cp-library
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cp_library/alg/graph/fast/snippets/two_edge_connected_components_fn.py
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- Last update: 2025-03-30 20:17:47+09:00
Depends on
- cp_library/alg/dp/chmin_fn.py
- cp_library/alg/graph/dfs_options_cls.py
- cp_library/alg/graph/fast/graph_base_cls.py
- cp_library/alg/iter/slice_iterator_reverse_cls.py
- cp_library/ds/array_init_fn.py
- cp_library/ds/elist_fn.py
- cp_library/ds/packet_list_cls.py
- cp_library/io/fast_io_cls.py
- cp_library/io/parser_cls.py
Verified with
Code
import cp_library.__header__
from typing import Iterable, Union
import cp_library.alg.__header__
from cp_library.alg.dp.chmin_fn import chmin
from cp_library.alg.iter.slice_iterator_reverse_cls import SliceIteratorReverse
import cp_library.alg.graph.__header__
import cp_library.alg.graph.fast.__header__
from cp_library.alg.graph.fast.graph_base_cls import GraphBase
def two_edge_connected_components(G: GraphBase, s: Union[int,list,None] = None) -> Iterable[list[int]]:
'''
Returns an iterator of vertex lists, each representing a two-edge-connected component.
'''
low, st, e2ccs, L = [N := G.N]*N, elist(G.M), elist(G.M), elist(G.M)
def enter(u):
st.append(u)
low[u] = G.tin[u]
def back(u,v,i):
chmin(low, u, G.tin[v])
def up(u,p,i):
chmin(low, p, low[u])
if low[u] > G.tin[p]:
# add new two-edge-connected component
L.append(len(e2ccs))
v = -1
while v != u:
e2ccs.append(v := st.pop())
def leave(u):
if G.back[u] < 0:
# add new two-edge-connected component
L.append(len(e2ccs))
e2ccs.extend(st)
st.clear()
G.dfs(s, enter_fn=enter, back_fn=back, up_fn=up, leave_fn=leave)
return SliceIteratorReverse(e2ccs, L)
from cp_library.ds.elist_fn import elist'''
╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
https://kobejean.github.io/cp-library
'''
from typing import Iterable, Union
def chmin(dp, i, v):
if ch:=dp[i]>v:dp[i]=v
return ch
from typing import Iterator, SupportsIndex
from typing import TypeVar
_T = TypeVar('T')
class SliceIteratorReverse(Iterator[_T]):
def __init__(self, A: list[_T], L: list[SupportsIndex]):
self.A, self.L, self.r = A, L, len(A)
def __len__(self): return len(self.L)
def __next__(self):
L = self.L
if not L: raise StopIteration
self.r, r = (l := L.pop()), self.r
return self.A[l:r]
from math import inf
from collections import deque
from typing import Callable, Sequence, Union, overload
import typing
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
from enum import auto, IntFlag, IntEnum
class DFSFlags(IntFlag):
ENTER = auto()
DOWN = auto()
BACK = auto()
CROSS = auto()
LEAVE = auto()
UP = auto()
MAXDEPTH = auto()
RETURN_PARENTS = auto()
RETURN_DEPTHS = auto()
BACKTRACK = auto()
CONNECT_ROOTS = auto()
# Common combinations
ALL_EDGES = DOWN | BACK | CROSS
EULER_TOUR = DOWN | UP
INTERVAL = ENTER | LEAVE
TOPDOWN = DOWN | CONNECT_ROOTS
BOTTOMUP = UP | CONNECT_ROOTS
RETURN_ALL = RETURN_PARENTS | RETURN_DEPTHS
class DFSEvent(IntEnum):
ENTER = DFSFlags.ENTER
DOWN = DFSFlags.DOWN
BACK = DFSFlags.BACK
CROSS = DFSFlags.CROSS
LEAVE = DFSFlags.LEAVE
UP = DFSFlags.UP
MAXDEPTH = DFSFlags.MAXDEPTH
class GraphBase(Sequence, Parsable):
def __init__(G, N: int, M: int, U: list[int], V: list[int],
deg: list[int], La: list[int], Ra: list[int],
Ua: list[int], Va: list[int], Ea: list[int], twin: list[int] = None):
G.N = N
'''The number of vertices.'''
G.M = M
'''The number of edges.'''
