結果
問題 | No.2507 Yet Another Subgraph Counting |
ユーザー | suisen |
提出日時 | 2023-08-21 22:39:46 |
言語 | PyPy3 (7.3.15) |
結果 |
TLE
(最新)
AC
(最初)
|
実行時間 | - |
コード長 | 4,621 bytes |
コンパイル時間 | 966 ms |
コンパイル使用メモリ | 86,756 KB |
実行使用メモリ | 129,684 KB |
最終ジャッジ日時 | 2023-10-13 18:25:21 |
合計ジャッジ時間 | 38,236 ms |
ジャッジサーバーID (参考情報) |
judge12 / judge14 |
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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 | 186 ms
82,448 KB |
testcase_01 | AC | 190 ms
82,272 KB |
testcase_02 | AC | 187 ms
82,172 KB |
testcase_03 | AC | 177 ms
81,628 KB |
testcase_04 | AC | 174 ms
81,072 KB |
testcase_05 | AC | 358 ms
85,060 KB |
testcase_06 | AC | 175 ms
81,096 KB |
testcase_07 | AC | 191 ms
82,152 KB |
testcase_08 | AC | 222 ms
83,032 KB |
testcase_09 | AC | 169 ms
81,040 KB |
testcase_10 | AC | 221 ms
82,832 KB |
testcase_11 | AC | 362 ms
85,816 KB |
testcase_12 | AC | 217 ms
82,992 KB |
testcase_13 | AC | 216 ms
82,768 KB |
testcase_14 | AC | 366 ms
85,208 KB |
testcase_15 | AC | 173 ms
80,924 KB |
testcase_16 | AC | 173 ms
80,724 KB |
testcase_17 | AC | 373 ms
84,672 KB |
testcase_18 | AC | 175 ms
81,008 KB |
testcase_19 | AC | 334 ms
83,820 KB |
testcase_20 | AC | 184 ms
80,836 KB |
testcase_21 | AC | 194 ms
82,192 KB |
testcase_22 | AC | 227 ms
82,888 KB |
testcase_23 | AC | 381 ms
84,392 KB |
testcase_24 | AC | 278 ms
84,068 KB |
testcase_25 | AC | 490 ms
87,520 KB |
testcase_26 | AC | 835 ms
95,944 KB |
testcase_27 | AC | 371 ms
84,480 KB |
testcase_28 | AC | 481 ms
87,580 KB |
testcase_29 | AC | 218 ms
82,664 KB |
testcase_30 | AC | 832 ms
96,056 KB |
testcase_31 | AC | 1,965 ms
128,012 KB |
testcase_32 | AC | 1,986 ms
127,912 KB |
testcase_33 | AC | 362 ms
84,664 KB |
testcase_34 | AC | 320 ms
83,768 KB |
testcase_35 | AC | 365 ms
85,296 KB |
testcase_36 | AC | 266 ms
83,236 KB |
testcase_37 | TLE | - |
testcase_38 | AC | 1,993 ms
125,396 KB |
testcase_39 | AC | 1,989 ms
123,068 KB |
testcase_40 | TLE | - |
testcase_41 | TLE | - |
testcase_42 | AC | 1,982 ms
125,032 KB |
testcase_43 | AC | 813 ms
91,588 KB |
testcase_44 | AC | 1,920 ms
127,112 KB |
testcase_45 | AC | 359 ms
85,624 KB |
testcase_46 | AC | 359 ms
85,696 KB |
testcase_47 | AC | 1,930 ms
127,332 KB |
testcase_48 | AC | 263 ms
83,096 KB |
testcase_49 | AC | 1,970 ms
129,684 KB |
testcase_50 | AC | 313 ms
83,680 KB |
testcase_51 | AC | 832 ms
92,288 KB |
ソースコード
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] for v in range(n): f += [0] * (1 << v) for C in range(1 << v, 1 << (v + 1)): mask = ((1 << (v + 1)) - 1) ^ C k = popcount[mask] g = [0] * (1 << k) for A in range(1 << k): T = bit_deposit(A, mask, v) g[A] = f[T] * (E[T | C] - E[T] - E[C]) h = exp(g, k) for A in range(1 << k): X = bit_deposit(A, mask, v) | C f[X] += cycle[C] * h[A] print(exp(f, n)[-1])