結果
| 問題 |
No.1136 Four Points Tour
|
| ユーザー |
👑  Kazun
|
| 提出日時 | 2020-07-29 02:01:26 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 63 ms / 2,000 ms |
| コード長 | 9,542 bytes |
| コンパイル時間 | 177 ms |
| コンパイル使用メモリ | 82,256 KB |
| 実行使用メモリ | 66,304 KB |
| 最終ジャッジ日時 | 2024-06-28 21:10:48 |
| 合計ジャッジ時間 | 3,807 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 41 |
ソースコード
class Matrix_Error(Exception):
pass
class Matrix():
#入力
def __init__(self,M=[]):
self.ele=M
R=len(M)
if R!=0:
C=len(M[1])
else:
C=0
self.row=R
self.col=C
self.size=(R,C)
#出力
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 __pos__(self):
return self
def __neg__(self):
return self.__scale__(-1)
#加法
def __add__(A,B):
if A.size!=B.size:
raise Matrix_Error("2つの行列のサイズが異なります.({},{})".format(A.size,B.size))
M=A.ele
N=B.ele
L=[]
for i in range(A.row):
E=[]
for j in range(A.col):
E.append(M[i][j]+N[i][j])
L.append(E)
return Matrix(L)
#減法
def __sub__(A,B):
return A+(-B)
#乗法
def __mul__(A,B):
if isinstance(B,Matrix):
R=A.row
C=B.col
if A.col!=B.row:
raise Matrix_Error("左側の列と右側の行が一致しません.({},{})".format(A.size,B.size))
G=A.col
M=A.ele
N=B.ele
E=[]
for i in range(R):
F=[]
for j in range(C):
S=0
for k in range(G):
S+=M[i][k]*N[k][j]
F.append(S)
E.append(F)
return Matrix(E)
elif isinstance(B,int):
return A.__scale__(B)
def __rmul__(A,B):
if isinstance(B,int):
return A*B
def Inverse(M):
if M.row!=M.col:
raise Matrix_Error("正方行列ではありません.")
R=M.row
I=[[1*(i==j) for j in range(R)] for i in range(R)]
G=M.Column_Union(Matrix(I))
G=G.Row_Reduce()
A,B=[],[]
for i in range(R):
A.append(copy(G.ele[i][:R]))
B.append(copy(G.ele[i][R:]))
if A==I:
return Matrix(B)
else:
raise Matrix_Error("正則ではありません.")
#スカラー倍
def __scale__(A,r):
M=A.ele
L=[[r*M[i][j] for j in range(A.col)] for i in range(A.row)]
return Matrix(L)
#累乗
def __pow__(A,n):
if A.row!=A.col:
raise Matrix_Error("正方行列ではありません.")
if n<0:
return (A**(-n)).Inverse()
R=Matrix([[1*(i==j) for j in range(A.row)] for i in range(A.row)])
D=A
while n>0:
if n%2==1:
R*=D
D*=D
n=n>>1
return R
#等号
def __eq__(A,B):
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
#不等号
def __neq__(A,B):
return not(A==B)
#転置
def Transpose(self):
self.col,self.row=self.row,self.col
self.ele=list(map(list,zip(*self.ele)))
#行基本変形
def Row_Reduce(M):
(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]
for j in range(C):
T[I][j]/=u
for i in range(R):
if i!=I:
v=T[i][J]
for j in range(C):
T[i][j]-=v*T[I][j]
I+=1
if I==R:
break
return Matrix(T)
#列基本変形
def Column_Reduce(M):
(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]
for i in range(R):
T[i][J]/=u
for j in range(C):
if j!=J:
v=T[I][j]
for i in range(R):
T[i][j]-=v*T[i][J]
J+=1
if J==C:
break
return Matrix(T)
#行列の階数
def Rank(M,ep=None):
M=M.Row_Reduce()
(R,C)=M.size
T=M.ele
S=0
for i in range(R):
f=False
if ep==None:
for j in range(C):
if T[i][j]!=0:
f=True
else:
for j in range(C):
if abs(T[i][j])>=ep:
f=True
if f:
S+=1
else:
break
return S
#行の結合
def Row_Union(self,other):
return Matrix(self.ele+other.ele)
#列の結合
def Column_Union(self,other):
E=[]
for i in range(self.row):
E.append(self.ele[i]+other.ele[i])
return Matrix(E)
#-------------------------------------------------
class Modulo_Error(Exception):
pass
class Modulo():
def __init__(self,a,n):
self.a=a%n
self.n=n
def __str__(self):
return "{} (mod {})".format(self.a,self.n)
#+,-
def __pos__(self):
return self
def __neg__(self):
return Modulo(-self.a,self.n)
#等号,不等号
def __eq__(self,other):
if isinstance(other,Modulo):
return (self.a==other.a) and (self.n==other.n)
elif isinstance(other,int):
return (self-other).a==0
def __neq__(self,other):
return not(self==other)
#加法
def __add__(self,other):
if isinstance(other,Modulo):
if self.n!=other.n:
raise Modulo_Error("異なる法同士の演算です.")
return Modulo(self.a+other.a,self.n)
elif isinstance(other,int):
return Modulo(self.a+other,self.n)
def __radd__(self,other):
if isinstance(other,int):
return Modulo(self.a+other,self.n)
#減法
def __sub__(self,other):
return self+(-other)
def __rsub__(self,other):
if isinstance(other,int):
return -self+other
#乗法
def __mul__(self,other):
if isinstance(other,Modulo):
if self.n!=other.n:
raise Modulo_Error("異なる法同士の演算です.")
return Modulo(self.a*other.a,self.n)
elif isinstance(other,int):
return Modulo(self.a*other,self.n)
def __rmul__(self,other):
if isinstance(other,int):
return Modulo(self.a*other,self.n)
#Modulo逆数
def Modulo_Inverse(self):
x0, y0, x1, y1 = 1, 0, 0, 1
a,b=self.a,self.n
while b != 0:
q, a, b = a // b, b, a % b
x0, x1 = x1, x0 - q * x1
y0, y1 = y1, y0 - q * y1
if a!=1:
raise Modulo_Error("{}の逆数が存在しません".format(self))
else:
return Modulo(x0,self.n)
#除法
def __truediv__(self,other):
return self*(other.Modulo_Inverse())
def __rtruediv__(self,other):
return other*(self.Modulo_Inverse())
#累乗
def __pow__(self,m):
u=abs(m)
r=Modulo(1,self.n)
while u>0:
if u%2==1:
r*=self
self*=self
u=u>>1
if m>=0:
return r
else:
return r.Modulo_Inverse()
#根号
def sqrt(self):
if self==0:
return self
elif self.n==2:
return self
elif self.n%4==3:
return self**((self.n+1)//4)
else:
p=self.n
u=2
s=1
while (p-1)%(2*u)==0:
u*=2
s+=1
z=Modulo(2,p)
while z**((p-1)//2)!=-1:
z+=1
q=(p-1)//u
m=s
c=z**q
t=self**q
r=self**((q+1)//2)
while m>1:
k=1
d=t*t
while d!=1:
k+=1
d*=d
print(m,k)
b=Modulo(2,p)**(2**(m-k-1))
c,t,r,m=b*b,t*b*b,r*b,k
return r
#-------------------------------------------------
N=int(input())
K=10**9+7
a=Modulo(1,K)
M=Matrix([[0,a,a,a],[a,0,a,a],[a,a,0,a],[a,a,a,0]])
print((M**N).ele[0][0].a)