G.U = U
'''A list of source vertices in the original edge list.'''
G.V = V
'''A list of destination vertices in the original edge list.'''
G.deg = deg
'''deg[u] is the out degree of vertex u.'''
G.La = La
'''La[u] stores the start index of the list of adjacent vertices from u.'''
G.Ra = Ra
'''Ra[u] stores the stop index of the list of adjacent vertices from u.'''
G.Ua = Ua
'''Ua[i] = u for La[u] <= i < Ra[u], useful for backtracking.'''
G.Va = Va
'''Va[i] lists adjacent vertices to u for La[u] <= i < Ra[u].'''
G.Ea = Ea
'''Ea[i] lists the edge ids that start from u for La[u] <= i < Ra[u].
For undirected graphs, edge ids in range M<= e <2*M are edges from V[e-M] -> U[e-M].
'''
G.twin = twin if twin is not None else range(len(Ua))
'''twin[i] in undirected graphs stores index j of the same edge but with u and v swapped.'''
G.st: list[int] = None
G.order: list[int] = None
G.vis: list[int] = None
G.back: list[int] = None
G.tin: list[int] = None
def prep_vis(G):
if G.vis is None: G.vis = u8f(G.N)
return G.vis
def prep_st(G):
if G.st is None: G.st = elist(G.N)
else: G.st.clear()
return G.st
def prep_order(G):
if G.order is None: G.order = elist(G.N)
else: G.order.clear()
return G.order
def prep_back(G):
if G.back is None: G.back = i32f(G.N, -2)
return G.back
def prep_tin(G):
if G.tin is None: G.tin = i32f(G.N, -1)
return G.tin
def __len__(G) -> int: return G.N
def __getitem__(G, u): return G.Va[G.La[u]:G.Ra[u]]
def range(G, u): return range(G.La[u],G.Ra[u])
@overload
def distance(G) -> list[list[int]]: ...
@overload
def distance(G, s: int = 0) -> list[int]: ...
@overload
def distance(G, s: int, g: int) -> int: ...
def distance(G, s = None, g = None):
if s == None: return G.floyd_warshall()
else: return G.bfs(s, g)
def recover_path(G, s, t):
Ua, back, vertices = G.Ua, G.back, u32f(1, v := t)
while v != s: vertices.append(v := Ua[back[v]])
return vertices
def recover_path_edge_ids(G, s, t):
Ea, Ua, back, edges, v = G.Ea, G.Ua, G.back, u32f(0), t
while v != s: edges.append(Ea[i := back[v]]), (v := Ua[i])
return edges
def shortest_path(G, s: int, t: int):
if G.distance(s, t) >= inf: return None
vertices = G.recover_path(s, t)
vertices.reverse()
return vertices
def shortest_path_edge_ids(G, s: int, t: int):
if G.distance(s, t) >= inf: return None
edges = G.recover_path_edge_ids(s, t)
edges.reverse()
return edges
@overload
def bfs(G, s: Union[int,list] = 0) -> list[int]: ...
@overload
def bfs(G, s: Union[int,list], g: int) -> int: ...
