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Oleksii Trekhleb 2018-06-22 15:15:54 +03:00
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@ -216,27 +216,27 @@ Below is the list of some of the most used Big O notations and their performance
### Data Structure Operations Complexity
| Data Structure | Access | Search | Insertion | Deletion | Comments |
| ----------------------- | :---------: | :---------: | :---------: | :---------: | :-------- |
| **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` | In case of perfect hash function costs would be `O(1)` |
| **Binary Search Tree** | `n` | `n` | `n` | `n` | In case of balanced tree costs would be `O(log(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** | 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 | In case of perfect hash function costs would be O(1) |
| **Binary Search Tree** | n | n | n | n | In case of balanced tree costs would be O(log(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 | Comments |
| --------------------- | :---------: | :---------: | :-------------: | :---------: | :-------: | :-------- |
| **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`<sup>`2`</sup> | `log(n)` | No | |
| **Shell sort** | `n log(n)` | depends on gap sequence | `n (log(n))`<sup>`2`</sup> | `1` | No | |
| **Counting sort** | `n + r` | `n + r` | `n + r` | `n + r` | Yes | `r` - biggest number in array |
| **Radix sort** | `n * k` | `n * k` | `n * k` | `n + k` | Yes | `k` - length of longest key |
| --------------------- | :-------: | :-------: | :-----------: | :-------: | :-------: | :-------- |
| **Bubble sort** | n | n<sup>2</sup> | n<sup>2</sup> | 1 | Yes | |
| **Insertion sort** | n | n<sup>2</sup> | n<sup>2</sup> | 1 | Yes | |
| **Selection sort** | n<sup>2</sup> | n<sup>2</sup> | n<sup>2</sup> | 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<sup>2</sup> | log(n) | No | |
| **Shell sort** | n log(n) | depends on gap sequence | n (log(n))<sup>2</sup> | 1 | No | |
| **Counting sort** | n + r | n + r | n + r | n + r | Yes | r - biggest number in array |
| **Radix sort** | n * k | n * k | n * k | n + k | Yes | k - length of longest key |