結果

問題 No.2507 Yet Another Subgraph Counting
ユーザー suisensuisen
提出日時 2023-08-21 04:56:10
言語 PyPy3
(7.3.15)
結果
TLE  
(最新)
AC  
(最初)
実行時間 -
コード長 4,644 bytes
コンパイル時間 429 ms
コンパイル使用メモリ 87,036 KB
実行使用メモリ 108,644 KB
最終ジャッジ日時 2023-08-31 23:09:30
合計ジャッジ時間 22,965 ms
ジャッジサーバーID
（参考情報） 		judge13 / judge15
このコードへのチャレンジ
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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 178 ms
82,124 KB
testcase_01 AC 177 ms
82,028 KB
testcase_02 AC 177 ms
82,448 KB
testcase_03 AC 168 ms
80,852 KB
testcase_04 AC 166 ms
81,132 KB
testcase_05 AC 235 ms
83,392 KB
testcase_06 AC 164 ms
81,044 KB
testcase_07 AC 174 ms
81,712 KB
testcase_08 AC 186 ms
82,480 KB
testcase_09 AC 167 ms
81,136 KB
testcase_10 AC 182 ms
82,584 KB
testcase_11 AC 243 ms
84,252 KB
testcase_12 AC 182 ms
82,448 KB
testcase_13 AC 189 ms
82,464 KB
testcase_14 AC 263 ms
84,680 KB
testcase_15 AC 165 ms
81,352 KB
testcase_16 AC 162 ms
81,180 KB
testcase_17 AC 259 ms
84,112 KB
testcase_18 AC 169 ms
80,904 KB
testcase_19 AC 220 ms
83,380 KB
testcase_20 AC 167 ms
81,036 KB
testcase_21 AC 178 ms
81,876 KB
testcase_22 AC 208 ms
82,812 KB
testcase_23 AC 382 ms
86,436 KB
testcase_24 AC 260 ms
83,788 KB
testcase_25 AC 375 ms
86,640 KB
testcase_26 AC 618 ms
89,124 KB
testcase_27 AC 334 ms
86,652 KB
testcase_28 AC 389 ms
86,676 KB
testcase_29 AC 213 ms
82,932 KB
testcase_30 AC 680 ms
89,432 KB
testcase_31 AC 324 ms
90,616 KB
testcase_32 AC 336 ms
90,812 KB
testcase_33 AC 247 ms
84,160 KB
testcase_34 AC 216 ms
83,364 KB
testcase_35 AC 228 ms
83,432 KB
testcase_36 AC 200 ms
82,692 KB
testcase_37 AC 966 ms
95,728 KB
testcase_38 TLE -
testcase_39 AC 491 ms
91,264 KB
testcase_40 AC 1,236 ms
98,724 KB
testcase_41 AC 1,902 ms
107,420 KB
testcase_42 TLE -
testcase_43 AC 274 ms
85,544 KB
testcase_44 AC 316 ms
90,872 KB
testcase_45 AC 229 ms
83,396 KB
testcase_46 AC 228 ms
83,420 KB
testcase_47 AC 312 ms
89,620 KB
testcase_48 AC 208 ms
83,172 KB
testcase_49 AC 406 ms
92,148 KB
testcase_50 AC 220 ms
83,192 KB
testcase_51 AC 287 ms
85,572 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

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 subset_conv(f: List[int], g: List[int], n: int):
    rf = ranked(f, n)
    rg = ranked(g, n)
    subset_zeta_poly(rf, n)
    subset_zeta_poly(rg, n)
    for i in range(1 << n):
        rf[i] = mul_poly(rf[i], rg[i])
    subset_mobius_poly(rf, n)
    return deranked(rf, n)

def exp(f: List[int], n: int):
    """
    Subset exp of Σ[S⊆{0,1,...,n-1}] f(S)
    """
    assert f[0] == 0
    g = [1]
    for i in range(n):
        g += subset_conv(g, f[1 << i: 1 << (i + 1)], i)
    return g

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)):
        if cycle[X] == 0:
            continue
        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])
0