cp-library
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cp_library/alg/graph/bit_graph_cls.py
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- Last update: 2025-03-30 20:17:47+09:00
Depends on
- cp_library/alg/graph/edge_cls.py
- cp_library/bit/ctz32_fn.py
- cp_library/bit/popcnt32_fn.py
- cp_library/io/fast_io_cls.py
- cp_library/io/parser_cls.py
Verified with
Code
import cp_library.alg.graph.__header__
from typing import Union
from cp_library.bit.popcnt32_fn import popcnt32
from cp_library.bit.ctz32_fn import ctz32
from cp_library.alg.graph.edge_cls import Edge
from cp_library.io.parser_cls import Parsable, Parser, TokenStream
class BitGraph(list, Parsable):
def __init__(G, N: int, E: list[Edge]=[]):
super().__init__([0]*N)
G.E, G.N, G.M = E, N, len(E)
for u,v in E:
G[u] |= 1 << v
G[v] |= 1 << u
def to_complement(G):
full = (1 << G.N) - 1
for u in range(G.N):
G[u] = full ^ G[u]
def chromatic_number(G):
Z = 1 << (N := len(G))
I, coef = [0]*Z, [1]*Z
I[0] = 1
for S in range(1, Z):
T = 1 << (v := ctz32(S)) ^ S
I[S] = I[T] + I[T & ~G[v]]
coef[S] = -1 if popcnt32(S) & 1 else 1
for k in range(1, N):
Pk = 0
for S in range(Z):
coef[S] *= I[S]
Pk += coef[S]
if Pk != 0: return k
return N
@classmethod
def compile(cls, N: int, M: int, E: Union[type,int] = Edge[-1]):
if isinstance(E, int): E = Edge[E]
edge = Parser.compile(E)
def parse(ts: TokenStream):
return cls(N, [edge(ts) for _ in range(M)])
return parse
'''
╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
https://kobejean.github.io/cp-library
'''
from typing import Union
def popcnt32(x):
x = ((x >> 1) & 0x55555555) + (x & 0x55555555)
x = ((x >> 2) & 0x33333333) + (x & 0x33333333)
x = ((x >> 4) & 0x0f0f0f0f) + (x & 0x0f0f0f0f)
x = ((x >> 8) & 0x00ff00ff) + (x & 0x00ff00ff)
x = ((x >> 16) & 0x0000ffff) + (x & 0x0000ffff)
return x
def ctz32(x): return popcnt32(~x & (x - 1))
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)
from typing import TypeVar
_T = TypeVar('T')
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 Edge(tuple, Parsable):
@classmethod
def compile(cls, I=-1):
def parse(ts: TokenStream):
u,v = ts.line()
return cls((int(u)+I,int(v)+I))
return parse
class BitGraph(list, Parsable):
def __init__(G, N: int, E: list[Edge]=[]):
super().__init__([0]*N)
G.E, G.N, G.M = E, N, len(E)
for u,v in E:
G[u] |= 1 << v
G[v] |= 1 << u
def to_complement(G):
full = (1 << G.N) - 1
for u in range(G.N):
G[u] = full ^ G[u]
def chromatic_number(G):
Z = 1 << (N := len(G))
I, coef = [0]*Z, [1]*Z
I[0] = 1
for S in range(1, Z):
T = 1 << (v := ctz32(S)) ^ S
I[S] = I[T] + I[T & ~G[v]]
coef[S] = -1 if popcnt32(S) & 1 else 1
for k in range(1, N):
Pk = 0
for S in range(Z):
coef[S] *= I[S]
Pk += coef[S]
if Pk != 0: return k
return N
@classmethod
def compile(cls, N: int, M: int, E: Union[type,int] = Edge[-1]):
if isinstance(E, int): E = Edge[E]
edge = Parser.compile(E)
def parse(ts: TokenStream):
return cls(N, [edge(ts) for _ in range(M)])
return parse