{"id":3754,"date":"2019-08-08T19:42:14","date_gmt":"2019-08-08T11:42:14","guid":{"rendered":"https:\/\/damogame.cn\/wordpress\/?p=3754"},"modified":"2019-08-08T19:42:14","modified_gmt":"2019-08-08T11:42:14","slug":"know-thy-complexities","status":"publish","type":"post","link":"https:\/\/i007.cc\/wordpress\/archives\/3754","title":{"rendered":"Know Thy Complexities!"},"content":{"rendered":"

\u539f\u6587\u5730\u5740<\/a><\/p>\n

 <\/p>\n

Hi there!\u00a0 This webpage covers the space and time Big-O complexities of common algorithms used in Computer Science.\u00a0 When preparing for technical interviews in the past, I found myself spending hours crawling the internet putting together the best, average, and worst case complexities for search and sorting algorithms so that I wouldn’t be stumped when asked about them.\u00a0 Over the last few years, I’ve interviewed at several Silicon Valley startups, and also some bigger companies, like Google, Facebook, Yahoo, LinkedIn, and Uber, and each time that I prepared for an interview, I thought to myself “Why hasn’t someone created a nice Big-O cheat sheet?”.\u00a0 So, to save all of you fine folks a ton of time, I went ahead and created one.\u00a0 Enjoy! –\u00a0Eric<\/a><\/p>\n

Check out El Grapho, a graph data visualization library that supports millions of nodes and edges<\/a><\/p>\n

Big-O Complexity Chart<\/h2>\n
\n\n\n\n
Horrible<\/code><\/td>\nBad<\/code><\/td>\nFair<\/code><\/td>\nGood<\/code><\/td>\nExcellent<\/code><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
O(log n), O(1)O(n)O(n log n)O(n^2)O(2^n)O(n!)OperationsElements<\/div>\n
\n

