結果

問題 No.1750 ラムドスウイルスの感染拡大-hard
ユーザー 👑 Kazun
提出日時 2021-11-19 21:41:55
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,538 ms / 2,000 ms
コード長 8,764 bytes
コンパイル時間 395 ms
コンパイル使用メモリ 82,596 KB
実行使用メモリ 82,116 KB
最終ジャッジ日時 2024-12-31 22:22:19
合計ジャッジ時間 18,589 ms
ジャッジサーバーID
(参考情報)
judge4 / judge1
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 * 4
other AC * 30
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

class Modulo_Matrix():
#
def __init__(self,M,Mod):
self.ele=[[x%Mod for x in X] for X in M]
self.Mod=Mod
R=len(M)
if R!=0:
C=len(M[0])
else:
C=0
self.row=R
self.col=C
self.size=(R,C)
#
def __str__(self):
T=""
(r,c)=self.size
for i in range(r):
U="["
for j in range(c):
U+=str(self.ele[i][j])+" "
T+=U[:-1]+"]\n"
return "["+T[:-1]+"]"
def __repr__(self):
return str(self)
#+,-
def __pos__(self):
return self
def __neg__(self):
return self.__scale__(-1)
#
def __add__(self,other):
self.__is_calculatable(other)
M=self.ele; N=other.ele
L=[[0]*self.col for _ in range(self.row)]
for i in range(self.row):
Li,Mi,Ni=L[i],M[i],N[i]
for j in range(self.col):
Li[j]=Mi[j]+Ni[j]
return Modulo_Matrix(L,self.Mod)
def __iadd__(self,other):
self.__is_calculatable(other)
M=self.ele; N=other.ele
for i in range(self.row):
Mi,Ni=M[i],N[i]
for j in range(self.col):
Mi[j]+=Ni[j]
Mi[j]%=self.Mod
return self
#
def __sub__(self,other):
self.__is_calculatable(other)
M=self.ele; N=other.ele
L=[[0]*self.col for _ in range(self.row)]
for i in range(self.row):
Li,Mi,Ni=L[i],M[i],N[i]
for j in range(self.col):
Li[j]=Mi[j]-Ni[j]
return Modulo_Matrix(L,self.Mod)
def __isub__(self,other):
self.__is_calculatable(other)
M=self.ele; N=other.ele
for i in range(self.row):
Mi,Ni=M[i],N[i]
for j in range(self.col):
Mi[j]-=Ni[j]
Mi[j]%=self.Mod
return self
#
def __mul__(self,other):
if isinstance(other,Modulo_Matrix):
if self.col!=other.row:
raise Modulo_Matrix_Error(".({},{})".format(self.size,other.size))
M=self.ele; N=other.ele
E=[[0]*other.col for _ in range(self.row)]
for i in range(self.row):
Ei,Mi=E[i],M[i]
for k in range(self.col):
m_ik,Nk=Mi[k],N[k]
for j in range(other.col):
Ei[j]+=m_ik*Nk[j]
Ei[j]%=self.Mod
return Modulo_Matrix(E,self.Mod)
elif isinstance(other,int):
return self.__scale__(other)
def __rmul__(self,other):
if isinstance(other,int):
return self.__scale__(other)
def Inverse(self):
if self.row!=self.col:
raise Modulo_Matrix_Error(".")
M=self
N=M.row; Mod=M.Mod
R=[[int(i==j) for j in range(N)] for i in range(N)]
T=deepcopy(M.ele)
for j in range(N):
if T[j][j]==0:
for i in range(j+1,N):
if T[i][j]:
break
else:
raise Modulo_Matrix_Error("")
T[j],T[i]=T[i],T[j]
R[j],R[i]=R[i],R[j]
Tj,Rj=T[j],R[j]
inv=pow(Tj[j],Mod-2,Mod)
for k in range(N):
Tj[k]*=inv; Tj[k]%=Mod
Rj[k]*=inv; Rj[k]%=Mod
for i in range(N):
if i==j: continue
c=T[i][j]
Ti,Ri=T[i],R[i]
for k in range(N):
Ti[k]-=Tj[k]*c; Ti[k]%=Mod
Ri[k]-=Rj[k]*c; Ri[k]%=Mod
return Modulo_Matrix(R,Mod)
#
def __scale__(self,r):
M=self.ele
L=[[(r*M[i][j])%self.Mod for j in range(self.col)] for i in range(self.row)]
return Modulo_Matrix(L,self.Mod)
#
def __pow__(self,n):
if self.row!=self.col:
raise Modulo_Matrix_Error(".")
