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