Common Data Structure Operations<\/h2>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Data Structure<\/th>\nTime Complexity<\/th>\nSpace Complexity<\/th>\n<\/tr>\n
<\/th>\nAverage<\/th>\nWorst<\/th>\nWorst<\/th>\n<\/tr>\n
<\/th>\nAccess<\/th>\nSearch<\/th>\nInsertion<\/th>\nDeletion<\/th>\nAccess<\/th>\nSearch<\/th>\nInsertion<\/th>\nDeletion<\/th>\n<\/th>\n<\/tr>\n
Array<\/a><\/td>\n\u0398(1)<\/code><\/td>\n\u0398(n)<\/code><\/td>\n\u0398(n)<\/code><\/td>\n\u0398(n)<\/code><\/td>\nO(1)<\/code><\/td>\nO(n)<\/code><\/td>\nO(n)<\/code><\/td>\nO(n)<\/code><\/td>\nO(n)<\/code><\/td>\n<\/tr>\n
Stack<\/a><\/td>\n\u0398(n)<\/code><\/td>\n\u0398(n)<\/code><\/td>\n\u0398(1)<\/code><\/td>\n\u0398(1)<\/code><\/td>\nO(n)<\/code><\/td>\nO(n)<\/code><\/td>\nO(1)<\/code><\/td>\nO(1)<\/code><\/td>\nO(n)<\/code><\/td>\n<\/tr>\n
Queue<\/a><\/td>\n\u0398(n)<\/code><\/td>\n\u0398(n)<\/code><\/td>\n\u0398(1)<\/code><\/td>\n\u0398(1)<\/code><\/td>\nO(n)<\/code><\/td>\nO(n)<\/code><\/td>\nO(1)<\/code><\/td>\nO(1)<\/code><\/td>\nO(n)<\/code><\/td>\n<\/tr>\n
Singly-Linked List<\/a><\/td>\n\u0398(n)<\/code><\/td>\n\u0398(n)<\/code><\/td>\n\u0398(1)<\/code><\/td>\n\u0398(1)<\/code><\/td>\nO(n)<\/code><\/td>\nO(n)<\/code><\/td>\nO(1)<\/code><\/td>\nO(1)<\/code><\/td>\nO(n)<\/code><\/td>\n<\/tr>\n
Doubly-Linked List<\/a><\/td>\n\u0398(n)<\/code><\/td>\n\u0398(n)<\/code><\/td>\n\u0398(1)<\/code><\/td>\n\u0398(1)<\/code><\/td>\nO(n)<\/code><\/td>\nO(n)<\/code><\/td>\nO(1)<\/code><\/td>\nO(1)<\/code><\/td>\nO(n)<\/code><\/td>\n<\/tr>\n
Skip List<\/a><\/td>\n\u0398(log(n))<\/code><\/td>\n\u0398(log(n))<\/code><\/td>\n\u0398(log(n))<\/code><\/td>\n\u0398(log(n))<\/code><\/td>\nO(n)<\/code><\/td>\nO(n)<\/code><\/td>\nO(n)<\/code><\/td>\nO(n)<\/code><\/td>\nO(n log(n))<\/code><\/td>\n<\/tr>\n
Hash Table<\/a><\/td>\nN\/A<\/code><\/td>\n\u0398(1)<\/code><\/td>\n\u0398(1)<\/code><\/td>\n\u0398(1)<\/code><\/td>\nN\/A<\/code><\/td>\nO(n)<\/code><\/td>\nO(n)<\/code><\/td>\nO(n)<\/code><\/td>\nO(n)<\/code><\/td>\n<\/tr>\n
Binary Search Tree<\/a><\/td>\n\u0398(log(n))<\/code><\/td>\n\u0398(log(n))<\/code><\/td>\n\u0398(log(n))<\/code><\/td>\n\u0398(log(n))<\/code><\/td>\nO(n)<\/code><\/td>\nO(n)<\/code><\/td>\nO(n)<\/code><\/td>\nO(n)<\/code><\/td>\nO(n)<\/code><\/td>\n<\/tr>\n
Cartesian Tree<\/a><\/td>\nN\/A<\/code><\/td>\n\u0398(log(n))<\/code><\/td>\n\u0398(log(n))<\/code><\/td>\n\u0398(log(n))<\/code><\/td>\nN\/A<\/code><\/td>\nO(n)<\/code><\/td>\nO(n)<\/code><\/td>\nO(n)<\/code><\/td>\nO(n)<\/code><\/td>\n<\/tr>\n
B-Tree<\/a><\/td>\n\u0398(log(n))<\/code><\/td>\n\u0398(log(n))<\/code><\/td>\n\u0398(log(n))<\/code><\/td>\n\u0398(log(n))<\/code><\/td>\nO(log(n))<\/code><\/td>\nO(log(n))<\/code><\/td>\nO(log(n))<\/code><\/td>\nO(log(n))<\/code><\/td>\nO(n)<\/code><\/td>\n<\/tr>\n
Red-Black Tree<\/a><\/td>\n\u0398(log(n))<\/code><\/td>\n\u0398(log(n))<\/code><\/td>\n\u0398(log(n))<\/code><\/td>\n\u0398(log(n))<\/code><\/td>\nO(log(n))<\/code><\/td>\nO(log(n))<\/code><\/td>\nO(log(n))<\/code><\/td>\nO(log(n))<\/code><\/td>\nO(n)<\/code><\/td>\n<\/tr>\n
