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import cp_library.ds.heap.__header__
from typing import Iterable
from cp_library.ds.heap.max_heap_cls import MaxHeap
from cp_library.ds.heap.k_heap_mixin import KHeapMixin
from cp_library.misc.typing import _T
class MinKHeap(KHeapMixin[_T], MaxHeap[_T]):
'''MinKHeap[K: int, T: type, N: Union[int,None]]'''
def __init__(self, K: int, iterable: Iterable[_T] = None):
MaxHeap.__init__(self, iterable)
KHeapMixin.__init__(self, K)
'''
╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
https://kobejean.github.io/cp-library
'''
from typing import Iterable
from collections import UserList
from typing import TypeVar
_T = TypeVar('T')
def heappop_max(heap: list[_T], /) -> _T: ...
def heapsiftdown_max(heap: list[_T], root: int, pos: int): ...
def heapsiftup_max(heap: list[_T], pos: int): ...
def heapsiftdown(heap: list[_T], root: int, pos: int): ...
def heapsiftup(heap: list[_T], pos: int): ...
from heapq import (
_heapify_max as heapify_max,
_heappop_max as heappop_max,
_siftdown_max as heapsiftdown_max,
_siftup_max as heapsiftup_max,
_siftdown as heapsiftdown,
_siftup as heapsiftup
)
def heappush_max(heap: list[_T], item: _T):
'''Push item onto heap, maintaining the heap invariant.'''
heap.append(item)
heapsiftdown_max(heap, 0, len(heap)-1)
def heapreplace_max(heap: list[_T], item: _T) -> _T:
'''Pop and return the current largest value, and add the new item.
This is more efficient than heappop_max() followed by heappush_max(), and can be
more appropriate when using a fixed-size heap. Note that the value
returned may be larger than item! That constrains reasonable uses of
this routine unless written as part of a conditional replacement:
if item > heap[0]:
item = heapreplace_max(heap, item)
'''
returnitem = heap[0]
heap[0] = item
heapsiftup_max(heap, 0)
return returnitem
def heappushpop_max(heap: list[_T], item: _T) -> _T:
'''Fast version of a heappush_max followed by a heappop_max.'''
if heap and heap[0] > item:
item, heap[0] = heap[0], item
heapsiftup_max(heap, 0)
return item
from typing import Generic
class HeapProtocol(Generic[_T]):
def pop(self) -> _T: ...
def push(self, item: _T): ...
def pushpop(self, item: _T) -> _T: ...
def replace(self, item: _T) -> _T: ...
class MaxHeap(HeapProtocol[_T], UserList[_T]):
def __init__(self, iterable: Iterable[_T] = None):
super().__init__(iterable)
heapify_max(self.data)
def pop(self): return heappop_max(self.data)
def push(self, item: _T): heappush_max(self.data, item)
def pushpop(self, item: _T): return heappushpop_max(self.data, item)
def replace(self, item: _T): return heapreplace_max(self.data, item)
from typing import Union
import typing
from collections import deque
from numbers import Number
from types import GenericAlias
from typing import Callable, Collection, Iterator, Union
import os
import sys
from io import BytesIO, IOBase
class FastIO(IOBase):
BUFSIZE = 8192
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
BUFSIZE = self.BUFSIZE
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
BUFSIZE = self.BUFSIZE
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
stdin: 'IOWrapper' = None
stdout: 'IOWrapper' = None
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
def write(self, s):
return self.buffer.write(s.encode("ascii"))
def read(self):
return self.buffer.read().decode("ascii")
def readline(self):
return self.buffer.readline().decode("ascii")
sys.stdin = IOWrapper.stdin = IOWrapper(sys.stdin)
sys.stdout = IOWrapper.stdout = IOWrapper(sys.stdout)
class TokenStream(Iterator):
stream = IOWrapper.stdin
def __init__(self):
self.queue = deque()
def __next__(self):
if not self.queue: self.queue.extend(self._line())
return self.queue.popleft()
def wait(self):
if not self.queue: self.queue.extend(self._line())
while self.queue: yield
def _line(self):
return TokenStream.stream.readline().split()
def line(self):
if self.queue:
A = list(self.queue)
self.queue.clear()
return A
return self._line()
TokenStream.default = TokenStream()
class CharStream(TokenStream):
def _line(self):
return TokenStream.stream.readline().rstrip()
