結果

問題 No.2507 Yet Another Subgraph Counting
ユーザー suisensuisen
提出日時 2023-08-21 22:42:49
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,856 ms / 2,000 ms
コード長 4,561 bytes
コンパイル時間 301 ms
コンパイル使用メモリ 81,920 KB
実行使用メモリ 127,140 KB
最終ジャッジ日時 2024-09-15 14:14:47
合計ジャッジ時間 31,703 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
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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 104 ms
77,952 KB
testcase_01 AC 104 ms
78,336 KB
testcase_02 AC 106 ms
78,080 KB
testcase_03 AC 80 ms
70,784 KB
testcase_04 AC 77 ms
69,248 KB
testcase_05 AC 269 ms
80,344 KB
testcase_06 AC 75 ms
68,864 KB
testcase_07 AC 103 ms
78,464 KB
testcase_08 AC 131 ms
78,848 KB
testcase_09 AC 76 ms
69,120 KB
testcase_10 AC 133 ms
78,976 KB
testcase_11 AC 269 ms
80,604 KB
testcase_12 AC 131 ms
79,104 KB
testcase_13 AC 132 ms
78,976 KB
testcase_14 AC 276 ms
80,760 KB
testcase_15 AC 76 ms
68,864 KB
testcase_16 AC 78 ms
69,504 KB
testcase_17 AC 275 ms
80,560 KB
testcase_18 AC 77 ms
69,632 KB
testcase_19 AC 229 ms
80,888 KB
testcase_20 AC 77 ms
69,120 KB
testcase_21 AC 105 ms
78,080 KB
testcase_22 AC 135 ms
79,488 KB
testcase_23 AC 280 ms
80,564 KB
testcase_24 AC 190 ms
80,016 KB
testcase_25 AC 392 ms
81,972 KB
testcase_26 AC 749 ms
91,068 KB
testcase_27 AC 279 ms
80,516 KB
testcase_28 AC 394 ms
81,576 KB
testcase_29 AC 134 ms
79,488 KB
testcase_30 AC 734 ms
91,588 KB
testcase_31 AC 1,825 ms
123,568 KB
testcase_32 AC 1,767 ms
125,616 KB
testcase_33 AC 274 ms
81,292 KB
testcase_34 AC 228 ms
80,576 KB
testcase_35 AC 273 ms
80,460 KB
testcase_36 AC 178 ms
79,636 KB
testcase_37 AC 1,771 ms
124,104 KB
testcase_38 AC 1,856 ms
124,756 KB
testcase_39 AC 1,846 ms
125,448 KB
testcase_40 AC 1,821 ms
124,240 KB
testcase_41 AC 1,845 ms
125,212 KB
testcase_42 AC 1,792 ms
124,384 KB
testcase_43 AC 724 ms
88,284 KB
testcase_44 AC 1,818 ms
123,688 KB
testcase_45 AC 268 ms
80,860 KB
testcase_46 AC 271 ms
80,604 KB
testcase_47 AC 1,790 ms
123,568 KB
testcase_48 AC 179 ms
79,760 KB
testcase_49 AC 1,833 ms
127,140 KB
testcase_50 AC 229 ms
80,880 KB
testcase_51 AC 720 ms
88,448 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 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: int, mask: int, bitwidth: int):
    dst = 0
    j = 0
    for i in range(bitwidth):
        if (mask >> i) & 1:
            dst |= ((src >> j) & 1) << i
            j += 1
    return dst

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

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 = count_cycles(n, edges)

f = [0] * (1 << n)
for C in range(1, 1 << n):
    v = C.bit_length() - 1
    mask = ((1 << (v + 1)) - 1) ^ C
    k = popcount[mask]

    g = [0] * (1 << k)
    for A in range(1 << k):
        T = bit_deposit(A, mask, v)
        g[A] = f[T] * (E[T | C] - E[T] - E[C])

    h = exp(g, k)
    for A in range(1 << k):
        X = bit_deposit(A, mask, v) | C
        f[X] += cycle[C] * h[A]

print(exp(f, n)[-1])
0