javascript-algorithms/Readme.zh-TW.md

JavaScript 演算法與資料結構

這個知識庫包含許多 JavaScript 的資料結構與演算法的基礎範例。 每個演算法和資料結構都有其個別的文件，內有相關的解釋以及更多相關的文章或Youtube影片連結。

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資料結構

資料結構是一個電腦用來組織和排序資料的特定方式，透過這樣的方式資料可以有效率地被讀取以及修改。更精確地說，一個資料結構是一個資料值的集合、彼此間的關係，函數或者運作可以應用於資料上。

• Linked List 鏈結串列
• Queue 貯列
• Stack 堆疊
• Hash Table 雜湊表
• Heap 堆
• Priority Queue 優先貯列
• Trie 字典樹
• Tree 樹
  • Binary Search Tree 二元搜尋樹
  • AVL Tree AVL樹
  • Red-Black Tree
  • Suffix Tree
  • Segment Tree or Interval Tree
  • Binary Indexed Tree or Fenwick Tree
• Graph 圖 (both directed and undirected)
• Disjoint Set 互斥集

演算法

演算法是一個如何解決一類問題的非模糊規格。演算法是一個具有精確地定義了一系列運作的規則的集合

演算法議題分類 TODO

• 數學類
  • Factorial
  • Fibonacci Number
  • Primality Test (trial division method)
  • Euclidean Algorithm - calculate the Greatest Common Divisor (GCD)
  • Least Common Multiple (LCM)
  • Integer Partition
• 集合
  • Cartesian Product - product of multiple sets
  • Power Set - all subsets of the set
  • Permutations (with and without repetitions)
  • Combinations (with and without repetitions)
  • Fisher–Yates Shuffle - random permutation of a finite sequence
  • Longest Common Subsequence (LCS)
  • Longest Increasing subsequence
  • Shortest Common Supersequence (SCS)
  • Knapsack Problem - "0/1" and "Unbound" ones
  • Maximum Subarray - "Brute Force" and "Dynamic Programming" (Kadane's) versions
• 字串
  • Levenshtein Distance - minimum edit distance between two sequences
  • Hamming Distance - number of positions at which the symbols are different
  • Knuth–Morris–Pratt Algorithm - substring search
  • Rabin Karp Algorithm - substring search
  • Longest Common Substring
• 搜尋
  • Binary Search
• 排序
  • Bubble Sort
  • Selection Sort
  • Insertion Sort
  • Heap Sort
  • Merge Sort
  • Quicksort
  • Shellsort
• 樹
  • Depth-First Search (DFS)
  • Breadth-First Search (BFS)
• 圖
  • Depth-First Search (DFS)
  • Breadth-First Search (BFS)
  • Dijkstra Algorithm - finding shortest path to all graph vertices
  • Bellman-Ford Algorithm - finding shortest path to all graph vertices
  • Detect Cycle - for both directed and undirected graphs (DFS and Disjoint Set based versions)
  • Prim’s Algorithm - finding Minimum Spanning Tree (MST) for weighted undirected graph
  • Kruskal’s Algorithm - finding Minimum Spanning Tree (MST) for weighted undirected graph
  • Topological Sorting - DFS method
  • Articulation Points - Tarjan's algorithm (DFS based)
  • Bridges - DFS based algorithm
  • Eulerian Path and Eulerian Circuit - Fleury's algorithm - Visit every edge exactly once
  • Hamiltonian Cycle - Visit every vertex exactly once
  • Strongly Connected Components - Kosaraju's algorithm
  • Travelling Salesman Problem - shortest possible route that visits each city and returns to the origin city
• 未分類
  • Tower of Hanoi
  • N-Queens Problem
  • Knight's Tour

Algorithms by Paradigm

An algorithmic paradigm is a generic method or approach which underlies the design of a class of algorithms. It is an abstraction higher than the notion of an algorithm, just as an algorithm is an abstraction higher than a computer program.

