結果

問題 No.2507 Yet Another Subgraph Counting
ユーザー suisen
提出日時 2023-08-31 22:10:59
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,194 ms / 2,000 ms
コード長 4,459 bytes
コンパイル時間 269 ms
コンパイル使用メモリ 81,920 KB
実行使用メモリ 96,492 KB
最終ジャッジ日時 2024-09-15 14:17:44
合計ジャッジ時間 12,763 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
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ファイルパターン 結果
other AC * 52
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 #
プレゼンテーションモードにする

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 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 = 1
    while block < n:
        offset = 0
        while offset < n:
            for p in range(offset, offset + block):
                f[p + block] += f[p]
            offset += 2 * block
        block <<= 1
def ranked_zeta(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 = 1
    while block < n:
        offset = 0
        while 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 * block
        block <<= 1
def ranked_mobius(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 = 1
    while block < n:
        offset = 0
        while 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 * block
        block <<= 1
def 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 exp of Σ[S⊆{0,1,...,n-1}] f(S) x^S
    """
    assert f[0] == 0
    n = 0
    while 1 << n != len(f):
        n += 1
    rf = add_rank([1])
    for i in range(n):
        rg = add_rank(f[1 << i: 1 << (i + 1)])
        ranked_zeta(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 = 0
                for x in range(k + 1):
                    v += a[k - x] * b[x]
                b[k] = v
            rf.append(b)
    ranked_mobius(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] = 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
if __name__ == '__main__':
    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)
    cycle = count_cycles(n, edges)
    f = [0] * (1 << n)
    for C in range(1, 1 << n):
        if cycle[C] == 0:
            continue
        # max C
        t = C.bit_length() - 1
        # {0, ..., tX} - C
        S = ((1 << (t + 1)) - 1) ^ C
        k = popcount[S]
        bit_deposit = [0] * (1 << k)
        bit_deposit[0] = S
        for A in range(1, 1 << k):
            bit_deposit[A] = (bit_deposit[A - 1] - 1) & S
        bit_deposit.reverse()
        g = [f[bit_deposit[A]] * (E[bit_deposit[A] | C] - E[bit_deposit[A]] - E[C]) for A in range(1 << k)]
        for A, hA in enumerate(subset_exp(g)):
            f[bit_deposit[A] | C] += cycle[C] * hA
    print(subset_exp(f)[-1])
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