Big-O Algorithm Complexity Cheat Sheet [译]

http://bigocheatsheet.com/

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Know Thy Complexities!

This webpage covers the space and time Big-O complexities of common algorithms used in Computer Science

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Big-O Complexity Chart

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表格代码

https://github.com/ericdrowell/BigOCheatSheet/blob/master/Tables.htmlqq

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Common Data Structure Operations

Data Structure Time Complexity Space Complexity Average Worst Worst Access Search Insertion Deletion Access Search Insertion Deletion Array Θ(1) Θ(n) Θ(n) Θ(n) O(1) O(n) O(n) O(n) O(n) Stack Θ(n) Θ(n) Θ(1) Θ(1) O(n) O(n) O(1) O(1) O(n) Queue Θ(n) Θ(n) Θ(1) Θ(1) O(n) O(n) O(1) O(1) O(n) Singly-Linked List Θ(n) Θ(n) Θ(1) Θ(1) O(n) O(n) O(1) O(1) O(n) Doubly-Linked List Θ(n) Θ(n) Θ(1) Θ(1) O(n) O(n) O(1) O(1) O(n) Skip List Θ(log(n)) Θ(log(n)) Θ(log(n)) Θ(log(n)) O(n) O(n) O(n) O(n) O(n log(n)) Hash Table N/A Θ(1) Θ(1) Θ(1) N/A O(n) O(n) O(n) O(n) Binary Search Tree Θ(log(n)) Θ(log(n)) Θ(log(n)) Θ(log(n)) O(n) O(n) O(n) O(n) O(n) Cartesian Tree N/A Θ(log(n)) Θ(log(n)) Θ(log(n)) N/A O(n) O(n) O(n) O(n) B-Tree Θ(log(n)) Θ(log(n)) Θ(log(n)) O(log(n)) O(log(n)) O(log(n)) O(log(n)) O(log(n)) O(n) Red-Black Tree Θ(log(n)) Θ(log(n)) Θ(log(n)) Θ(log(n)) O(log(n)) O(log(n)) O(log(n)) O(log(n)) O(n) Splay Tree N/A Θ(log(n)) Θ(log(n)) Θ(log(n)) N/A O(log(n)) O(log(n)) O(log(n)) O(n) AVL Tree Θ(log(n)) Θ(log(n)) Θ(log(n)) Θ(log(n)) O(log(n)) O(log(n)) O(log(n)) O(log(n)) O(n) KD Tree Θ(log(n)) Θ(log(n)) Θ(log(n)) Θ(log(n)) O(n) O(n) O(n) O(n) O(n)

Array Sorting Algorithms

Algorithm Time Complexity Space Complexity Best Average Worst Worst Quicksort Ω(n log(n)) Θ(n log(n)) O(n^2) O(log(n)) Mergesort Ω(n log(n)) Θ(n log(n)) O(n log(n)) O(n) Timsort Ω(n) Θ(n log(n)) O(n log(n)) O(n) Heapsort Ω(n log(n)) Θ(n log(n)) O(n log(n)) O(1) Bubble Sort Ω(n) Θ(n^2) O(n^2) O(1) Insertion Sort Ω(n) Θ(n^2) O(n^2) O(1) Selection Sort Ω(n^2) Θ(n^2) O(n^2) O(1) Tree Sort Ω(n log(n)) Θ(n log(n)) O(n^2) O(n) Shell Sort Ω(n log(n)) Θ(n(log(n))^2) O(n(log(n))^2) O(1) Bucket Sort Ω(n+k) Θ(n+k) O(n^2) O(n) Radix Sort Ω(nk) Θ(nk) O(nk) O(n+k) Counting Sort Ω(n+k) Θ(n+k) O(n+k) O(k) Cubesort Ω(n) Θ(n log(n)) O(n log(n)) O(n)