def bfs(G, s: int = 0, g: int = None):
S, Va, back, D = G.starts(s), G.Va, i32f(N := G.N, -1), [inf]*N
G.back, G.D = back, D
for u in S: D[u] = 0
que = deque(S)
while que:
nd = D[u := que.popleft()]+1
if u == g: return nd-1
for i in G.range(u):
if nd < D[v := Va[i]]:
D[v], back[v] = nd, i
que.append(v)
return D if g is None else inf
def floyd_warshall(G) -> list[list[int]]:
G.D = D = [[inf]*G.N for _ in range(G.N)]
for u in range(G.N): D[u][u] = 0
for i in range(len(G.Ua)): D[G.Ua[i]][G.Va[i]] = 1
for k, Dk in enumerate(D):
for Di in D:
if (Dik := Di[k]) == inf: continue
for j in range(G.N):
chmin(Di, j, Dik+Dk[j])
return D
def find_cycle_indices(G, s: Union[int, None] = None):
Ea, Ua, Va, vis, back = G.Ea, G. Ua, G.Va, u8f(N := G.N), u32f(N, i32_max)
G.vis, G.back, st = vis, back, elist(N)
for s in G.starts(s):
if vis[s]: continue
st.append(s)
while st:
if not vis[u := st.pop()]:
st.append(u)
vis[u], pe = 1, Ea[j] if (j := back[u]) != i32_max else i32_max
for i in G.range(u):
if not vis[v := Va[i]]:
back[v] = i
st.append(v)
elif vis[v] == 1 and pe != Ea[i]:
I = u32f(1,i)
while v != u: I.append(i := back[u]), (u := Ua[i])
I.reverse()
return I
else:
vis[u] = 2
# check for self loops
for i in range(len(Ua)):
if Ua[i] == Va[i]:
return u32f(1,i)
def find_cycle(G, s: Union[int, None] = None):
if I := G.find_cycle_indices(s): return [G.Ua[i] for i in I]
def find_cycle_edge_ids(G, s: Union[int, None] = None):
if I := G.find_cycle_indices(s): return [G.Ea[i] for i in I]
def find_minimal_cycle(G, s=0):
D, par, que, Va = u32f(N := G.N, u32_max), i32f(N, -1), deque([s]), G.Va
D[s] = 0
while que:
for i in G.range(u := que.popleft()):
if (v := Va[i]) == s: # Found cycle back to start
cycle = [u]
while u != s: cycle.append(u := par[u])
return cycle
if D[v] < u32_max: continue
D[v], par[v] = D[u]+1, u; que.append(v)
def dfs_topdown(G, s: Union[int,list] = None) -> list[int]:
'''Returns lists of indices i where Ua[i] -> Va[i] are edges in order of top down discovery'''
vis, st, order = G.prep_vis(), G.prep_st(), G.prep_order()
for s in G.starts(s):
if vis[s]: continue
vis[s] = 1; st.append(s)
while st:
for i in G.range(st.pop()):
if vis[v := G.Va[i]]: continue
vis[v] = 1; order.append(i); st.append(v)
return order
def dfs(G, s: Union[int,list] = None, /,
backtrack = False,
max_depth = None,
enter_fn: Callable[[int],None] = None,
leave_fn: Callable[[int],None] = None,
max_depth_fn: Callable[[int],None] = None,
down_fn: Callable[[int,int,int],None] = None,
back_fn: Callable[[int,int,int],None] = None,
forward_fn: Callable[[int,int,int],None] = None,
cross_fn: Callable[[int,int,int],None] = None,
up_fn: Callable[[int,int,int],None] = None):
I, time, vis, st, back, tin = G.La[:], -1, G.prep_vis(), G.prep_st(), G.prep_back(), G.prep_tin()
for s in G.starts(s):
if vis[s]: continue
back[s], tin[s] = -1, (time := time+1); st.append(s)
while st:
if vis[u := st[-1]] == 0:
vis[u] = 1
if enter_fn: enter_fn(u)
if max_depth is not None and len(st) > max_depth:
I[u] = G.Ra[u]
if max_depth_fn: max_depth_fn(u)
if (i := I[u]) < G.Ra[u]:
I[u] += 1
if (s := vis[v := G.Va[i]]) == 0:
back[v], tin[v] = i, (time := time+1); st.append(v)
if down_fn: down_fn(u,v,i)
elif back_fn and s == 1 and back[u] != G.twin[i]: back_fn(u,v,i)
elif (cross_fn or forward_fn) and s == 2:
if forward_fn and tin[u] < tin[v]: forward_fn(u,v,i)
elif cross_fn: cross_fn(u,v,i)
else:
vis[u] = 2; st.pop()
if backtrack: vis[u], I[u] = 0, G.La[u]
if leave_fn: leave_fn(u)
if up_fn and st: up_fn(u, st[-1], back[u])
def dfs_enter_leave(G, s: Union[int,list[int],None] = None) -> Sequence[tuple[DFSEvent,int]]:
N, I = G.N, G.La[:]
st, back, plst = elist(N), i32f(N,-2), PacketList(order := elist(2*N), N-1)
G.back, ENTER, LEAVE = back, int(DFSEvent.ENTER) << plst.shift, int(DFSEvent.LEAVE) << plst.shift
for s in G.starts(s):
if back[s] >= -1: continue
back[s] = -1
order.append(ENTER | s), st.append(s)
while st:
if (i := I[u := st[-1]]) < G.Ra[u]:
I[u] += 1
if back[v := G.Va[i]] >= -1: continue
back[v] = i; order.append(ENTER | v); st.append(v)
else:
order.append(LEAVE | u); st.pop()
return plst
def starts(G, s: Union[int,list[int],None]) -> list[int]:
if isinstance(s, int): return [s]
elif s is None: return range(G.N)
elif isinstance(s, list): return s
else: return list(s)
@classmethod
def compile(cls, N: int, M: int, shift: int = -1):
def parse(ts: TokenStream):
U, V = u32f(M), u32f(M)
for i in range(M):
u, v = ts._line()
U[i], V[i] = int(u)+shift, int(v)+shift
return cls(N, U, V)
return parse
def elist(est_len: int) -> list: ...
