Struct orx_priority_queue::DaryHeapOfIndices

pub struct DaryHeapOfIndices<N, K, const D: usize = 2>
where
    N: HasIndex,
    K: PartialOrd + Clone,
{ /* private fields */ }

A d-ary heap which implements both PriorityQueue and PriorityQueueDecKey.

See PriorityQueueDecKey for additional functionalities.

DaryHeapOfIndices achieves the additional features by making use of a fixed size position array which allows to track the position of nodes on the heap.

It has the limitation that the nodes must implement HasIndex. This trait has a single simple method fn index(&self) -> usize which acts as a unique identifier of the actual underlying node which is coming from a closed set.

Consider for instance the usage of the heap as the priority queue of Dijkstra’s shortest path algorithm. The nodes are actual nodes of the graph which is a closed set and can be identified by node indices from zero to N-1, where N is the number of nodes. This heap fits very well such mathematical algorithms due to the following:

• using a fixed size array could be considered as a fast HashMap.
• we often reuse such heaps many times to solve many problems on the same network, compensating for the allocation of the positions array once.
• further, compared to a basic priority queue (or to std::collections::BinaryHeap), it reduces the space complexity of the Dijkstra’s algorithm from O(N^2) to O(N) by enabling the decrease_key operation.

However, for situations where

• the number of nodes entering the queue is very sparse compared to the size of the set of nodes, or
• it is not convenient to index the sets,

DaryHeapWithMap provides a more flexible approach.

Flexibility (DaryHeapWithMap) vs Performance (DaryHeapOfIndices)

DaryHeapWithMap (hence its variants such as BinaryHeapWithMap) does not require to know the absolute size of the closed set. Furthermore, the node type needs to implement Hash + Eq rather than HasIndex trait defined in this crate. Due to these, DaryHeapWithMap might be considered as the more flexible PriorityQueueDecKey variant.

On the other hand, DaryHeapOfIndices (hence its variants such as BinaryHeapOfIndices), provides significantly faster accesses to positions of nodes on the heap. This is important for PriorityQueueDecKey operations such as decrease_key or contains. Furthermore, in many algorithms such as certain network algorithms where nodes enter and exit the queue, index_bound can often trivially be set to number of nodes.

Examples

Heap as a PriorityQueue

Usage of d-ary heap as a basic priority queue.

use orx_priority_queue::*;

fn test_priority_queue<P>(mut pq: P)
where
    P: PriorityQueue<usize, f64>
{
    pq.clear();

    pq.push(0, 42.0);
    assert_eq!(Some(&0), pq.peek().map(|x| x.node()));
    assert_eq!(Some(&42.0), pq.peek().map(|x| x.key()));

    pq.push(1, 7.0);
    assert_eq!(Some(&1), pq.peek().map(|x| x.node()));
    assert_eq!(Some(&7.0), pq.peek().map(|x| x.key()));

    let popped = pq.pop();
    assert_eq!(Some((1, 7.0)), popped);

    let popped = pq.pop();
    assert_eq!(Some((0, 42.0)), popped);

    assert!(pq.is_empty());
}

// d-hap heap using id's to locate existing nodes (although decrease-key is not used here)
test_priority_queue(DaryHeapOfIndices::<_, _, 4>::with_index_bound(32));
// using type aliases to simplify signatures
test_priority_queue(BinaryHeapOfIndices::with_index_bound(16));
test_priority_queue(QuarternaryHeapOfIndices::with_index_bound(16));
test_priority_queue(QuarternaryHeapOfIndices::with_index_bound(16));

Heap as a PriorityQueueDecKey

Usage of a d-ary heap as a priority queue with decrease key operation and its variants.

use orx_priority_queue::*;

fn test_priority_queue_deckey<P>(mut pq: P)
where
    P: PriorityQueueDecKey<usize, f64>
{
    pq.clear();

    pq.push(0, 42.0);
    assert_eq!(Some(&0), pq.peek().map(|x| x.node()));
    assert_eq!(Some(&42.0), pq.peek().map(|x| x.key()));

    pq.push(1, 17.0);
    assert_eq!(Some(&1), pq.peek().map(|x| x.node()));
    assert_eq!(Some(&17.0), pq.peek().map(|x| x.key()));

    pq.decrease_key(&0, 7.0);
    assert_eq!(Some(&0), pq.peek().map(|x| x.node()));
    assert_eq!(Some(&7.0), pq.peek().map(|x| x.key()));

    let res_try_deckey = pq.try_decrease_key(&1, 20.0);
    assert_eq!(res_try_deckey, ResTryDecreaseKey::Unchanged);

    let popped = pq.pop();
    assert_eq!(Some((0, 7.0)), popped);

    let popped = pq.pop();
    assert_eq!(Some((1, 17.0)), popped);

    assert!(pq.is_empty());
}
// d-ary heap using id's to locate existing nodes
test_priority_queue_deckey(DaryHeapOfIndices::<_, _, 3>::with_index_bound(32));
// using type aliases to simplify signatures
test_priority_queue_deckey(BinaryHeapOfIndices::with_index_bound(16));
test_priority_queue_deckey(QuarternaryHeapOfIndices::with_index_bound(16));
test_priority_queue_deckey(QuarternaryHeapOfIndices::with_index_bound(16));

Implementations

impl<N, K, const D: usize> DaryHeapOfIndices<N, K, D>

where N: HasIndex, K: PartialOrd + Clone,

pub fn with_index_bound(index_bound: usize) -> Self

As explained in DaryHeapOfIndices, this heap is useful when the nodes come from a closed set with a known size. Therefore, the heap has a strict exclusive upper bound on the index of a node which can enter the heap, defined by the argument with_index_bound.

