算法的同学。笔记内容除去了书中晦涩难懂的部分，截取的书中精华部分，我认为这本书的精华就是一张张插图，所以我几乎把所有的帮助理解的图都用上了，这一点你可以看3-3-平衡查找树的笔记，其次是每段都会贴出相应的关键代码，以便让我以后复习时不理解可以直接看代码。这本笔记在我反复复习也会随时更新，预计以后刷 LeetCode 时，也会将对应题型放在对应章节里，如果有其他建议欢迎提 issue 。
笔记目录
算法集合
排序：
| ALGORITHM | CODE | IN PLACE | STABLE | BEST | AVERAGE | WORST | REMARKS |
|---|---|---|---|---|---|---|---|
| 选择排序 | Selection.java | ✔ | ½ n 2 | ½ n 2 | ½ n 2 | n exchanges; quadratic in best case | |
| 插入排序 | Insertion.java | ✔ | ✔ | n | ¼ n 2 | ½ n 2 | use for small or partially-sorted arrays |
| 冒泡排序 | Bubble.java | ✔ | ✔ | n | ½ n 2 | ½ n 2 | rarely useful; use insertion sort instead |
| 希尔排序 | Shell.java | ✔ | n log3 n | unknown | c n 3/2 | tight code; subquadratic | |
| 合并排序 | Merge.java | ✔ | ½ n lg n | n lg n | n lg n | n log n guarantee; stable | |
| 快速排序 | Quick.java | ✔ | n lg n | 2 n ln n | ½ n 2 | n log n probabilistic guarantee; fastest in practice | |
| 堆排序 | Heap.java | ✔ | n † | 2 n lg n | 2 n lg n | n log n guarantee; in place |
优先队列
| DATA STRUCTURE | CODE | INSERT | DEL-MIN | MIN | DEC-KEY | DELETE | MERGE |
|---|---|---|---|---|---|---|---|
| 数组 | BruteIndexMinPQ.java | 1 | n | n | 1 | 1 | n |
| 二叉堆 | IndexMinPQ.java | log n | log n | 1 | log n | log n | n |
| d-way heap | IndexMultiwayMinPQ.java | logd n | d logd n | 1 | logd n | d logd n | n |
| 二项堆 | IndexBinomialMinPQ.java | 1 | log n | 1 | log n | log n | log n |
| 斐波那契堆 | IndexFibonacciMinPQ.java | 1 | log n † | 1 | 1 † | log n † | log n |
查找
| worst case | average case | ||||||
|---|---|---|---|---|---|---|---|
| DATA STRUCTURE | CODE | SEARCH | INSERT | DELETE | SEARCH | INSERT | DELETE |
| 顺序查找 (无序列表) | SequentialSearchST.java | n | n | n | n | n | n |
| 二分查找 (有序列表) | BinarySearchST.java | log n | n | n | log n | n | n |
| 二叉树 (不平衡) | BST.java | n | n | n | log n | log n | sqrt(n) |
| 红黑二叉树 (左倾) | RedBlackBST.java | log n | log n | log n | log n | log n | log n |
| 散列表 (分离链接法) | SeparateChainingHashST.java | n | n | n | 1 † | 1 † | 1 † |
| 散列表 (线性探测) | LinearProbingHashST.java | n | n | n | 1 † | 1 † | 1 † |
图
| PROBLEM | ALGORITHM | CODE | TIME | SPACE |
|---|---|---|---|---|
| 路径 | DFS | DepthFirstPaths.java | E + V | V |
| 最短路径(最少边缘) | BFS | BreadthFirstPaths.java | E + V | V |
| 环 | DFS | Cycle.java | E + V | V |
| 有向路径 | DFS | DepthFirstDirectedPaths.java | E + V | V |
| 最短有向路径 (最少边缘) | BFS | BreadthFirstDirectedPaths.java | E + V | V |
| 有向环 | DFS | DirectedCycle.java | E + V | V |
| 拓扑排序 | DFS | Topological.java | E + V | V |
| bipartiteness / odd cycle | DFS | Bipartite.java | E + V | V |
| 连通分量 | DFS | CC.java | E + V | V |
| 强连通分量 | Kosaraju–Sharir | KosarajuSharirSCC.java | E + V | V |
| 强连通分量 | Tarjan | TarjanSCC.java | E + V | V |
| 强连通分量 | Gabow | GabowSCC.java | E + V | V |
| 欧拉回路 | DFS | EulerianCycle.java | E + V | E + V |
| 定向欧拉循环 | DFS | DirectedEulerianCycle.java | E + V | V |
| 传递闭包 | DFS | TransitiveClosure.java | V (E + V) | V 2 |
| 最小生成树 | Kruskal | KruskalMST.java | E log E | E + V |
| 最小生成树 | Prim | PrimMST.java | E log V | V |
| 最小生成树 | Boruvka | BoruvkaMST.java | E log V | V |
| 最短路径(非负权) | Dijkstra | DijkstraSP.java | E log V | V |
| 最短路径(无负循环) | Bellman–Ford | BellmanFordSP.java | V (V + E) | V |
| s最短路径（无环） | topological sort | AcyclicSP.java | V + E | V |
| 所有节点对之间的最短路 | Floyd–Warshall | FloydWarshall.java | V 3 | V 2 |
| 最大流/最小割 | Ford–Fulkerson | FordFulkerson.java | E V (E + V) | V |
| 二分图匹配 | Hopcroft–Karp | HopcroftKarp.java | V ½ (E + V) | V |
| 任务分配问题 | successive shortest paths | AssignmentProblem.java | n 3 log n | n 2 |
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