結果

問題 No.2507 Yet Another Subgraph Counting
ユーザー suisensuisen
提出日時 2023-08-21 04:38:39
言語 PyPy3
(7.3.15)
結果
TLE  
(最新)
AC  
(最初)
実行時間 -
コード長 4,597 bytes
コンパイル時間 557 ms
コンパイル使用メモリ 87,076 KB
実行使用メモリ 116,496 KB
最終ジャッジ日時 2023-08-31 23:09:07
合計ジャッジ時間 43,190 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 186 ms
82,556 KB
testcase_01 AC 192 ms
82,376 KB
testcase_02 AC 189 ms
82,216 KB
testcase_03 AC 173 ms
81,836 KB
testcase_04 AC 167 ms
81,104 KB
testcase_05 AC 395 ms
86,184 KB
testcase_06 AC 167 ms
81,100 KB
testcase_07 AC 188 ms
82,292 KB
testcase_08 AC 214 ms
82,816 KB
testcase_09 AC 167 ms
81,148 KB
testcase_10 AC 217 ms
82,768 KB
testcase_11 AC 396 ms
86,168 KB
testcase_12 AC 217 ms
82,936 KB
testcase_13 AC 217 ms
83,112 KB
testcase_14 AC 395 ms
85,712 KB
testcase_15 AC 166 ms
81,224 KB
testcase_16 AC 166 ms
80,856 KB
testcase_17 AC 399 ms
85,868 KB
testcase_18 AC 164 ms
80,996 KB
testcase_19 AC 332 ms
84,936 KB
testcase_20 AC 169 ms
81,252 KB
testcase_21 AC 187 ms
82,536 KB
testcase_22 AC 221 ms
82,964 KB
testcase_23 AC 409 ms
88,124 KB
testcase_24 AC 275 ms
83,828 KB
testcase_25 AC 535 ms
88,360 KB
testcase_26 AC 966 ms
93,868 KB
testcase_27 AC 412 ms
86,744 KB
testcase_28 AC 534 ms
88,416 KB
testcase_29 AC 223 ms
82,900 KB
testcase_30 AC 958 ms
93,524 KB
testcase_31 TLE -
testcase_32 TLE -
testcase_33 AC 398 ms
86,484 KB
testcase_34 AC 329 ms
85,248 KB
testcase_35 AC 385 ms
86,064 KB
testcase_36 AC 264 ms
83,772 KB
testcase_37 TLE -
testcase_38 TLE -
testcase_39 TLE -
testcase_40 TLE -
testcase_41 TLE -
testcase_42 TLE -
testcase_43 AC 950 ms
91,468 KB
testcase_44 TLE -
testcase_45 AC 396 ms
86,096 KB
testcase_46 AC 392 ms
86,140 KB
testcase_47 TLE -
testcase_48 AC 268 ms
84,084 KB
testcase_49 TLE -
testcase_50 AC 343 ms
84,916 KB
testcase_51 AC 959 ms
94,124 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)):
        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