from typing import Iterable, List, Optional


class Heap:
    """A Max Heap Implementation

    >>> unsorted = [103, 9, 1, 7, 11, 15, 25, 201, 209, 107, 5]
    >>> h = Heap()
    >>> h.build_max_heap(unsorted)
    >>> print(h)
    [209, 201, 25, 103, 107, 15, 1, 9, 7, 11, 5]
    >>>
    >>> h.extract_max()
    209
    >>> print(h)
    [201, 107, 25, 103, 11, 15, 1, 9, 7, 5]
    >>>
    >>> h.insert(100)
    >>> print(h)
    [201, 107, 25, 103, 100, 15, 1, 9, 7, 5, 11]
    >>>
    >>> h.heap_sort()
    >>> print(h)
    [1, 5, 7, 9, 11, 15, 25, 100, 103, 107, 201]
    """

    def __init__(self) -> None:
        self.h: List[float] = []
        self.heap_size: int = 0

    def __repr__(self) -> str:
        return str(self.h)

    def parent_index(self, child_idx: int) -> Optional[int]:
        """ return the parent index of given child """
        if child_idx > 0:
            return (child_idx - 1) // 2
        return None

    def left_child_idx(self, parent_idx: int) -> Optional[int]:
        """
        return the left child index if the left child exists.
        if not, return None.
        """
        left_child_index = 2 * parent_idx + 1
        if left_child_index < self.heap_size:
            return left_child_index
        return None

    def right_child_idx(self, parent_idx: int) -> Optional[int]:
        """
        return the right child index if the right child exists.
        if not, return None.
        """
        right_child_index = 2 * parent_idx + 2
        if right_child_index < self.heap_size:
            return right_child_index
        return None

    def max_heapify(self, index: int) -> None:
        """
        correct a single violation of the heap property in a subtree's root.
        """
        if index < self.heap_size:
            violation: int = index
            left_child = self.left_child_idx(index)
            right_child = self.right_child_idx(index)
            # check which child is larger than its parent
            if left_child is not None and self.h[left_child] > self.h[violation]:
                violation = left_child
            if right_child is not None and self.h[right_child] > self.h[violation]:
                violation = right_child
            # if violation indeed exists
            if violation != index:
                # swap to fix the violation
                self.h[violation], self.h[index] = self.h[index], self.h[violation]
                # fix the subsequent violation recursively if any
                self.max_heapify(violation)

    def build_max_heap(self, collection: Iterable[float]) -> None:
        """ build max heap from an unsorted array"""
        self.h = list(collection)
        self.heap_size = len(self.h)
        if self.heap_size > 1:
            # max_heapify from right to left but exclude leaves (last level)
            for i in range(self.heap_size // 2 - 1, -1, -1):
                self.max_heapify(i)

    def max(self) -> float:
        """ return the max in the heap """
        if self.heap_size >= 1:
            return self.h[0]
        else:
            raise Exception("Empty heap")

    def extract_max(self) -> float:
        """ get and remove max from heap """
        if self.heap_size >= 2:
            me = self.h[0]
            self.h[0] = self.h.pop(-1)
            self.heap_size -= 1
            self.max_heapify(0)
            return me
        elif self.heap_size == 1:
            self.heap_size -= 1
            return self.h.pop(-1)
        else:
            raise Exception("Empty heap")

    def insert(self, value: float) -> None:
        """ insert a new value into the max heap """
        self.h.append(value)
        idx = (self.heap_size - 1) // 2
        self.heap_size += 1
        while idx >= 0:
            self.max_heapify(idx)
            idx = (idx - 1) // 2

    def heap_sort(self) -> None:
        size = self.heap_size
        for j in range(size - 1, 0, -1):
            self.h[0], self.h[j] = self.h[j], self.h[0]
            self.heap_size -= 1
            self.max_heapify(0)
        self.heap_size = size


if __name__ == "__main__":
    import doctest

    # run doc test
    doctest.testmod()

    # demo
    for unsorted in [
        [0],
        [2],
        [3, 5],
        [5, 3],
        [5, 5],
        [0, 0, 0, 0],
        [1, 1, 1, 1],
        [2, 2, 3, 5],
        [0, 2, 2, 3, 5],
        [2, 5, 3, 0, 2, 3, 0, 3],
        [6, 1, 2, 7, 9, 3, 4, 5, 10, 8],
        [103, 9, 1, 7, 11, 15, 25, 201, 209, 107, 5],
        [-45, -2, -5],
    ]:
        print(f"unsorted array: {unsorted}")

        heap = Heap()
        heap.build_max_heap(unsorted)
        print(f"after build heap: {heap}")

        print(f"max value: {heap.extract_max()}")
        print(f"after max value removed: {heap}")

        heap.insert(100)
        print(f"after new value 100 inserted: {heap}")

        heap.heap_sort()
        print(f"heap-sorted array: {heap}\n")