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 The node at the "top" of the heap with no parents is
called the root node. 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 ## References
- [Wikipedia](https://en.wikipedia.org/wiki/Heap_(data_structure)) - [Wikipedia](https://en.wikipedia.org/wiki/Heap_(data_structure))