The closed set of indices which can enter the heap is [0, 1, …, index_bound).

The upper bound on the indices of a DaryHeapOfIndices can be obtained by the index_bound method.

Examples

use orx_priority_queue::*;

// set of possible nodes which can enter the heap is closed and has 16 elements
let mut pq = BinaryHeapOfIndices::with_index_bound(16);

assert_eq!(16, pq.index_bound());

// 8-th node enters the queue with key of 100.0
pq.push(7usize, 100.0);

// third node enters
pq.push(2, 42.0);

// the following line would've panicked since there exist no node with index 16 in the closed set [0, 1, ..., 15]
// pq.push(16, 7.0);

pub fn index_bound(&self) -> usize

Cardinality of the closed set which the nodes are sampled from.

Panics

Panics if a node with an index greater than or equal to the index_bound is pushed to the queue.

pub const fn d() -> usize

Returns the ‘d’ of the d-ary heap. In other words, it represents the maximum number of children that each node on the heap can have.

pub fn as_slice(&self) -> &[(N, K)]

Returns the nodes and keys currently in the queue as a slice; not necessarily sorted.

Examples

use orx_priority_queue::*;

let mut queue = QuarternaryHeapWithMap::default();
queue.push("x", 42);
queue.push("y", 7);
queue.push("z", 99);

let slice = queue.as_slice();

assert_eq!(3, slice.len());
assert!(slice.contains(&("x", 42)));
assert!(slice.contains(&("y", 7)));
assert!(slice.contains(&("z", 99)));

Trait Implementations

impl<N, K, const D: usize> Clone for DaryHeapOfIndices<N, K, D>

where N: HasIndex + Clone, K: PartialOrd + Clone + Clone,

fn clone(&self) -> DaryHeapOfIndices<N, K, D>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<N, K, const D: usize> Debug for DaryHeapOfIndices<N, K, D>

where N: HasIndex + Debug, K: PartialOrd + Clone + Debug,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<N, K, const D: usize> PriorityQueue<N, K> for DaryHeapOfIndices<N, K, D>

where N: HasIndex, K: PartialOrd + Clone,

type NodeKey<'a> = &'a (N, K) where Self: 'a, N: 'a, K: 'a

Item providing references to node & key pairs which are yielded by the iterator.

type Iter<'a> = Iter<'a, (N, K)> where Self: 'a, N: 'a, K: 'a

An iterator over the (node, key) pairs on the priority queue in an arbitrary order.

fn len(&self) -> usize

Number of elements in the queue.

fn capacity(&self) -> usize

Capacity of the heap.

fn peek(&self) -> Option<&(N, K)>

Returns, without popping, a reference to the foremost element of the queue; returns None if the queue is empty.

fn clear(&mut self)

Clears the queue.

fn pop(&mut self) -> Option<(N, K)>

Removes and returns the (node, key) pair with the lowest key in the queue; returns None if the queue is empty.

fn pop_node(&mut self) -> Option<N>

Removes and returns the node with the lowest key in the queue; returns None if the queue is empty.

fn pop_key(&mut self) -> Option<K>

Removes and returns the key of the node with the lowest key in the queue; returns None if the queue is empty.

fn push(&mut self, node: N, key: K)

Pushes the given (node, key) pair to the queue.

fn push_then_pop(&mut self, node: N, key: K) -> (N, K)

Performs the push with given (node, key) followed by the pop operation.

fn iter(&self) -> Self::Iter<'_>

Returns an iterator visiting all values on the heap in arbitrary order.

fn is_empty(&self) -> bool

Returns whether he queue is empty or not.

impl<N, K, const D: usize> PriorityQueueDecKey<N, K> for DaryHeapOfIndices<N, K, D>

where N: HasIndex, K: PartialOrd + Clone,

fn contains(&self, node: &N) -> bool

Returns whether the given node is in the queue or not.

fn key_of(&self, node: &N) -> Option<K>

Returns the key of the given node if it is in the queue; returns None otherwise.

fn decrease_key(&mut self, node: &N, decreased_key: K)

Decreases key of the node which is already in the queue to the given decreased_key.

fn update_key(&mut self, node: &N, new_key: K) -> ResUpdateKey

Updates key of the node which is already in the queue as the given new_key; and returns the result of the operation:

fn remove(&mut self, node: &N) -> K

Removes the node from the queue; and returns its current key.

fn try_decrease_key(&mut self, node: &N, new_key: K) -> ResTryDecreaseKey

Tries to decrease the key of the node which is already in the queue if its prior key is strictly larger than the new_key; otherwise, it does nothing leaving the queue unchanged.

fn decrease_key_or_push(&mut self, node: &N, key: K) -> ResDecreaseKeyOrPush

If the node is present in the queue:

fn update_key_or_push(&mut self, node: &N, key: K) -> ResUpdateKeyOrPush

If the node is present in the queue:

fn try_decrease_key_or_push( &mut self, node: &N, key: K ) -> ResTryDecreaseKeyOrPush

If the node is present in the queue, tries to decrease its key to the given key: