"""Priority queue class with updatable priorities.
"""

import heapq

__all__ = ["MappedQueue"]


class _HeapElement:
    """This proxy class separates the heap element from its priority.

    The idea is that using a 2-tuple (priority, element) works
    for sorting, but not for dict lookup because priorities are
    often floating point values so round-off can mess up equality.

    So, we need inequalities to look at the priority (for sorting)
    and equality (and hash) to look at the element to enable
    updates to the priority.

    Unfortunately, this class can be tricky to work with if you forget that
    `__lt__` compares the priority while `__eq__` compares the element.
    In `greedy_modularity_communities()` the following code is
    used to check that two _HeapElements differ in either element or priority:

        if d_oldmax != row_max or d_oldmax.priority != row_max.priority:

    If the priorities are the same, this implementation uses the element
    as a tiebreaker. This provides compatibility with older systems that
    use tuples to combine priority and elements.
    """

    __slots__ = ["priority", "element", "_hash"]

    def __init__(self, priority, element):
        self.priority = priority
        self.element = element
        self._hash = hash(element)

    def __lt__(self, other):
        try:
            other_priority = other.priority
        except AttributeError:
            return self.priority < other
        # assume comparing to another _HeapElement
        if self.priority == other_priority:
            return self.element < other.element
        return self.priority < other_priority

    def __gt__(self, other):
        try:
            other_priority = other.priority
        except AttributeError:
            return self.priority > other
        # assume comparing to another _HeapElement
        if self.priority == other_priority:
            return self.element < other.element
        return self.priority > other_priority

    def __eq__(self, other):
        try:
            return self.element == other.element
        except AttributeError:
            return self.element == other

    def __hash__(self):
        return self._hash

    def __getitem__(self, indx):
        return self.priority if indx == 0 else self.element[indx - 1]

    def __iter__(self):
        yield self.priority
        try:
            yield from self.element
        except TypeError:
            yield self.element

    def __repr__(self):
        return f"_HeapElement({self.priority}, {self.element})"


class MappedQueue:
    """The MappedQueue class implements a min-heap with removal and update-priority.

    The min heap uses heapq as well as custom written _siftup and _siftdown
    methods to allow the heap positions to be tracked by an additional dict
    keyed by element to position. The smallest element can be popped in O(1) time,
    new elements can be pushed in O(log n) time, and any element can be removed
    or updated in O(log n) time. The queue cannot contain duplicate elements
    and an attempt to push an element already in the queue will have no effect.

    MappedQueue complements the heapq package from the python standard
    library. While MappedQueue is designed for maximum compatibility with
    heapq, it adds element removal, lookup, and priority update.

    Examples
    --------

    A `MappedQueue` can be created empty or optionally given an array of
    initial elements. Calling `push()` will add an element and calling `pop()`
    will remove and return the smallest element.

    >>> q = MappedQueue([916, 50, 4609, 493, 237])
    >>> q.push(1310)
    True
    >>> [q.pop() for i in range(len(q.heap))]
    [50, 237, 493, 916, 1310, 4609]

    Elements can also be updated or removed from anywhere in the queue.

    >>> q = MappedQueue([916, 50, 4609, 493, 237])
    >>> q.remove(493)
    >>> q.update(237, 1117)
    >>> [q.pop() for i in range(len(q.heap))]
    [50, 916, 1117, 4609]