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<h2 id="data-structures">Common Data Structure Operations</h2><table class="table table-bordered table-striped">    <tr>      <th>Data Structure</th>      <th colspan="8">Time Complexity</th>      <th>Space Complexity</th>    </tr>    <tr>      <th></th>      <th colspan="4">Average</th>      <th colspan="4">Worst</th>      <th>Worst</th>    </tr>    <tr>      <th></th>      <th>Access</th>      <th>Search</th>      <th>Insertion</th>      <th>Deletion</th>      <th>Access</th>      <th>Search</th>      <th>Insertion</th>      <th>Deletion</th>      <th></th>    </tr>    <tr>      <td><a href="http://en.wikipedia.org/wiki/Array_data_structure">Array</a></td>      <td><code class="green">&Theta;(1)</code></td>      <td><code class="yellow">&Theta;(n)</code></td>      <td><code class="yellow">&Theta;(n)</code></td>      <td><code class="yellow">&Theta;(n)</code></td>      <td><code class="green">O(1)</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="yellow">O(n)</code></td>    </tr>    <tr>      <td><a href="http://en.wikipedia.org/wiki/Stack_(abstract_data_type)">Stack</a></td>      <td><code class="yellow">&Theta;(n)</code></td>      <td><code class="yellow">&Theta;(n)</code></td>      <td><code class="green">&Theta;(1)</code></td>      <td><code class="green">&Theta;(1)</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="green">O(1)</code></td>      <td><code class="green">O(1)</code></td>      <td><code class="yellow">O(n)</code></td>    </tr>    <tr>      <td><a href="http://en.wikipedia.org/wiki/Queue_(abstract_data_type)">Queue</a></td>      <td><code class="yellow">&Theta;(n)</code></td>      <td><code class="yellow">&Theta;(n)</code></td>      <td><code class="green">&Theta;(1)</code></td>      <td><code class="green">&Theta;(1)</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="green">O(1)</code></td>      <td><code class="green">O(1)</code></td>      <td><code class="yellow">O(n)</code></td>    </tr>    <tr>      <td><a href="http://en.wikipedia.org/wiki/Singly_linked_list#Singly_linked_lists">Singly-Linked List</a></td>      <td><code class="yellow">&Theta;(n)</code></td>      <td><code class="yellow">&Theta;(n)</code></td>      <td><code class="green">&Theta;(1)</code></td>      <td><code class="green">&Theta;(1)</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="green">O(1)</code></td>      <td><code class="green">O(1)</code></td>      <td><code class="yellow">O(n)</code></td>    </tr>    <tr>      <td><a href="http://en.wikipedia.org/wiki/Doubly_linked_list">Doubly-Linked List</a></td>      <td><code class="yellow">&Theta;(n)</code></td>      <td><code class="yellow">&Theta;(n)</code></td>      <td><code class="green">&Theta;(1)</code></td>      <td><code class="green">&Theta;(1)</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="green">O(1)</code></td>      <td><code class="green">O(1)</code></td>      <td><code class="yellow">O(n)</code></td>    </tr>    <tr>      <td><a href="http://en.wikipedia.org/wiki/Skip_list">Skip List</a></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="orange">O(n log(n))</code></td>    </tr>    <tr>      <td><a href="http://en.wikipedia.org/wiki/Hash_table">Hash Table</a></td>      <td><code class="gray">N/A</code></td>      <td><code class="green">&Theta;(1)</code></td>      <td><code class="green">&Theta;(1)</code></td>      <td><code class="green">&Theta;(1)</code></td>      <td><code class="gray">N/A</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="yellow">O(n)</code></td>    </tr>    <tr>      <td><a href="http://en.wikipedia.org/wiki/Binary_search_tree">Binary Search Tree</a></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="yellow">O(n)</code></td>    </tr>    <tr>      <td><a href="https://en.wikipedia.org/wiki/Cartesian_tree">Cartesian Tree</a></td>      <td><code class="gray">N/A</code></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="gray">N/A</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="yellow">O(n)</code></td>    </tr>    <tr>      <td><a href="http://en.wikipedia.org/wiki/B_tree">B-Tree</a></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow-green">O(log(n))</code></td>      <td><code class="yellow-green">O(log(n))</code></td>      <td><code class="yellow-green">O(log(n))</code></td>      <td><code class="yellow-green">O(log(n))</code></td>      <td><code class="yellow-green">O(log(n))</code></td>      <td><code class="yellow">O(n)</code></td>    </tr>    <tr>      <td><a href="http://en.wikipedia.org/wiki/Red-black_tree">Red-Black Tree</a></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow-green">O(log(n))</code></td>      <td><code class="yellow-green">O(log(n))</code></td>      <td><code class="yellow-green">O(log(n))</code></td>      <td><code class="yellow-green">O(log(n))</code></td>      <td><code class="yellow">O(n)</code></td>    </tr>    <tr>      <td><a href="https://en.wikipedia.org/wiki/Splay_tree">Splay Tree</a></td>      <td><code class="gray">N/A</code></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="gray">N/A</code></td>      <td><code class="yellow-green">O(log(n))</code></td>      <td><code class="yellow-green">O(log(n))</code></td>      <td><code class="yellow-green">O(log(n))</code></td>      <td><code class="yellow">O(n)</code></td>    </tr>    <tr>      <td><a href="http://en.wikipedia.org/wiki/AVL_tree">AVL Tree</a></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow-green">O(log(n))</code></td>      <td><code class="yellow-green">O(log(n))</code></td>      <td><code class="yellow-green">O(log(n))</code></td>      <td><code class="yellow-green">O(log(n))</code></td>      <td><code class="yellow">O(n)</code></td>    </tr>    <tr>      <td><a href="http://en.wikipedia.org/wiki/K-d_tree">KD Tree</a></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow-green">&Theta;(log(n))</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="yellow">O(n)</code></td>      <td><code class="yellow">O(n)</code></td>    </tr></table><h2 id="sorting">Array Sorting Algorithms</h2><table class="table table-bordered table-striped">    <tr>      <th>Algorithm</th>      <th colspan="3">Time Complexity</th>      <th>Space Complexity</th>    </tr>    <tr>      <th></th>      <th>Best</th>      <th>Average</th>      <th>Worst</th>      <th>Worst</th>    </tr>    <tr>      <td><a href="http://en.wikipedia.org/wiki/Quicksort">Quicksort</a></td>      <td><code class="orange">&Omega;(n log(n))</code></td>      <td><code class="orange">&Theta;(n log(n))</code></td>      <td><code class="red">O(n^2)</code></td>      <td><code class="yellow-green">O(log(n))</code></td>    </tr>    <tr>      <td><a href="http://en.wikipedia.org/wiki/Merge_sort">Mergesort</a></td>      <td><code class="orange">&Omega;(n log(n))</code></td>      <td><code class="orange">&Theta;(n log(n))</code></td>      <td><code class="orange">O(n log(n))</code></td>      <td><code class="yellow">O(n)</code></td>    </tr>    <tr>      <td><a href="http://en.wikipedia.org/wiki/Timsort">Timsort</a></td>      <td><code class="yellow">&Omega;(n)</code></td>      <td><code class="orange">&Theta;(n log(n))</code></td>      <td><code class="orange">O(n log(n))</code></td>      <td><code class="yellow">O(n)</code></td>    </tr>    <tr>      <td><a href="http://en.wikipedia.org/wiki/Heapsort">Heapsort</a></td>      <td><code class="orange">&Omega;(n log(n))</code></td>      <td><code class="orange">&Theta;(n log(n))</code></td>      <td><code class="orange">O(n log(n))</code></td>      <td><code class="green">O(1)</code></td>    </tr>    <tr>      <td><a href="http://en.wikipedia.org/wiki/Bubble_sort">Bubble Sort</a></td>      <td><code class="yellow">&Omega;(n)</code></td>      <td><code class="red">&Theta;(n^2)</code></td>      <td><code class="red">O(n^2)</code></td>      <td><code class="green">O(1)</code></td>    </tr>    <tr>      <td><a href="http://en.wikipedia.org/wiki/Insertion_sort">Insertion Sort</a></td>      <td><code class="yellow">&Omega;(n)</code></td>      <td><code class="red">&Theta;(n^2)</code></td>      <td><code class="red">O(n^2)</code></td>      <td><code class="green">O(1)</code></td>    </tr>    <tr>      <td><a href="http://en.wikipedia.org/wiki/Selection_sort">Selection Sort</a></td>      <td><code class="red">&Omega;(n^2)</code></td>      <td><code class="red">&Theta;(n^2)</code></td>      <td><code class="red">O(n^2)</code></td>      <td><code class="green">O(1)</code></td>    </tr>    <tr>      <td><a href="https://en.wikipedia.org/wiki/Tree_sort">Tree Sort</a></td>      <td><code class="orange">&Omega;(n log(n))</code></td>      <td><code class="orange">&Theta;(n log(n))</code></td>      <td><code class="red">O(n^2)</code></td>      <td><code class="yellow">O(n)</code></td>    </tr>    <tr>      <td><a href="http://en.wikipedia.org/wiki/Shellsort">Shell Sort</a></td>      <td><code class="orange">&Omega;(n log(n))</code></td>      <td><code class="red">&Theta;(n(log(n))^2)</code></td>      <td><code class="red">O(n(log(n))^2)</code></td>      <td><code class="green">O(1)</code></td>    </tr>    <tr>      <td><a rel="tooltip" title="Only for integers. k is a number of buckets" href="http://en.wikipedia.org/wiki/Bucket_sort">Bucket Sort</a></td>      <td><code class="green">&Omega;(n+k)</code></td>      <td><code class="green">&Theta;(n+k)</code></td>      <td><code class="red">O(n^2)</code></td>      <td><code class="yellow">O(n)</code></td>    </tr>    <tr>      <td><a rel="tooltip" title="Constant number of digits 'k'" href="http://en.wikipedia.org/wiki/Radix_sort">Radix Sort</a></td>      <td><code class="green">&Omega;(nk)</code></td>      <td><code class="green">&Theta;(nk)</code></td>      <td><code class="green">O(nk)</code></td>      <td><code class="yellow">O(n+k)</code></td>    </tr>    <tr>      <td><a rel="tooltip" title="Difference between maximum and minimum number 'k'" href="https://en.wikipedia.org/wiki/Counting_sort">Counting Sort</a></td>      <td><code class="green">&Omega;(n+k)</code></td>      <td><code class="green">&Theta;(n+k)</code></td>      <td><code class="green">O(n+k)</code></td>      <td><code class="yellow">O(k)</code></td>    </tr>    <tr>      <td><a href="https://en.wikipedia.org/wiki/Cubesort">Cubesort</a></td>      <td><code class="yellow">&Omega;(n)</code></td>      <td><code class="orange">&Theta;(n log(n))</code></td>      <td><code class="orange">O(n log(n))</code></td>      <td><code class="yellow">O(n)</code></td>   </tr></table>

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