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182 lines
12 KiB
Markdown
182 lines
12 KiB
Markdown
# JavaScript Algorithms and Data Structures
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[](https://travis-ci.org/trekhleb/javascript-algorithms)
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[](https://codecov.io/gh/trekhleb/javascript-algorithms)
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## Data Structures
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1. [Linked List](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/linked-list)
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2. [Queue](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/queue)
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3. [Stack](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/stack)
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4. [Hash Table](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/hash-table)
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5. [Heap](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/heap)
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6. [Priority Queue](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/priority-queue)
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7. [Trie](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/trie)
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8. [Tree](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree)
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* [Binary Search Tree](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree/binary-search-tree)
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* [AVL Tree](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree/avl-tree)
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* Red-Black Tree
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* Suffix Tree
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* Segment Tree or Interval Tree
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* Binary Indexed Tree or Fenwick Tree
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9. [Graph](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/graph) (both directed and undirected)
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## Algorithms
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### Algorithms by Topic
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* **Math**
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* [Factorial](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/factorial)
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* [Fibonacci Number](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/fibonacci)
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* [Primality Test](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/primality-test) (trial division method)
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* [Euclidean Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/euclidean-algorithm) - calculate the Greatest Common Divisor (GCD)
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* [Least Common Multiple](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/least-common-multiple) (LCM)
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* [Integer Partition](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/integer-partition)
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* **Sets**
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* [Cartesian Product](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/cartesian-product) - product of multiple sets
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* [Power Set](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/power-set) - all subsets of the set
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* [Permutations](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/permutations) (with and without repetitions)
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* [Combinations](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/combinations) (with and without repetitions)
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* [Fisher–Yates Shuffle](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/fisher-yates) - random permutation of a finite sequence
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* [Longest Common Subsequence](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/longest-common-subsequnce) (LCS)
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* [Longest Increasing subsequence](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/longest-increasing-subsequence)
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* [Shortest Common Supersequence](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/shortest-common-supersequence) (SCS)
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* [Knapsack Problem](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/knapsack-problem) - 0/1 and unbound versions
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* **String**
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* [Levenshtein Distance](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/levenshtein-distance) - minimum edit distance between two sequences
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* [Hamming Distance](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/hamming-distance) - number of positions at which the symbols are different
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* [Knuth–Morris–Pratt Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/knuth-morris-pratt) - substring search
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* [Rabin Karp Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/rabin-karp) - substring search
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* [Longest Common Substring](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/longest-common-substring)
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* **Search**
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* [Binary Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/search/binary-search)
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* **Sorting**
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* [Bubble Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/bubble-sort)
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* [Selection Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/selection-sort)
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* [Insertion Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/insertion-sort)
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* [Heap Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/heap-sort)
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* [Merge Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/merge-sort)
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* [Quicksort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/quick-sort)
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* [Shellsort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/shell-sort)
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* **Tree**
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* [Depth-First Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/tree/depth-first-search) (DFS)
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* [Breadth-First Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/tree/breadth-first-search) (BFS)
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* **Graph**
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* [Depth-First Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/depth-first-search) (DFS)
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* [Breadth-First Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/breadth-first-search) (BFS)
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* Detect Cycle
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* Topological Sorting
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* Dijkstra Algorithm to Find Shortest Path
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* Eulerian path, Eulerian circuit
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* Bellman Ford
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* Strongly Connected Component algorithm
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* Shortest Path Faster Algorithm (SPFA)
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* **Minimum Spanning Tree**
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* Prim’s algorithm
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* Kruskal’s algorithm
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* **Uncategorized**
