結果
問題 | No.2507 Yet Another Subgraph Counting |
ユーザー | suisen |
提出日時 | 2023-08-31 21:58:05 |
言語 | PyPy3 (7.3.15) |
結果 |
AC
|
実行時間 | 1,157 ms / 2,000 ms |
コード長 | 4,865 bytes |
コンパイル時間 | 491 ms |
コンパイル使用メモリ | 82,304 KB |
実行使用メモリ | 97,444 KB |
最終ジャッジ日時 | 2024-09-15 14:17:04 |
合計ジャッジ時間 | 12,122 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge6 |
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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 | 73 ms
73,600 KB |
testcase_01 | AC | 76 ms
74,496 KB |
testcase_02 | AC | 74 ms
74,240 KB |
testcase_03 | AC | 67 ms
70,144 KB |
testcase_04 | AC | 69 ms
68,608 KB |
testcase_05 | AC | 111 ms
78,848 KB |
testcase_06 | AC | 62 ms
68,736 KB |
testcase_07 | AC | 73 ms
73,216 KB |
testcase_08 | AC | 84 ms
78,080 KB |
testcase_09 | AC | 64 ms
68,736 KB |
testcase_10 | AC | 82 ms
77,568 KB |
testcase_11 | AC | 115 ms
79,232 KB |
testcase_12 | AC | 85 ms
77,952 KB |
testcase_13 | AC | 86 ms
77,824 KB |
testcase_14 | AC | 141 ms
79,480 KB |
testcase_15 | AC | 64 ms
68,352 KB |
testcase_16 | AC | 64 ms
68,864 KB |
testcase_17 | AC | 134 ms
79,616 KB |
testcase_18 | AC | 65 ms
68,480 KB |
testcase_19 | AC | 98 ms
78,532 KB |
testcase_20 | AC | 63 ms
68,480 KB |
testcase_21 | AC | 72 ms
73,344 KB |
testcase_22 | AC | 100 ms
78,720 KB |
testcase_23 | AC | 190 ms
79,396 KB |
testcase_24 | AC | 139 ms
79,744 KB |
testcase_25 | AC | 197 ms
80,780 KB |
testcase_26 | AC | 298 ms
80,516 KB |
testcase_27 | AC | 184 ms
79,788 KB |
testcase_28 | AC | 215 ms
80,980 KB |
testcase_29 | AC | 102 ms
78,464 KB |
testcase_30 | AC | 316 ms
81,396 KB |
testcase_31 | AC | 160 ms
83,712 KB |
testcase_32 | AC | 159 ms
83,928 KB |
testcase_33 | AC | 125 ms
79,488 KB |
testcase_34 | AC | 105 ms
78,716 KB |
testcase_35 | AC | 109 ms
78,208 KB |
testcase_36 | AC | 99 ms
78,464 KB |
testcase_37 | AC | 521 ms
87,436 KB |
testcase_38 | AC | 1,157 ms
97,444 KB |
testcase_39 | AC | 243 ms
84,968 KB |
testcase_40 | AC | 718 ms
88,428 KB |
testcase_41 | AC | 815 ms
88,680 KB |
testcase_42 | AC | 953 ms
94,704 KB |
testcase_43 | AC | 149 ms
80,464 KB |
testcase_44 | AC | 156 ms
83,900 KB |
testcase_45 | AC | 113 ms
78,440 KB |
testcase_46 | AC | 112 ms
78,848 KB |
testcase_47 | AC | 158 ms
83,896 KB |
testcase_48 | AC | 100 ms
78,464 KB |
testcase_49 | AC | 197 ms
84,304 KB |
testcase_50 | AC | 107 ms
78,208 KB |
testcase_51 | AC | 151 ms
81,088 KB |
ソースコード
from typing import List, TupleN_MAX = 13popcount = [0] * (1 << N_MAX)for S in range(1, 1 << N_MAX):popcount[S] = popcount[S & (S - 1)] + 1def subset_zeta(f: List[int]):"""Inplace conversion from f to ζf. ζf is defined as follows:(ζf)(S) = Σ[T⊆S] f(T)"""n = len(f)block = 1while block < n:offset = 0while offset < n:for p in range(offset, offset + block):f[p + block] += f[p]offset += 2 * blockblock <<= 1def subset_zeta_poly(f: List[List[int]]):"""Inplace conversion from f to ζf. ζf is defined as follows:(ζf)(S) = Σ[T⊆S] f(T)"""n = len(f)block = 1while block < n:offset = 0while offset < n:for p in range(offset, offset + block):a = f[p + block]b = f[p]for i in range(N_MAX + 1):a[i] += b[i]offset += 2 * blockblock <<= 1def subset_mobius_poly(f: List[List[int]]):"""Inplace conversion from f to μf. μf is defined as follows:(μf)(S) = Σ[T⊆S] (-1)^(|S/T|) f(T)"""n = len(f)block = 1while block < n:offset = 0while offset < n:for p in range(offset, offset + block):a = f[p + block]b = f[p]for i in range(N_MAX + 1):a[i] -= b[i]offset += 2 * blockblock <<= 1def muleq(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] * nfor i in range(n):for j in range(n - i):h[i + j] += f[i] * g[j]return hdef add_rank(f: List[int]):"""Add rank"""return [[(i == popcount[S]) * f[S] for i in range(N_MAX + 1)] for S in range(len(f))]def remove_rank(rf: List[List[int]]):"""Remove rank"""return [rf[S][popcount[S]] for S in range(len(rf))]def subset_exp(f: List[int]):"""Subset subset_exp of Σ[S⊆{0,1,...,n-1}] f(S)"""assert f[0] == 0n = 0while 1 << n != len(f):n += 1rf = add_rank([1])for i in range(n):rg = add_rank(f[1 << i: 1 << (i + 1)])subset_zeta_poly(rg)for S in range(1 << i):rf[S].append(0)rg[S].insert(0, 1)a = rf[S]b = rg[S]for k in reversed(range(i + 2)):v = 0for x in range(k + 1):v += a[k - x] * b[x]b[k] = vrf.append(b)subset_mobius_poly(rf)return remove_rank(rf)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] = 1for s in range(1, 1 << n):start = 0while not ((s >> start) & 1):start += 1for cur in range(n):if cycle_dp[s][cur] == 0:continuefor 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] = 1elif popcount[s] == 2:cycle[s] = 0else:cycle[s] //= 2return cycleif __name__ == '__main__':n, m = map(int, input().split())edges = []for _ in range(m):u, v = map(int, input().split())u -= 1v -= 1edges.append((u, v))# E[S] = # of edges connecting vertices in SE = [0] * (1 << n)for u, v in edges:E[(1 << u) | (1 << v)] += 1subset_zeta(E)cycle = count_cycles(n, edges)f = [0] * (1 << n)for C in range(1, 1 << n):if cycle[C] == 0:continue# max Ct = C.bit_length() - 1# {0, ..., tX} - CS = ((1 << (t + 1)) - 1) ^ Ck = popcount[S]bit_deposit = [0] * (1 << k)bit_deposit[0] = Sfor A in range(1, 1 << k):bit_deposit[A] = (bit_deposit[A - 1] - 1) & Sbit_deposit.reverse()g = [0] * (1 << k)for A in range(1 << k):g[A] = f[bit_deposit[A]] * (E[bit_deposit[A] | C] - E[bit_deposit[A]] - E[C])for A, hA in enumerate(subset_exp(g)):f[bit_deposit[A] | C] += cycle[C] * hAprint(subset_exp(f)[-1])