結果

問題 No.2507 Yet Another Subgraph Counting
ユーザー suisensuisen
提出日時 2023-08-21 04:57:32
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,740 ms / 2,000 ms
コード長 4,612 bytes
コンパイル時間 198 ms
コンパイル使用メモリ 82,048 KB
実行使用メモリ 114,180 KB
最終ジャッジ日時 2024-09-15 14:13:41
合計ジャッジ時間 16,492 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge6
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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 # 

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)):
        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