結果

問題 No.2507 Yet Another Subgraph Counting
ユーザー suisensuisen
提出日時 2023-08-21 22:49:00
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,814 ms / 2,000 ms
コード長 4,575 bytes
コンパイル時間 441 ms
コンパイル使用メモリ 82,176 KB
実行使用メモリ 125,732 KB
最終ジャッジ日時 2024-09-15 14:15:32
合計ジャッジ時間 30,057 ms
ジャッジサーバーID
(参考情報)
judge5 / judge1
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ファイルパターン 結果
other AC * 52
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ソースコード

diff #
プレゼンテーションモードにする

from typing import List, Tuple
N_MAX = 13
popcount = [0] * (1 << N_MAX)
for S in range(1, 1 << N_MAX):
popcount[S] = popcount[S & (S - 1)] + 1
def addeq_poly(f: List[int], g: List[int]):
"""
f += g
"""
for i, gi in enumerate(g):
f[i] += gi
def subeq_poly(f: List[int], g: List[int]):
"""
f -= g
"""
for i, gi in enumerate(g):
f[i] -= gi
def subset_zeta(f: List[int], n: int):
"""
Inplace conversion from f to ζf. ζf is defined as follows:
(ζf)(S) = Σ[T⊆S] f(T)
"""
block = 1
while block < 1 << n:
offset = 0
while offset < 1 << n:
for p in range(offset, offset + block):
f[p + block] += f[p]
offset += 2 * block
block <<= 1
def subset_zeta_poly(f: List[List[int]], n: int):
"""
Inplace conversion from f to ζf. ζf is defined as follows:
(ζf)(S) = Σ[T⊆S] f(T)
"""
block = 1
while block < 1 << n:
offset = 0
while offset < 1 << n:
for p in range(offset, offset + block):
addeq_poly(f[p + block], f[p])
offset += 2 * block
block <<= 1
def subset_mobius_poly(f: List[List[int]], n: int):
"""
Inplace conversion from f to μf. μf is defined as follows:
(μf)(S) = Σ[T⊆S] (-1)^(|S/T|) f(T)
"""
block = 1
while block < 1 << n:
offset = 0
while offset < 1 << n:
for p in range(offset, offset + block):
subeq_poly(f[p + block], f[p])
offset += 2 * block
block <<= 1
def mul_poly(f: List[int], g: List[int]):
"""
Returns h = fg mod x^n, where f, g are polynomials with degree n-1 defined as follows:
f(x) = Σ_i f[i] x^i,
g(x) = Σ_i g[i] x^i.
"""
n = len(f)
h = [0] * n
for i in range(n):
for j in range(n - i):
h[i + j] += f[i] * g[j]
return h
def ranked(f: List[int], n: int):
"""
Add rank
"""
return [[(i == popcount[S]) * f[S] for i in range(n + 1)] for S in range(1 << n)]
def deranked(rf: List[List[int]], n: int):
"""
Remove rank
"""
return [rf[S][popcount[S]] for S in range(1 << n)]
def exp(f: List[int], n: int):
"""
Subset exp of Σ[S⊆{0,1,...,n-1}] f(S)
"""
assert f[0] == 0
rf = ranked([1], 0)
for i in range(n):
rg = ranked(f[1 << i: 1 << (i + 1)], i)
subset_zeta_poly(rg, i)
for S in range(1 << i):
rf[S].append(0)
rg[S].insert(0, 1)
rh = mul_poly(rf[S], rg[S])
rf.append(rh)
subset_mobius_poly(rf, n)
return deranked(rf, n)
def bit_deposit(src: int, mask: int, bitwidth: int):
dst = 0
j = 0
for i in range(bitwidth):
if (mask >> i) & 1:
dst |= ((src >> j) & 1) << i
j += 1
return dst
def count_cycles(n: int, edges: List[Tuple[int, int]]):
cycle = [0] * (1 << n)
adj = [[] for _ in range(n)]
for u, v in edges:
adj[u].append(v)
adj[v].append(u)
cycle_dp = [[0] * n for _ in range(1 << n)]
for v in range(n):
cycle_dp[1 << v][v] = 1
for s in range(1, 1 << n):
start = 0
while not ((s >> start) & 1):
start += 1
for cur in range(n):
if cycle_dp[s][cur] == 0:
continue
for nxt in adj[cur]:
if start == nxt:
cycle[s] += cycle_dp[s][cur]
elif start < nxt and not ((s >> nxt) & 1):
cycle_dp[s | (1 << nxt)][nxt] += cycle_dp[s][cur]
for s in range(1, 1 << n):
if popcount[s] == 1:
cycle[s] = 1
elif popcount[s] == 2:
cycle[s] = 0
else:
cycle[s] //= 2
return cycle
n, m = map(int, input().split())
edges = []
for _ in range(m):
u, v = map(int, input().split())
u -= 1
v -= 1
edges.append((u, v))
# E[S] = # of edges connecting vertices in S
E = [0] * (1 << n)
for u, v in edges:
E[(1 << u) | (1 << v)] += 1
subset_zeta(E, n)
cycle = count_cycles(n, edges)
f = [0] * (1 << n)
for C in range(1, 1 << n):
# max C
t = C.bit_length() - 1
# {0, ..., tX} - C
S = ((1 << (t + 1)) - 1) ^ C
k = popcount[S]
g = [0] * (1 << k)
for A in range(1 << k):
T = bit_deposit(A, S, t)
g[A] = f[T] * (E[T | C] - E[T] - E[C])
for A, hA in enumerate(exp(g, k)):
X = bit_deposit(A, S, t) | C
f[X] += cycle[C] * hA
print(exp(f, n)[-1])
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