結果
| 問題 |
No.2907 Business Revealing Dora Tiles
|
| コンテスト | |
| ユーザー |
|
| 提出日時 | 2024-06-06 14:42:33 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 7,434 bytes |
| コンパイル時間 | 5,465 ms |
| コンパイル使用メモリ | 82,448 KB |
| 実行使用メモリ | 114,584 KB |
| 最終ジャッジ日時 | 2024-09-23 12:00:41 |
| 合計ジャッジ時間 | 74,707 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 41 TLE * 1 -- * 15 |
ソースコード
from collections import deque
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_jordan(r: int, c: int, m: list[list[int]]) -> tuple[int, list[int], list[int]]:
members=[]
not_members=[]
rank=0
for i in range(c):
pivot=-1
for j in range(rank, r):
if m[j][i]>0:
pivot=j
break
if pivot==-1:
not_members.append(i)
continue
members.append(i)
m[pivot], m[rank]=m[rank], m[pivot]
inv=nim_inv(m[rank][i])
m[rank][i]=1
for k in range(i+1, c):
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(i+1, c):
m[j][k]^=nim_product(m[rank][k], factor)
rank+=1
if rank==r:
not_members+=[j for j in range(i+1, c)]
break
return rank, members, not_members
def dynamic_matrix_rank(rank: int, a_col: int, from_col: int, to_col: int, u: list[list[int]], m: list[list[int]]) -> int:
v=[0]*rank
for i in range(rank):
v[i]=m[i][from_col]^m[i][to_col]
v2=[0]*rank
for i in range(rank):
for j in range(rank):
v2[i]^=nim_product(u[i][j], v[j])
if v2[a_col]==1:
return 0
clean=[0]*rank
inv=nim_inv(v2[a_col]^1)
for i in range(rank):
if i==a_col:
clean[i]=inv ^ 1
else:
clean[i]=nim_product(v2[i], inv)
u_row=u[a_col][:]
for i in range(rank):
for j in range(rank):
u[i][j]^=nim_product(clean[i], u_row[j])
return 1
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)]
rank, members, not_members=gauss_jordan(t, n, h)
s=sum(1 << i for i in members)
seen=[0]*(1<<n)
ranks=[0]*(1<<n)
seen[s]=1
ranks[s]=rank
u=[[int(i==j) for j in range(rank)] for i in range(rank)]
stack=deque[tuple[int, int]]()
stack.append((s+(1<<n), n*(1<<n)))
stack.append((s, n*(1<<n)))
while stack:
s, ij=stack.pop()
i=ij>>n
j=ij-(i<<n)
if s<(1<<n):
if i<n:
if dynamic_matrix_rank(rank, i, members[i], not_members[j], u, h):
ranks[s]=rank
members[i],not_members[j]=not_members[j],members[i]
else:
continue
for i in range(len(members)):
for j in range(len(not_members)):
new_s=s-(1<<members[i])+(1<<not_members[j])
if seen[new_s]:
continue
seen[new_s]=1
stack.append((new_s+(1<<n), i*(1<<n)+j))
stack.append((new_s, i*(1<<n)+j))
else:
s-=1<<n
if i<n and ranks[s]>0:
members[i],not_members[j]=not_members[j],members[i]
dynamic_matrix_rank(rank, i, members[i], not_members[j], u, h)
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)