# priq
Priority queue (min/max heap) using raw binary heap.
`PriorityQueue` is built using raw array for efficient performance.
There are two major reasons what makes this `PriorityQueue` different from
other binary heap implementations currently available:
1 - Allows data ordering to scores with `PartialOrd`.
- Every other min-max heap requires [total ordering](https://bit.ly/3GCWvYL)
of scores (e.g. should implement `Ord` trait). This can be an issue,
for example, when you want to order items based on a float scores,
which doesn't implement `Ord` trait.
- Because of partial ordering, non-comparable values are thrown in
the end of the queue. One will see non-comparable values only after all
the comparable elements have been `pop`-ed.
- You can read about Rust's implementation or `Ord`, `PartialOrd` and
what's the different [here](https://bit.ly/3J7NwQI)
2 - Separation of score and item you wish to store.
- This frees enforcement for associated items to implement any ordering.
- Makes easier to evaluate items' order.
3 - Equal scoring items are stored at first available free space.
- This gives performance boost for large number of entries.
4 - Easy to use!
You can read more about this crate on [my blog](https://www.bexxmodd.com)
## Implementation
A Min-Max Heap with designated arguments for `score` and associated `item`!
A `Default` implementation is a Min-Heap where the top node (root) is the
lowest scoring element:
<center><p>10<p></center>
<center><p>/  \</p></center>
<center><p>58  70</p></center>
<center><p>/ \  / \</p></center>
<center><p>80  92 97  99</p></center>
> The value of Parent Node is small than Child Node.
Every parent node, including the top (root) node, is less than or equal to
equal to the right child.
`PriorityQueue ` allows duplicate score/item values. When you [`put`]the
item with a similar score that’s already in the queue new entry will be
stored at the first empty location in memory. This gives an incremental
performance boost (instead of resolving by using the associated item as a
secondary tool to priority evaluation). Also, this form of implementation
doesn’t enforce for the element `T` to have any implemented ordering. This
guarantees that the top node will always be of minimum value.
You can initialize an empty `PriorityQueue` and later add items:
```
use priq::PriorityQueue;
// create queue with `usize` key and `String` elements
let pq: PriorityQueue<usize, String> = PriorityQueue::new();
```
Or you can _heapify_ a `Vec` and/or a `slice`:
```
use priq::PriorityQueue;
let pq_from_vec = PriorityQueue::from(vec![(5, 55), (1, 11), (4, 44)]);
let pq_from_slice = PriorityQueue::from([(5, 55), (1, 11), (4, 44)]);
```
# Partial Ordering
Because `priq` allows `score` arguments that only implement `PartialOrd`,
elements that can't be compared are evaluated and are put in the back of
the queue:
```
use priq::PriorityQueue;
let mut pq: PriorityQueue<f32, isize> = PriorityQueue::new();
pq.put(1.1, 10);
pq.put(f32::NAN, -1);
pq.put(2.2, 20);
pq.put(3.3, 30);
pq.put(f32::NAN, -3);
pq.put(4.4, 40);
(1..=4).for_each(|i| assert_eq!(i * 10, pq.pop().unwrap().1));
// NAN scores will not have deterministic order
// they are just stored after all the comparable scores
assert!(0 > pq.pop().unwrap().1);
assert!(0 > pq.pop().unwrap().1);
```
# Time
The standard usage of this data structure is to [`put`] an element to the
queue and [`pop`] to remove the top element and peek to check what’s the
top element in the queue. The stored structure of the elements is a balanced
tree realized using an array with a contiguous memory location. This allows
maintaining a proper parent-child relationship between put-ed items.
[`put`]: PriorityQueue::put
[`peek`]: PriorityQueue::peek
[`pop`]: PriorityQueue::pop
Runtime complexity with Big-O Notation:
| [`put`] | _O(log(n))_ |
| [`pop`] | _O(log(n))_ |
| [`peek`] | _O(1)_ |
You can also iterate over elements using for loop but the returned slice
will not be properly order as the heap is re-balanced after each insertion
and deletion. If you want to grab items in a proper priority call [`pop`]
in a loop until it returns `None`.
# Custom `struct`
What if you want to custom `struct ` without having a separate and
specific score? You can pass the `struct`’s clone as a `score` and as an
associated value, but if in this kind of scenario I’d recommend using
[`BinaryHeap`] as it better fits the purpose.
# Min-Heap
If instead of Min-Heap you want to have Max-Heap, where the highest-scoring
element is on top you can pass score using [`Reverse`] or a custom [`Ord`]
implementation can be used to have custom prioritization logic.
[`BinaryHeap`]: std::collections::BinaryHeap
[`Reverse`]: std::cmp::Reverse
# Example
```
use priq::PriorityQueue;
use std::cmp::Reverse;
let mut pq: PriorityQueue<Reverse<u8>, String> = PriorityQueue::new();
pq.put(Reverse(26), "Z".to_string());
pq.put(Reverse(1), "A".to_string());
assert_eq!(pq.pop().unwrap().1, "Z");
```
## Performance
This are the benchmark results for `priq::PriorityQueue`:
| pq_pop_100 | 146 | ns/iter | (+/- 1)
| pq_pop_100k | 291,818 | ns/iter | (+/- 5,686)
| pq_pop_10k | 14,129 | ns/iter | (+/- 39)
| pq_pop_1k | 1,646 | ns/iter | (+/- 32)
| pq_pop_1mil | 16,517,047 | ns/iter | (+/- 569,128|
| pq_put_100 | 488 | ns/iter | (+/- 21)
| pq_put_100k | 758,422 | ns/iter | (+/- 13,961)
| pq_put_100k_wcap| 748,824 | ns/iter | (+/- 7,926)
| pq_put_10k | 80,668 | ns/iter | (+/- 1,324)
| pq_put_1k | 8,769 | ns/iter | (+/- 78)
| pq_put_1mil | 6,728,203 | ns/iter | (+/- 76,416)
| pq_put_1mil_wcap| 6,622,341 | ns/iter | (+/- 77,162)
How it compares to `std::collections::BinaryHeap`:
| bh_pop_100 | 272 | ns/iter | (+/- 90)
| bh_pop_100k | 171,071 | ns/iter | (+/- 6,131)
| bh_pop_10k | 13,904 | ns/iter | (+/- 130)
| bh_pop_1k | 1,847 | ns/iter | (+/- 6)
| bh_pop_1mil | 8,772,066 | ns/iter | (+/- 611,613)
| bh_push_100 | 857 | ns/iter | (+/- 50)
| bh_push_100k| 943,465 | ns/iter | (+/- 108,698)
| bh_push_10k | 92,807 | ns/iter | (+/- 7,930)
| bh_push_1k | 8,606 | ns/iter | (+/- 639)
| bh_push_1mil| 12,946,815 | ns/iter | (+/- 900,347)