Splay Tree<\/a><\/td>\nN\/A<\/code><\/td>\n\u0398(log(n))<\/code><\/td>\n\u0398(log(n))<\/code><\/td>\n\u0398(log(n))<\/code><\/td>\nN\/A<\/code><\/td>\nO(log(n))<\/code><\/td>\nO(log(n))<\/code><\/td>\nO(log(n))<\/code><\/td>\nO(n)<\/code><\/td>\n<\/tr>\n
AVL Tree<\/a><\/td>\n\u0398(log(n))<\/code><\/td>\n\u0398(log(n))<\/code><\/td>\n\u0398(log(n))<\/code><\/td>\n\u0398(log(n))<\/code><\/td>\nO(log(n))<\/code><\/td>\nO(log(n))<\/code><\/td>\nO(log(n))<\/code><\/td>\nO(log(n))<\/code><\/td>\nO(n)<\/code><\/td>\n<\/tr>\n
KD Tree<\/a><\/td>\n\u0398(log(n))<\/code><\/td>\n\u0398(log(n))<\/code><\/td>\n\u0398(log(n))<\/code><\/td>\n\u0398(log(n))<\/code><\/td>\nO(n)<\/code><\/td>\nO(n)<\/code><\/td>\nO(n)<\/code><\/td>\nO(n)<\/code><\/td>\nO(n)<\/code><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Array Sorting Algorithms<\/h2>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Algorithm<\/th>\nTime Complexity<\/th>\nSpace Complexity<\/th>\n<\/tr>\n
<\/th>\nBest<\/th>\nAverage<\/th>\nWorst<\/th>\nWorst<\/th>\n<\/tr>\n
Quicksort<\/a><\/td>\n\u03a9(n log(n))<\/code><\/td>\n\u0398(n log(n))<\/code><\/td>\nO(n^2)<\/code><\/td>\nO(log(n))<\/code><\/td>\n<\/tr>\n
Mergesort<\/a><\/td>\n\u03a9(n log(n))<\/code><\/td>\n\u0398(n log(n))<\/code><\/td>\nO(n log(n))<\/code><\/td>\nO(n)<\/code><\/td>\n<\/tr>\n
Timsort<\/a><\/td>\n\u03a9(n)<\/code><\/td>\n\u0398(n log(n))<\/code><\/td>\nO(n log(n))<\/code><\/td>\nO(n)<\/code><\/td>\n<\/tr>\n
Heapsort<\/a><\/td>\n\u03a9(n log(n))<\/code><\/td>\n\u0398(n log(n))<\/code><\/td>\nO(n log(n))<\/code><\/td>\nO(1)<\/code><\/td>\n<\/tr>\n
Bubble Sort<\/a><\/td>\n\u03a9(n)<\/code><\/td>\n\u0398(n^2)<\/code><\/td>\nO(n^2)<\/code><\/td>\nO(1)<\/code><\/td>\n<\/tr>\n
Insertion Sort<\/a><\/td>\n\u03a9(n)<\/code><\/td>\n\u0398(n^2)<\/code><\/td>\nO(n^2)<\/code><\/td>\nO(1)<\/code><\/td>\n<\/tr>\n
Selection Sort<\/a><\/td>\n\u03a9(n^2)<\/code><\/td>\n\u0398(n^2)<\/code><\/td>\nO(n^2)<\/code><\/td>\nO(1)<\/code><\/td>\n<\/tr>\n
Tree Sort<\/a><\/td>\n\u03a9(n log(n))<\/code><\/td>\n\u0398(n log(n))<\/code><\/td>\nO(n^2)<\/code><\/td>\nO(n)<\/code><\/td>\n<\/tr>\n
Shell Sort<\/a><\/td>\n\u03a9(n log(n))<\/code><\/td>\n\u0398(n(log(n))^2)<\/code><\/td>\nO(n(log(n))^2)<\/code><\/td>\nO(1)<\/code><\/td>\n<\/tr>\n
Bucket Sort<\/a><\/td>\n\u03a9(n+k)<\/code><\/td>\n\u0398(n+k)<\/code><\/td>\nO(n^2)<\/code><\/td>\nO(n)<\/code><\/td>\n<\/tr>\n
Radix Sort<\/a><\/td>\n\u03a9(nk)<\/code><\/td>\n\u0398(nk)<\/code><\/td>\nO(nk)<\/code><\/td>\nO(n+k)<\/code><\/td>\n<\/tr>\n
Counting Sort<\/a><\/td>\n\u03a9(n+k)<\/code><\/td>\n\u0398(n+k)<\/code><\/td>\nO(n+k)<\/code><\/td>\nO(k)<\/code><\/td>\n<\/tr>\n
Cubesort<\/a><\/td>\n\u03a9(n)<\/code><\/td>\n\u0398(n log(n))<\/code><\/td>\nO(n log(n))<\/code><\/td>\nO(n)<\/code><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

Learn More<\/h2>\n