CharStream.default = CharStream()
ParseFn = Callable[[TokenStream],_T]
class Parser:
def __init__(self, spec: Union[type[_T],_T]):
self.parse = Parser.compile(spec)
def __call__(self, ts: TokenStream) -> _T:
return self.parse(ts)
@staticmethod
def compile_type(cls: type[_T], args = ()) -> _T:
if issubclass(cls, Parsable):
return cls.compile(*args)
elif issubclass(cls, (Number, str)):
def parse(ts: TokenStream): return cls(next(ts))
return parse
elif issubclass(cls, tuple):
return Parser.compile_tuple(cls, args)
elif issubclass(cls, Collection):
return Parser.compile_collection(cls, args)
elif callable(cls):
def parse(ts: TokenStream):
return cls(next(ts))
return parse
else:
raise NotImplementedError()
@staticmethod
def compile(spec: Union[type[_T],_T]=int) -> ParseFn[_T]:
if isinstance(spec, (type, GenericAlias)):
cls = typing.get_origin(spec) or spec
args = typing.get_args(spec) or tuple()
return Parser.compile_type(cls, args)
elif isinstance(offset := spec, Number):
cls = type(spec)
def parse(ts: TokenStream): return cls(next(ts)) + offset
return parse
elif isinstance(args := spec, tuple):
return Parser.compile_tuple(type(spec), args)
elif isinstance(args := spec, Collection):
return Parser.compile_collection(type(spec), args)
elif isinstance(fn := spec, Callable):
def parse(ts: TokenStream): return fn(next(ts))
return parse
else:
raise NotImplementedError()
@staticmethod
def compile_line(cls: _T, spec=int) -> ParseFn[_T]:
if spec is int:
fn = Parser.compile(spec)
def parse(ts: TokenStream): return cls([int(token) for token in ts.line()])
return parse
else:
fn = Parser.compile(spec)
def parse(ts: TokenStream): return cls([fn(ts) for _ in ts.wait()])
return parse
@staticmethod
def compile_repeat(cls: _T, spec, N) -> ParseFn[_T]:
fn = Parser.compile(spec)
def parse(ts: TokenStream): return cls([fn(ts) for _ in range(N)])
return parse
@staticmethod
def compile_children(cls: _T, specs) -> ParseFn[_T]:
fns = tuple((Parser.compile(spec) for spec in specs))
def parse(ts: TokenStream): return cls([fn(ts) for fn in fns])
return parse
@staticmethod
def compile_tuple(cls: type[_T], specs) -> ParseFn[_T]:
if isinstance(specs, (tuple,list)) and len(specs) == 2 and specs[1] is ...:
return Parser.compile_line(cls, specs[0])
else:
return Parser.compile_children(cls, specs)
@staticmethod
def compile_collection(cls, specs):
if not specs or len(specs) == 1 or isinstance(specs, set):
return Parser.compile_line(cls, *specs)
elif (isinstance(specs, (tuple,list)) and len(specs) == 2 and isinstance(specs[1], int)):
return Parser.compile_repeat(cls, specs[0], specs[1])
else:
raise NotImplementedError()
class Parsable:
@classmethod
def compile(cls):
def parser(ts: TokenStream): return cls(next(ts))
return parser
class KHeapMixin(HeapProtocol[_T], Parsable):
'''KHeapMixin[K: int, T: type, N: Union[int,None]]'''
def __init__(heap, K: int):
heap.K = K
def added(heap, item: _T): ...
def removed(heap, item: _T): ...
def pop(heap):
item = super().pop()
heap.removed(item)
return item
def push(heap, item: _T):
if len(heap) < heap._K:
heap.added(item)
super().push(item)
elif heap._K:
assert len(heap) == heap._K, f'{len(heap)=} {heap._K}'
heap.pushpop(item)
def pushpop(heap, item: _T):
if item != (remove := super().pushpop(item)):
heap.removed(remove)
heap.added(item)
return remove
else:
return item
def replace(heap, item: _T):
remove = super().replace(item)
heap.removed(remove)
heap.added(item)
return remove
@property
def K(heap):
return heap._K
@K.setter
def K(heap, K):
heap._K = K
if K is not None:
while len(heap) > K:
heap.pop()
@classmethod
def compile(cls, K: int, T: type, N: Union[int,None] = None):
elm = Parser.compile(T)
if N is None:
def parse(ts: TokenStream):
return cls(K, (elm(ts) for _ in ts.wait()))
else:
def parse(ts: TokenStream):
return cls(K, (elm(ts) for _ in range(N)))
return parse
class MinKHeap(KHeapMixin[_T], MaxHeap[_T]):
'''MinKHeap[K: int, T: type, N: Union[int,None]]'''
def __init__(self, K: int, iterable: Iterable[_T] = None):
MaxHeap.__init__(self, iterable)
KHeapMixin.__init__(self, K)