algorithm and data structure
| Complexity | Example |
|---|---|
| O(1) | Fetching the first element from a set of data |
| O(lg n) | Splitting a set of data in half, then splitting the halves in half, etc. |
| O(n) | Traversing a set of data |
| O(n lg n) | Splitting a set of data in half repeatedly and traversing each half |
| O(n²) | Traversing a set of data once for each member of another set of equal size |
| O(2^n) | Generating all possible subsets of a set of data |
| O(n!) | Generating all possible permutations of a set of data |
Sample :
| n = 1 | n = 16 | n = 256 | n = 4K | n = 64K | n = 1M | |
|---|---|---|---|---|---|---|
| O(1) | 1.000E+00 | 1.000E+00 | 1.000E+00 | 1.000E+00 | 1.000E+00 | 1.000E+00 |
| O(lg n) | 0.000E+00 | 4.000E+00 | 8.000E+00 | 1.200E+01 | 1.600E+01 | 2.000E+01 |
| O(n) | 1.000E+00 | 1.600E+01 | 2.560E+02 | 4.096E+03 | 6.554E+04 | 1.049E+06 |
| O(n lg n) | 0.000E+00 | 6.400E+01 | 2.048E+03 | 4.915E+04 | 1.049E+06 | 2.097E+07 |
| O(n²) | 1.000E+00 | 2.560E+02 | 6.554E+04 | 1.678E+07 | 4.295E+09 | 1.100E+12 |
| O(2^n) | 2.000E+00 | 6.554E+04 | 1.158E+77 | — | — | — |
| O(n!) | 1.000E+00 | 2.092E+13 | — | — | — | — |
| Internal Implement- ation | Add/insert | Add beyond capacity | Queue/Push | Dequeue/Pop/Peek | Remove/ RemoveAt | Item[index]/ElementAt(index) | GetEnumerator | Contains(value)/IndexOf/ContainsValue/Find | |
|---|---|---|---|---|---|---|---|---|---|
| List | Array | O(1) to add, O(n) to insert | O(n) | - | - | O(n) | O(1) | O(1) | O(n) |
| LinkedList | Doubly linked list | O(1), before/after given node | O(1) | O(1) | O(1) | O(1), before/after given node | O(n) | O(1) | O(n) |
| Stack | Array | O(1) | O(n) | O(1) | O(1) | - | - | O(1) | O(n) |
| Queue | Array | O(1) | O(n) | O(1) | O(1) | - | - | O(1) | O(n) |
| Dictionary | Hashtable with links to another array index for collision | O(1), O(n) if collision | O(n) | - | - | O(1), O(n) if collision | O(1), O(n) if collision | O(1) | O(n) |
| HashSet | Hashtable with links to another array index for collision | O(1), O(n) if collision | O(n) | - | - | O(1), O(n) if collision | O(1), O(n) if collision | O(1) | - |
| SortedDictionary | Red-black tree | O(log n) | O(log n) | - | - | O(log n) | O(log n) | O(log n) | O(n) |
| SortedList | Array | O(n), O(log n) if added to end of list | O(n) | - | - | O(n) | O(log n) | O(1) | O(n) |
| SortedSet | Red-black tree | O(log n) | O(log n) | - | - | O(log n) | O(log n) | O(log n) | - |
- Union Find : ◻️
- Deque ◻️
- RandomizedQueue ◻️
- GraphTraversal
