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#!/usr/bin/env python3

from __future__ import annotations

import random

from collections.abc import Iterable

from typing import Any, TypeVar

T = TypeVar("T", bound=bool)

class RandomizedHeapNode[T: bool]:

"""

One node of the randomized heap. Contains the value and references to

two children.

"""

def __init__(self, value: T) -> None:

self._value: T = value

self.left: RandomizedHeapNode[T] | None = None

self.right: RandomizedHeapNode[T] | None = None

@property

def value(self) -> T:

"""

Return the value of the node.

>>> rhn = RandomizedHeapNode(10)

>>> rhn.value

>>> rhn = RandomizedHeapNode(-10)

>>> rhn.value

-10

"""

return self._value

@staticmethod

def merge(

root1: RandomizedHeapNode[T] | None, root2: RandomizedHeapNode[T] | None

) -> RandomizedHeapNode[T] | None:

"""

Merge 2 nodes together.

>>> rhn1 = RandomizedHeapNode(10)

>>> rhn2 = RandomizedHeapNode(20)

>>> RandomizedHeapNode.merge(rhn1, rhn2).value

>>> rhn1 = RandomizedHeapNode(20)

>>> rhn2 = RandomizedHeapNode(10)

>>> RandomizedHeapNode.merge(rhn1, rhn2).value

>>> rhn1 = RandomizedHeapNode(5)

>>> rhn2 = RandomizedHeapNode(0)

>>> RandomizedHeapNode.merge(rhn1, rhn2).value

"""

if not root1:

return root2

if not root2:

return root1

if root1.value > root2.value:

root1, root2 = root2, root1

if random.choice([True, False]):

root1.left, root1.right = root1.right, root1.left

root1.left = RandomizedHeapNode.merge(root1.left, root2)

return root1

class RandomizedHeap[T: bool]:

"""

A data structure that allows inserting a new value and to pop the smallest

values. Both operations take O(logN) time where N is the size of the

structure.

Wiki: https://en.wikipedia.org/wiki/Randomized_meldable_heap

>>> RandomizedHeap([2, 3, 1, 5, 1, 7]).to_sorted_list()

[1, 1, 2, 3, 5, 7]

>>> rh = RandomizedHeap()

>>> rh.pop()

Traceback (most recent call last):

...

IndexError: Can't get top element for the empty heap.

>>> rh.insert(1)

>>> rh.insert(-1)

>>> rh.insert(0)

>>> rh.to_sorted_list()

[-1, 0, 1]

"""

def __init__(self, data: Iterable[T] | None = ()) -> None:

"""

>>> rh = RandomizedHeap([3, 1, 3, 7])

>>> rh.to_sorted_list()

[1, 3, 3, 7]

"""

self._root: RandomizedHeapNode[T] | None = None

if data:

for item in data:

self.insert(item)

def insert(self, value: T) -> None:

"""

Insert the value into the heap.

>>> rh = RandomizedHeap()

>>> rh.insert(3)

>>> rh.insert(1)

>>> rh.insert(3)

>>> rh.insert(7)

>>> rh.to_sorted_list()

[1, 3, 3, 7]

"""

self._root = RandomizedHeapNode.merge(self._root, RandomizedHeapNode(value))

def pop(self) -> T | None:

"""

Pop the smallest value from the heap and return it.

>>> rh = RandomizedHeap([3, 1, 3, 7])

>>> rh.pop()

Traceback (most recent call last):

...

IndexError: Can't get top element for the empty heap.

"""

result = self.top()

if self._root is None:

return None

self._root = RandomizedHeapNode.merge(self._root.left, self._root.right)

return result

def top(self) -> T:

"""

Return the smallest value from the heap.

>>> rh = RandomizedHeap()

>>> rh.insert(3)

>>> rh.top()

>>> rh.insert(1)

>>> rh.top()

>>> rh.insert(3)

>>> rh.top()

>>> rh.insert(7)

>>> rh.top()

"""

if not self._root:

raise IndexError("Can't get top element for the empty heap.")

return self._root.value

def clear(self) -> None:

"""

Clear the heap.

>>> rh = RandomizedHeap([3, 1, 3, 7])

>>> rh.clear()

>>> rh.pop()

Traceback (most recent call last):

...

IndexError: Can't get top element for the empty heap.

"""

self._root = None

def to_sorted_list(self) -> list[Any]:

"""

Returns sorted list containing all the values in the heap.

>>> rh = RandomizedHeap([3, 1, 3, 7])

>>> rh.to_sorted_list()

[1, 3, 3, 7]

"""

result = []

while self:

result.append(self.pop())

return result

def __bool__(self) -> bool:

"""

Check if the heap is not empty.

>>> rh = RandomizedHeap()

>>> bool(rh)

False

>>> rh.insert(1)

>>> bool(rh)

True

>>> rh.clear()

>>> bool(rh)

False

"""

return self._root is not None

if __name__ == "__main__":

import doctest

doctest.testmod()

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