結果

問題 No.2907 Business Revealing Dora Tiles
ユーザー 👑 獅子座じゃない人
提出日時 2024-06-07 10:37:18
言語 PyPy3
(7.3.15)
結果
TLE  
実行時間 -
コード長 5,871 bytes
コンパイル時間 6,068 ms
コンパイル使用メモリ 82,180 KB
実行使用メモリ 100,728 KB
最終ジャッジ日時 2024-09-23 12:17:54
合計ジャッジ時間 72,881 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 41 TLE * 1 -- * 15
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 itertools import combinations
nim_prod_table=[[0]*256 for _ in range(256)]
nim_inv_table=[0]*65536
def nim_prod_precalc():
    nim_prod_table[0][0]=0
    nim_prod_table[0][1]=0
    nim_prod_table[1][0]=0
    nim_prod_table[1][1]=1
    nim_inv_table[1]=1
    for d in range(3):
        p=1<<d
        for a in range(1<<(2*p)):
            for b in range(1<<p, 1<<(2*p)):
                a_h=a>>p
                a_l=a-(a_h<<p)
                b_h=b>>p
                b_l=b-(b_h<<p)
                al_bl=nim_prod_table[a_l][b_l]
                ahl_bhl=nim_prod_table[a_h^a_l][b_h^b_l]
                ah_bh=nim_prod_table[a_h][b_h]
                ah_bh_h=nim_prod_table[ah_bh][1<<(p-1)]
                nim_prod_table[a][b]=nim_prod_table[b][a]=((al_bl^ahl_bhl)<<p)^(al_bl^ah_bh_h)
                if nim_prod_table[a][b]==1:
                    nim_inv_table[a]=b
                    nim_inv_table[b]=a
def nim_product_power(a: int, n: int, p: int=64) -> int:
    if p==64:
        if a<(1<<8) and n<8:
            p=8
        elif a<(1<<16) and n<16:
            p=16
        elif a<(1<<32) and n<32:
            p=32
    if p==8:
        return nim_prod_table[a][1<<n]
    p//=2
    a_h=a>>p
    a_l=a-(a_h<<p)
    if n<p:
        return (nim_product_power(a_h, n, p)<<p)^nim_product_power(a_l, n, p)
    else:
        n-=p
        return (nim_product_power(a_h^a_l, n, p)<<p)^nim_product_power(nim_product_power(a_h, n, p), p-1, p)
def nim_square(a: int, p: int=64) -> int:
    if p==64:
        if a<(1<<8):
            p=8
        elif a<(1<<16):
            p=16
        elif a<(1<<32):
            p=32
    if p==8:
        return nim_prod_table[a][a]
    p//=2
    a_h=a>>p
    a_l=a-(a_h << p)
    h_sq=nim_square(a_h, p)
    l_sq=nim_square(a_l, p)
    return (h_sq<<p)^nim_product_power(h_sq, p-1, p)^l_sq
def nim_product(a: int, b: int, p: int=64) -> int:
    if a==0 or b==0:
        return 0
    if a==1:
        return b
    if b==1:
        return a
    if p==64:
        if a<(1<<8) and b<(1<<8):
            p=8
        elif a<(1<<16) and b<(1<<16):
            p=16
        elif a<(1<<32) and b<(1<<32):
            p=32
    if p==8:
        return nim_prod_table[a][b]
    p//=2
    a_h=a>>p
    a_l=a-(a_h<<p)
    b_h=b>>p
    b_l=b-(b_h<<p)
    al_bl=nim_product(a_l, b_l, p)
    ahl_bhl=nim_product(a_h^a_l, b_h^b_l, p)
    ah_bh=nim_product(a_h, b_h, p)
    ah_bh_h=nim_product_power(ah_bh, p-1, p)
    return ((al_bl^ahl_bhl)<<p)^(al_bl^ah_bh_h)
def nim_inv_precalc():
    for a in range(1<<8, 1<<16):
        p=8
        a_h=a>>p
        a_l=a-(a_h<<p)
        half_inv=nim_inv_table[nim_product(a_h^a_l, a_l, p)^nim_product_power(nim_square(a_h, p), p-1, p)]
        nim_inv_table[a]=(nim_product(half_inv, a_h, p)<<p)^nim_product(half_inv, a_h^a_l, p)
def nim_inv(a: int, p: int=64) -> int:
    if p==64:
        if a<(1<<16):
            p=16
        elif a<(1<<32):
            p=32
    if p==16:
        return nim_inv_table[a]
    p//=2
    a_h=a>>p
    a_l=a-(a_h<<p)
    half_inv=nim_inv(nim_product(a_h^a_l, a_l, p)^nim_product_power(nim_square(a_h, p), p-1, p), p)
    return (nim_product(half_inv, a_h, p)<<p)^nim_product(half_inv, a_h^a_l, p)
def gauss(r: int, c: int, m: list[list[int]], exists: list[int]) -> int:
    rank=0
    for i in range(c):
        if not exists[i]:
            continue
        pivot=-1
        for j in range(rank, r):
            if m[j][i]>0:
                pivot=j
                break
        if pivot==-1:
            continue
        m[pivot], m[rank]=m[rank], m[pivot]
        if rank==r-1:
            rank+=1
            break
        inv=nim_inv(m[rank][i])
        m[rank][i]=1
        for k in range(0, c):
            if k==i:
                continue
            m[rank][k]=nim_product(m[rank][k], inv)
        for j in range(r):
            if j==rank:
                continue
            factor=m[j][i]
            m[j][i]=0
            for k in range(0, c):
                if k==i:
                    continue
                m[j][k]^=nim_product(m[rank][k], factor)
        rank+=1
    return rank
nim_prod_precalc()
nim_inv_precalc()
n,t=map(int, input().split())
h=[list(map(lambda a: int(a)-1, input().split())) for _ in range(t)]
for i in range(t):
    h[i].reverse()
rank=gauss(t, n, h, [1]*n)
ranks=[0]*(1<<n)
for members_tuple in combinations(range(n), rank):
    members=list(members_tuple)
    is_member=[0]*n
    s=0
    for i in members:
        is_member[i]=1
        s+=1<<i
    if gauss(rank, n, h, is_member)==rank:
        ranks[s]=rank
for r in reversed(range(rank)):
    for members_tuple in combinations(range(n), r):
        members=list(members_tuple)
        is_member=[0]*n
        s=0
        for i in members:
            is_member[i]=1
            s+=1<<i
        for i in range(n):
            if is_member[i]:
                continue
            if ranks[s+(1<<i)]>0:
                ranks[s]=r
                break
for r in range(n):
    for members_tuple in combinations(range(n), r):
        members=list(members_tuple)
        is_member=[0]*n
        s=0
        for i in members:
            is_member[i]=1
            s+=1<<i
        for i in range(n):
            if is_member[i]:
                continue
            ranks[s+(1<<i)]=max(ranks[s], ranks[s+(1<<i)])
ans=0
mods=[1, 932051910, 299560064, 268998206, 169907034, 617122664, 934978948, 751815647, 60241440, 910883406, 623687709, 299771973, 824242875, 286857587
    , 12424206, 89078497, 595200811, 971438438, 608817788, 778210505, 170380535]
MOD=998244353
for s in range(1<<n):
    count=s.bit_count()
    if n%2>0:
        if count%2>0:
            ans+=mods[count-ranks[s]]
        else:
            ans-=mods[count-ranks[s]]
    else:
        if count%2>0:
            ans-=mods[count-ranks[s]]
        else:
            ans+=mods[count-ranks[s]]
    ans%=MOD
print(ans)
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