# 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:

                        10
                       /  \
                    58      70
                   /  \    /  \
                 80   92  97   99

> 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:

```rust
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`:

```rust
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:

```rust
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:

| method    | Time Complexity |
|-----------|-----------------|
| [`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

```rust
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");
```
# Merging and Combining 

You can merge another priority queue to this one. Right hand side priority
queue will be drained into the left hand side priority queue.

# Examples

```rust
use priq::PriorityQueue;

let mut pq1 = PriorityQueue::from([(5, 55), (6, 66), (3, 33), (2, 22)]);
let mut pq2 = PriorityQueue::from([(4, 44), (1, 11)]);

pq1.merge(&mut pq2);
// at this point `pq2` is empty

assert_eq!(6, pq1.len());
assert_eq!(11, pq1.peek().unwrap().1);
```

You can also use `+` operator to combine two priority queues. Operands will
be intact. New priority queue will be build from cloning and merging them.

# Example

```rust
use priq::PriorityQueue;

let pq1 = PriorityQueue::from([(5, 55), (1, 11), (4, 44), (2, 22)]);
let pq2 = PriorityQueue::from([(8, 44), (1, 22)]);

let res = pq1 + pq2;

assert_eq!(6, res.len());
assert_eq!(11, res.peek().unwrap().1);
```

## Performance

This are the benchmark results for `priq::PriorityQueue`:


| `priq` benches | median | nanosecs | std.dev |
|-----|-------:|:----------:|:--------|
| 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`:

| `BinaryHeap` benches | median | nanosecs | std.dev |
|-----|-------:|:----------:|:--------|
| 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)


------------
Project is distributed under the MIT license. Please see the `LICENSE` for more information.