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/// A priority queue which allows pushing ([N], [K])=(node, key) pairs to the collection,
/// and popping the foremost element having the lowest key.
pub trait PriorityQueue<N, K>
where
    K: PartialOrd,
{
    /// Number of elements in the queue.
    fn len(&self) -> usize;

    /// Returns whether he queue is empty or not.
    fn is_empty(&self) -> bool {
        self.len() == 0
    }
    /// Returns, without popping, a reference to the foremost element of the queue;
    /// returns None if the queue is empty.
    fn peek(&self) -> Option<&(N, K)>;

    /// Clears the queue.
    fn clear(&mut self);

    /// Removes and returns the (node, key) pair with the lowest key in the queue;
    /// returns None if the queue is empty.
    fn pop(&mut self) -> Option<(N, K)>;
    /// Removes and returns the node 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 key of the node with the lowest key in the queue;
    /// returns None if the queue is empty.
    fn pop_key(&mut self) -> Option<K>;

    /// Pushes the given ([node], [key]) pair to the queue.
    fn push(&mut self, node: N, key: K);
}