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Adding Heap time complexities

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Oleksii Trekhleb 2023-02-01 08:11:25 +01:00 committed by GitHub
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@ -33,6 +33,31 @@ to the key of `C`
The node at the "top" of the heap with no parents is
called the root node.
## Time Complexities
Here are time complexities of various heap data structures. Function names assume a max-heap.
| Operation | find-max | delete-max | insert| increase-key| meld |
| --------- | -------- | ---------- | ----- | ----------- | ---- |
| [Binary](https://en.wikipedia.org/wiki/Binary_heap) | `Θ(1)` | `Θ(log n)` | `O(log n)` | `O(log n)` | `Θ(n)` |
| [Leftist](https://en.wikipedia.org/wiki/Leftist_tree) | `Θ(1)` | `Θ(log n)` | `Θ(log n)` | `O(log n)` | `Θ(log n)` |
| [Binomial](https://en.wikipedia.org/wiki/Binomial_heap) | `Θ(1)` | `Θ(log n)` | `Θ(1)` | `O(log n)` | `O(log n)` |
| [Fibonacci](https://en.wikipedia.org/wiki/Fibonacci_heap) | `Θ(1)` | `Θ(log n)` | `Θ(1)` | `Θ(1)` | `Θ(1)` |
| [Pairing](https://en.wikipedia.org/wiki/Pairing_heap) | `Θ(1)` | `Θ(log n)` | `Θ(1)` | `o(log n)` | `Θ(1)` |
| [Brodal](https://en.wikipedia.org/wiki/Brodal_queue) | `Θ(1)` | `Θ(log n)` | `Θ(1)` | `Θ(1)` | `Θ(1)` |
| [Rank-pairing](https://en.wikipedia.org/w/index.php?title=Rank-pairing_heap&action=edit&redlink=1) | `Θ(1)` | `Θ(log n)` | `Θ(1)` | `Θ(1)` | `Θ(1)` |
| [Strict Fibonacci](https://en.wikipedia.org/wiki/Fibonacci_heap) | `Θ(1)` | `Θ(log n)` | `Θ(1)` | `Θ(1)` | `Θ(1)` |
| [2-3 heap](https://en.wikipedia.org/wiki/2%E2%80%933_heap) | `O(log n)` | `O(log n)` | `O(log n)` | `Θ(1)` | `?` |
Where:
- **find-max (or find-min):** find a maximum item of a max-heap, or a minimum item of a min-heap, respectively (a.k.a. *peek*)
- **delete-max (or delete-min):** removing the root node of a max heap (or min heap), respectively
- **insert:** adding a new key to the heap (a.k.a., *push*)
- **increase-key or decrease-key:** updating a key within a max- or min-heap, respectively
- **meld:** joining two heaps to form a valid new heap containing all the elements of both, destroying the original heaps.
> In this repository, the [MaxHeap.js](./MaxHeap.js) and [MinHeap.js](./MinHeap.js) are examples of the **Binary** heap.
## References
- [Wikipedia](https://en.wikipedia.org/wiki/Heap_(data_structure))