try:
from __pypy__ import newlist_hint
except:
def newlist_hint(hint):
return []
elist = newlist_hint
from array import array
def i8f(N: int, elm: int = 0): return array('b', (elm,))*N # signed char
def u8f(N: int, elm: int = 0): return array('B', (elm,))*N # unsigned char
def i16f(N: int, elm: int = 0): return array('h', (elm,))*N # signed short
def u16f(N: int, elm: int = 0): return array('H', (elm,))*N # unsigned short
def i32f(N: int, elm: int = 0): return array('i', (elm,))*N # signed int
def u32f(N: int, elm: int = 0): return array('I', (elm,))*N # unsigned int
def i64f(N: int, elm: int = 0): return array('q', (elm,))*N # signed long long
# def u64f(N: int, elm: int = 0): return array('Q', (elm,))*N # unsigned long long
def f32f(N: int, elm: float = 0.0): return array('f', (elm,))*N # float
def f64f(N: int, elm: float = 0.0): return array('d', (elm,))*N # double
def i8a(init = None): return array('b') if init is None else array('b', init) # signed char
def u8a(init = None): return array('B') if init is None else array('B', init) # unsigned char
def i16a(init = None): return array('h') if init is None else array('h', init) # signed short
def u16a(init = None): return array('H') if init is None else array('H', init) # unsigned short
def i32a(init = None): return array('i') if init is None else array('i', init) # signed int
def u32a(init = None): return array('I') if init is None else array('I', init) # unsigned int
def i64a(init = None): return array('q') if init is None else array('q', init) # signed long long
# def u64a(init = None): return array('Q') if init is None else array('Q', init) # unsigned long long
def f32a(init = None): return array('f') if init is None else array('f', init) # float
def f64a(init = None): return array('d') if init is None else array('d', init) # double
i8_max = (1 << 7)-1
u8_max = (1 << 8)-1
i16_max = (1 << 15)-1
u16_max = (1 << 16)-1
i32_max = (1 << 31)-1
u32_max = (1 << 32)-1
i64_max = (1 << 63)-1
u64_max = (1 << 64)-1
class PacketList(Sequence[tuple[int,int]]):
def __init__(lst, A: list[int], max1: int):
lst.A = A
lst.mask = (1 << (shift := (max1).bit_length())) - 1
lst.shift = shift
def __len__(lst): return lst.A.__len__()
def __contains__(lst, x: tuple[int,int]): return lst.A.__contains__(x[0] << lst.shift | x[1])
def __getitem__(lst, key) -> tuple[int,int]:
x = lst.A[key]
return x >> lst.shift, x & lst.mask
def two_edge_connected_components(G: GraphBase, s: Union[int,list,None] = None) -> Iterable[list[int]]:
'''
Returns an iterator of vertex lists, each representing a two-edge-connected component.
'''
low, st, e2ccs, L = [N := G.N]*N, elist(G.M), elist(G.M), elist(G.M)
def enter(u):
st.append(u)
low[u] = G.tin[u]
def back(u,v,i):
chmin(low, u, G.tin[v])
def up(u,p,i):
chmin(low, p, low[u])
if low[u] > G.tin[p]:
# add new two-edge-connected component
L.append(len(e2ccs))
v = -1
while v != u:
e2ccs.append(v := st.pop())
def leave(u):
if G.back[u] < 0:
# add new two-edge-connected component
L.append(len(e2ccs))
e2ccs.extend(st)
st.clear()
G.dfs(s, enter_fn=enter, back_fn=back, up_fn=up, leave_fn=leave)
return SliceIteratorReverse(e2ccs, L)