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* Union-Find
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* Maze
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* Sudoku
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### Algorithms by Paradigm
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* **Greedy**
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* [Unbound Knapsack Problem](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/knapsack-problem)
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* **Divide and Conquer**
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* [Euclidean Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/euclidean-algorithm) - calculate the Greatest Common Divisor (GCD)
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* [Permutations](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/permutations) (with and without repetitions)
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* [Combinations](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/combinations) (with and without repetitions)
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* [Merge Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/merge-sort)
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* [Quicksort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/quick-sort)
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* [Tree Depth-First Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/tree/depth-first-search) (DFS)
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* [Graph Depth-First Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/depth-first-search) (DFS)
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* **Dynamic Programming**
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* [Fibonacci Number](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/fibonacci)
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* [Levenshtein Distance](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/levenshtein-distance) - minimum edit distance between two sequences
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* [Longest Common Subsequence](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/longest-common-subsequnce) (LCS)
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* [Longest Common Substring](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/longest-common-substring)
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* [Longest Increasing subsequence](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/longest-increasing-subsequence)
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* [Shortest Common Supersequence](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/shortest-common-supersequence)
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* [0/1 Knapsack Problem](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/knapsack-problem)
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* [Integer Partition](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/integer-partition)
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* Maximum subarray
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* Maximum sum path
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* **Backtracking**
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* **Branch & Bound**
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## Running Tests
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**Run all tests**
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```
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npm test
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```
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**Run tests by name**
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```
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npm test -- -t 'LinkedList'
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```
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## Playground
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You may play with data-structures and algorithms in `./src/playground/playground.js` file and write
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tests for it in `./src/playground/__test__/playground.test.js`.
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Then just simply run the following command to test if your playground code works as expected:
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```
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npm test -- -t 'playground'
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```
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## Useful links
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[▶ Data Structures and Algorithms on YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
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## Useful Information
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### Big O Notation
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Order of growth of algorithms specified in Big O notation.
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Source: [Big O Cheat Sheet](http://bigocheatsheet.com/).
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Below is the list of some of the most used Big O notations and their performance comparisons against different sizes of the input data.
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| Big O Notation | Computations for 10 elements | Computations for 100 elements | Computations for 1000 elements |
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| -------------- | ---------------------------- | ----------------------------- | ------------------------------- |
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| **O(1)** | 1 | 1 | 1 |
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| **O(log N)** | 3 | 6 | 9 |
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| **O(N)** | 10 | 100 | 1000 |
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| **O(N log N)** | 30 | 60 | 9000 |
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| **O(N^2)** | 100 | 10000 | 1000000 |
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| **O(2^N)** | 1024 | 1.26e+29 | 1.07e+301 |
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| **O(N!)** | 3628800 | 9.3e+157 | 4.02e+2567 |
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### Data Structure Operations Complexity
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| Data Structure | Access | Search | Insertion | Deletion |
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| ----------------------- | :-------: | :-------: | :-------: | :-------: |
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| **Array** | 1 | n | n | n |
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| **Stack** | n | n | 1 | 1 |
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| **Queue** | n | n | 1 | 1 |
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| **Linked List** | n | n | 1 | 1 |
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| **Hash Table** | - | n | n | n |
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| **Binary Search Tree** | n | n | n | n |
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| **B-Tree** | log(n) | log(n) | log(n) | log(n) |
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| **Red-Black Tree** | log(n) | log(n) | log(n) | log(n) |
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| **AVL Tree** | log(n) | log(n) | log(n) | log(n) |
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### Array Sorting Algorithms Complexity
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| Name | Best | Average | Worst | Memory | Stable |
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| --------------------- | :-------: | :-------: | :-----------: | :-------: | :-------: |
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| **Bubble sort** | n | n^2 | n^2 | 1 | Yes |
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| **Insertion sort** | n | n^2 | n^2 | 1 | Yes |
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| **Selection sort** | n^2 | n^2 | n^2 | 1 | No |
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| **Heap sort** | n log(n) | n log(n) | n log(n) | 1 | No |
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| **Merge sort** | n log(n) | n log(n) | n log(n) | n | Yes |
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| **Quick sort** | n log(n) | n log(n) | n^2 | log(n) | No |
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| **Shell sort** | n log(n) | depends on gap sequence | n (log(n))^2 | 1 | No |
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