    References
    ----------
    .. [1] Cormen, T. H., Leiserson, C. E., Rivest, R. L., & Stein, C. (2001).
       Introduction to algorithms second edition.
    .. [2] Knuth, D. E. (1997). The art of computer programming (Vol. 3).
       Pearson Education.
    """

    def __init__(self, data=[]):
        """Priority queue class with updatable priorities."""
        if isinstance(data, dict):
            self.heap = [_HeapElement(v, k) for k, v in data.items()]
        else:
            self.heap = list(data)
        self.position = dict()
        self._heapify()

    def _heapify(self):
        """Restore heap invariant and recalculate map."""
        heapq.heapify(self.heap)
        self.position = {elt: pos for pos, elt in enumerate(self.heap)}
        if len(self.heap) != len(self.position):
            raise AssertionError("Heap contains duplicate elements")

    def __len__(self):
        return len(self.heap)

    def push(self, elt, priority=None):
        """Add an element to the queue."""
        if priority is not None:
            elt = _HeapElement(priority, elt)
        # If element is already in queue, do nothing
        if elt in self.position:
            return False
        # Add element to heap and dict
        pos = len(self.heap)
        self.heap.append(elt)
        self.position[elt] = pos
        # Restore invariant by sifting down
        self._siftdown(0, pos)
        return True

    def pop(self):
        """Remove and return the smallest element in the queue."""
        # Remove smallest element
        elt = self.heap[0]
        del self.position[elt]
        # If elt is last item, remove and return
        if len(self.heap) == 1:
            self.heap.pop()
            return elt
        # Replace root with last element
        last = self.heap.pop()
        self.heap[0] = last
        self.position[last] = 0
        # Restore invariant by sifting up
        self._siftup(0)
        # Return smallest element
        return elt

    def update(self, elt, new, priority=None):
        """Replace an element in the queue with a new one."""
        if priority is not None:
            new = _HeapElement(priority, new)
        # Replace
        pos = self.position[elt]
        self.heap[pos] = new
        del self.position[elt]
        self.position[new] = pos
        # Restore invariant by sifting up
        self._siftup(pos)

    def remove(self, elt):
        """Remove an element from the queue."""
        # Find and remove element
        try:
            pos = self.position[elt]
            del self.position[elt]
        except KeyError:
            # Not in queue
            raise
        # If elt is last item, remove and return
        if pos == len(self.heap) - 1:
            self.heap.pop()
            return
        # Replace elt with last element
        last = self.heap.pop()
        self.heap[pos] = last
        self.position[last] = pos
        # Restore invariant by sifting up
        self._siftup(pos)

    def _siftup(self, pos):
        """Move smaller child up until hitting a leaf.

        Built to mimic code for heapq._siftup
        only updating position dict too.
        """
        heap, position = self.heap, self.position
        end_pos = len(heap)
        startpos = pos
        newitem = heap[pos]
        # Shift up the smaller child until hitting a leaf
        child_pos = (pos << 1) + 1  # start with leftmost child position
        while child_pos < end_pos:
            # Set child_pos to index of smaller child.
            child = heap[child_pos]
            right_pos = child_pos + 1
            if right_pos < end_pos:
                right = heap[right_pos]
                if not child < right:
                    child = right
                    child_pos = right_pos
            # Move the smaller child up.
            heap[pos] = child
            position[child] = pos
            pos = child_pos
            child_pos = (pos << 1) + 1
        # pos is a leaf position. Put newitem there, and bubble it up
        # to its final resting place (by sifting its parents down).
        while pos > 0:
            parent_pos = (pos - 1) >> 1
            parent = heap[parent_pos]
            if not newitem < parent:
                break
            heap[pos] = parent
            position[parent] = pos
            pos = parent_pos
        heap[pos] = newitem
        position[newitem] = pos

    def _siftdown(self, start_pos, pos):
        """Restore invariant. keep swapping with parent until smaller.

        Built to mimic code for heapq._siftdown
        only updating position dict too.
        """
        heap, position = self.heap, self.position
        newitem = heap[pos]
        # Follow the path to the root, moving parents down until finding a place
        # newitem fits.
        while pos > start_pos:
            parent_pos = (pos - 1) >> 1
            parent = heap[parent_pos]
            if not newitem < parent:
                break
            heap[pos] = parent
            position[parent] = pos
            pos = parent_pos
        heap[pos] = newitem
        position[newitem] = pos
