結果

問題 No.2507 Yet Another Subgraph Counting
ユーザー suisensuisen
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
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 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
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, 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 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 = 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 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 = 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 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] * n
    for i in range(n):
        for j in range(n - i):
            h[i + j] += f[i] * g[j]

    return h

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 subset_exp of Σ[S⊆{0,1,...,n-1}] f(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)])
        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 = 0
                for x in range(k + 1):
                    v += a[k - x] * b[x]
                b[k] = v
            rf.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] = 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 = [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] * hA

    print(subset_exp(f)[-1])
0