Python/data_structures/heap/randomized_heap.py

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#!/usr/bin/env python3
from __future__ import annotations
import random
from typing import Any, Generic, Iterable, TypeVar
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T = TypeVar("T", bound=bool)
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class RandomizedHeapNode(Generic[T]):
"""
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
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@property
def value(self) -> T:
"""Return the value of the node."""
return self._value
@staticmethod
def merge(
root1: RandomizedHeapNode[T] | None, root2: RandomizedHeapNode[T] | None
) -> RandomizedHeapNode[T] | None:
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"""Merge 2 nodes together."""
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(Generic[T]):
"""
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:
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"""
>>> 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)
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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:
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"""
Pop the smallest value from the heap and return it.
>>> rh = RandomizedHeap([3, 1, 3, 7])
>>> rh.pop()
1
>>> rh.pop()
3
>>> rh.pop()
3
>>> rh.pop()
7
>>> rh.pop()
Traceback (most recent call last):
...
IndexError: Can't get top element for the empty heap.
"""
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result = self.top()
if self._root is None:
return None
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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()
3
>>> rh.insert(1)
>>> rh.top()
1
>>> rh.insert(3)
>>> rh.top()
1
>>> rh.insert(7)
>>> rh.top()
1
"""
if not self._root:
raise IndexError("Can't get top element for the empty heap.")
return self._root.value
def clear(self) -> None:
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"""
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]:
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"""
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()