• Brute Force - look at all the possibilities and selects the best solution
  • Maximum Subarray
  • Travelling Salesman Problem - shortest possible route that visits each city and returns to the origin city
• Greedy - choose the best option at the current time, without any consideration for the future
  • Unbound Knapsack Problem
  • Dijkstra Algorithm - finding shortest path to all graph vertices
  • Prim’s Algorithm - finding Minimum Spanning Tree (MST) for weighted undirected graph
  • Kruskal’s Algorithm - finding Minimum Spanning Tree (MST) for weighted undirected graph
• Divide and Conquer - divide the problem into smaller parts and then solve those parts
  • Binary Search
  • Tower of Hanoi
  • Euclidean Algorithm - calculate the Greatest Common Divisor (GCD)
  • Permutations (with and without repetitions)
  • Combinations (with and without repetitions)
  • Merge Sort
  • Quicksort
  • Tree Depth-First Search (DFS)
  • Graph Depth-First Search (DFS)
• Dynamic Programming - build up to a solution using previously found sub-solutions
  • Fibonacci Number
  • Levenshtein Distance - minimum edit distance between two sequences
  • Longest Common Subsequence (LCS)
  • Longest Common Substring
  • Longest Increasing subsequence
  • Shortest Common Supersequence
  • 0/1 Knapsack Problem
  • Integer Partition
  • Maximum Subarray
  • Bellman-Ford Algorithm - finding shortest path to all graph vertices
• Backtracking - similarly to brute force try to generate all possible solutions but each time you generate a solution test if it satisfies all conditions, and only then continue generating subsequent solutions. Otherwise backtrack and go on a different path of finding solution
  • Hamiltonian Cycle - Visit every vertex exactly once
  • N-Queens Problem
  • Knight's Tour
• Branch & Bound

如何使用本知識庫

安裝所有必須套件

npm install

執行所有測試

npm test

以名稱執行該測試

npm test -- -t 'LinkedList'

Playground

You may play with data-structures and algorithms in ./src/playground/playground.js file and write tests for it in ./src/playground/__test__/playground.test.js.

Then just simply run the following command to test if your playground code works as expected:

npm test -- -t 'playground'

有用的資訊

參考

▶ Data Structures and Algorithms on YouTube

大 O 標記

Order of growth of algorithms specified in Big O notation.

資料來源: Big O Cheat Sheet.

Below is the list of some of the most used Big O notations and their performance comparisons against different sizes of the input data.

Big O Notation	Computations for 10 elements	Computations for 100 elements	Computations for 1000 elements
O(1)	1	1	1
O(log N)	3	6	9
O(N)	10	100	1000
O(N log N)	30	600	9000
O(N^2)	100	10000	1000000
O(2^N)	1024	1.26e+29	1.07e+301
O(N!)	3628800	9.3e+157	4.02e+2567

Data Structure Operations Complexity

Data Structure	Access	Search	Insertion	Deletion
Array	1	n	n	n
Stack	n	n	1	1
Queue	n	n	1	1
Linked List	n	n	1	1
Hash Table	-	n	n	n
Binary Search Tree	n	n	n	n
B-Tree	log(n)	log(n)	log(n)	log(n)
Red-Black Tree	log(n)	log(n)	log(n)	log(n)
AVL Tree	log(n)	log(n)	log(n)	log(n)

Array Sorting Algorithms Complexity

Name	Best	Average	Worst	Memory	Stable
Bubble sort	n	n^2	n^2	1	Yes
Insertion sort	n	n^2	n^2	1	Yes
Selection sort	n^2	n^2	n^2	1	No
Heap sort	n log(n)	n log(n)	n log(n)	1	No
Merge sort	n log(n)	n log(n)	n log(n)	n	Yes
Quick sort	n log(n)	n log(n)	n^2	log(n)	No
Shell sort	n log(n)	depends on gap sequence	n (log(n))^2	1	No