結果
| 問題 | No.2507 Yet Another Subgraph Counting |
| ユーザー |
 suisen
|
| 提出日時 | 2023-08-21 04:17:36 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
TLE
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 4,556 bytes |
| コンパイル時間 | 746 ms |
| コンパイル使用メモリ | 86,932 KB |
| 実行使用メモリ | 132,628 KB |
| 最終ジャッジ日時 | 2023-08-31 23:08:24 |
| 合計ジャッジ時間 | 38,175 ms |
|
ジャッジサーバーID （参考情報） |
judge13 / judge15 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 188 ms
82,452 KB |
| testcase_01 | AC | 190 ms
82,656 KB |
| testcase_02 | AC | 191 ms
82,200 KB |
| testcase_03 | AC | 179 ms
81,784 KB |
| testcase_04 | AC | 172 ms
80,944 KB |
| testcase_05 | AC | 362 ms
84,536 KB |
| testcase_06 | AC | 170 ms
81,156 KB |
| testcase_07 | AC | 190 ms
82,460 KB |
| testcase_08 | AC | 219 ms
83,116 KB |
| testcase_09 | AC | 169 ms
81,008 KB |
| testcase_10 | AC | 217 ms
83,008 KB |
| testcase_11 | AC | 357 ms
84,844 KB |
| testcase_12 | AC | 221 ms
83,252 KB |
| testcase_13 | AC | 218 ms
83,192 KB |
| testcase_14 | AC | 364 ms
85,372 KB |
| testcase_15 | AC | 167 ms
81,132 KB |
| testcase_16 | AC | 171 ms
81,012 KB |
| testcase_17 | AC | 356 ms
85,004 KB |
| testcase_18 | AC | 167 ms
81,264 KB |
| testcase_19 | AC | 320 ms
84,540 KB |
| testcase_20 | AC | 167 ms
81,232 KB |
| testcase_21 | AC | 185 ms
82,684 KB |
| testcase_22 | AC | 215 ms
82,792 KB |
| testcase_23 | AC | 367 ms
84,840 KB |
| testcase_24 | AC | 268 ms
84,016 KB |
| testcase_25 | AC | 480 ms
86,272 KB |
| testcase_26 | AC | 839 ms
95,216 KB |
| testcase_27 | AC | 362 ms
84,864 KB |
| testcase_28 | AC | 477 ms
86,616 KB |
| testcase_29 | AC | 218 ms
82,976 KB |
| testcase_30 | AC | 849 ms
95,624 KB |
| testcase_31 | AC | 1,949 ms
132,628 KB |
| testcase_32 | AC | 1,970 ms
131,756 KB |
| testcase_33 | AC | 355 ms
84,996 KB |
| testcase_34 | AC | 312 ms
84,780 KB |
| testcase_35 | AC | 351 ms
84,552 KB |
| testcase_36 | AC | 267 ms
84,224 KB |
| testcase_37 | AC | 1,999 ms
125,968 KB |
| testcase_38 | TLE | - |
| testcase_39 | AC | 1,977 ms
127,500 KB |
| testcase_40 | TLE | - |
| testcase_41 | AC | 1,979 ms
125,876 KB |
| testcase_42 | AC | 1,980 ms
127,348 KB |
| testcase_43 | AC | 811 ms
94,832 KB |
| testcase_44 | AC | 1,944 ms
132,244 KB |
| testcase_45 | AC | 350 ms
84,716 KB |
| testcase_46 | AC | 348 ms
84,412 KB |
| testcase_47 | AC | 1,969 ms
132,072 KB |
| testcase_48 | AC | 260 ms
83,976 KB |
| testcase_49 | AC | 1,981 ms
131,232 KB |
| testcase_50 | AC | 309 ms
84,712 KB |
| testcase_51 | AC | 828 ms
94,248 KB |
ソースコード
from typing import List
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, mask):
dst = 0
j = 0
for i in range(N_MAX):
if (mask >> i) & 1:
dst |= ((src >> j) & 1) << i
j += 1
return dst
def bit_extract(src, mask):
dst = 0
j = 0
for i in range(N_MAX):
if (mask >> i) & 1:
dst |= ((src >> i) & 1) << j
j += 1
return dst
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 = [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
f = [0]
for v in range(n):
f += [0] * (1 << v)
for X in range(1 << v, 1 << (v + 1)):
mask = ((1 << (v + 1)) - 1) ^ X
k = popcount[mask]
g = [0] * (1 << k)
for T in range(1 << k):
S = bit_deposit(T, mask)
g[T] = f[S] * (E[S | X] - E[S] - E[X])
exp_g = exp(g, k)
for T in range(1 << k):
S = bit_deposit(T, mask)
f[S | X] += cycle[X] * exp_g[T]
print(exp(f, n)[-1])