def __mat_mul(A,B,r,Mod):
E=[[0]*r for _ in range(r)]
for i in range(r):
a=A[i]; e=E[i]
for k in range(r):
b=B[k]
for j in range(r):
e[j]+=a[k]*b[j]
e[j]%=Mod
return E
def __mat_pow(A,n,r,Mod):
if n==0:
return [[1 if i==j else 0 for j in range(r)] for i in range(r)]
else:
return __mat_mul(__mat_pow(A,n-1,r,Mod),A,r,Mod) if n&1 else __mat_pow(__mat_mul(A,A,r,Mod),n>>1,r,Mod)
S=__mat_pow(self.ele,abs(n),self.col,self.Mod)
if n>=0:
return Modulo_Matrix(S,self.Mod)
else:
return Modulo_Matrix(S,self.Mod).Inverse()
#
def __eq__(self,other):
A=self
B=other
if A.size!=B.size:
return False
for i in range(A.row):
for j in range(A.col):
if A.ele[i][j]!=B.ele[i][j]:
return False
return True
#
def __neq__(self,other):
return not(self==other)
#
def Transpose(self):
self.col,self.row=self.row,self.col
self.ele=list(map(list,zip(*self.ele)))
#
def Row_Reduce(self):
M=self
(R,C)=M.size
T=[]
for i in range(R):
U=[]
for j in range(C):
U.append(M.ele[i][j])
T.append(U)
I=0
for J in range(C):
if T[I][J]==0:
for i in range(I+1,R):
if T[i][J]!=0:
T[i],T[I]=T[I],T[i]
break
if T[I][J]!=0:
u=T[I][J]
u_inv=pow(u,self.Mod-2,self.Mod)
for j in range(C):
T[I][j]*=u_inv
T[I][j]%=self.Mod
for i in range(R):
if i!=I:
v=T[i][J]
for j in range(C):
T[i][j]-=v*T[I][j]
T[i][j]%=self.Mod
I+=1
if I==R:
break
return Modulo_Matrix(T,self.Mod)
#
def Column_Reduce(self):
M=self
(R,C)=M.size
T=[]
for i in range(R):
U=[]
for j in range(C):
U.append(M.ele[i][j])
T.append(U)
J=0
for I in range(R):
if T[I][J]==0:
for j in range(J+1,C):
if T[I][j]!=0:
for k in range(R):
T[k][j],T[k][J]=T[k][J],T[k][j]
break
if T[I][J]!=0:
u=T[I][J]
u_inv=pow(u,self.Mod-2,self.Mod)
for i in range(R):
T[i][J]*=u_inv
T[i][J]%=self.Mod
for j in range(C):
if j!=J:
v=T[I][j]
for i in range(R):
T[i][j]-=v*T[i][J]
T[i][j]%=self.Mod
J+=1
if J==C:
break
return Modulo_Matrix(T,self.Mod)
#
def Rank(self):
M=self.Row_Reduce()
(R,C)=M.size
T=M.ele
S=0
for i in range(R):
f=False
for j in range(C):
if T[i][j]!=0:
f=True
break
if f:
S+=1
else:
break
return S
#
def Row_Union(self,other):
return Modulo_Matrix(self.ele+other.ele,self.Mod)
#
def Column_Union(self,other):
E=[]
for i in range(self.row):
E.append(self.ele[i]+other.ele[i])
return Modulo_Matrix(E,self.Mod)
def __getitem__(self,index):
assert isinstance(index,tuple) and len(index)==2
return self.ele[index[0]][index[1]]
def __setitem__(self,index,val):
assert isinstance(index,tuple) and len(index)==2
self.ele[index[0]][index[1]]=val
#==================================================
N,M,T=map(int,input().split())
Mod=998244353
A=Modulo_Matrix([[0]*N for _ in range(N)],Mod)
for _ in range(M):
s,t=map(int,input().split())
A[s,t]=A[t,s]=1
print(pow(A,T)[0,0])
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