結果
| 問題 | No.1704 Many Bus Stops (easy) |
| ユーザー |
👑  Kazun
|
| 提出日時 | 2022-01-12 01:11:34 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 350 ms / 2,000 ms |
| コード長 | 8,873 bytes |
| コンパイル時間 | 279 ms |
| コンパイル使用メモリ | 82,368 KB |
| 実行使用メモリ | 81,296 KB |
| 最終ジャッジ日時 | 2024-04-26 21:16:24 |
| 合計ジャッジ時間 | 13,712 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
（要ログイン）
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 | 57 ms
64,640 KB |
| testcase_01 | AC | 307 ms
78,752 KB |
| testcase_02 | AC | 243 ms
79,112 KB |
| testcase_03 | AC | 241 ms
78,520 KB |
| testcase_04 | AC | 251 ms
79,364 KB |
| testcase_05 | AC | 243 ms
78,552 KB |
| testcase_06 | AC | 264 ms
79,492 KB |
| testcase_07 | AC | 243 ms
79,244 KB |
| testcase_08 | AC | 242 ms
78,452 KB |
| testcase_09 | AC | 243 ms
79,616 KB |
| testcase_10 | AC | 249 ms
78,364 KB |
| testcase_11 | AC | 244 ms
78,472 KB |
| testcase_12 | AC | 276 ms
80,436 KB |
| testcase_13 | AC | 255 ms
79,416 KB |
| testcase_14 | AC | 252 ms
79,296 KB |
| testcase_15 | AC | 245 ms
79,460 KB |
| testcase_16 | AC | 254 ms
79,804 KB |
| testcase_17 | AC | 262 ms
78,780 KB |
| testcase_18 | AC | 261 ms
81,296 KB |
| testcase_19 | AC | 265 ms
80,428 KB |
| testcase_20 | AC | 255 ms
78,920 KB |
| testcase_21 | AC | 247 ms
78,512 KB |
| testcase_22 | AC | 335 ms
79,680 KB |
| testcase_23 | AC | 315 ms
78,532 KB |
| testcase_24 | AC | 331 ms
79,020 KB |
| testcase_25 | AC | 331 ms
79,424 KB |
| testcase_26 | AC | 350 ms
79,300 KB |
| testcase_27 | AC | 338 ms
79,296 KB |
| testcase_28 | AC | 321 ms
78,516 KB |
| testcase_29 | AC | 323 ms
78,424 KB |
| testcase_30 | AC | 313 ms
78,268 KB |
| testcase_31 | AC | 340 ms
80,312 KB |
| testcase_32 | AC | 311 ms
78,840 KB |
| testcase_33 | AC | 323 ms
79,276 KB |
| testcase_34 | AC | 328 ms
79,336 KB |
| testcase_35 | AC | 308 ms
78,456 KB |
| testcase_36 | AC | 307 ms
78,380 KB |
| testcase_37 | AC | 313 ms
78,528 KB |
| testcase_38 | AC | 334 ms
78,956 KB |
| testcase_39 | AC | 322 ms
78,764 KB |
| testcase_40 | AC | 346 ms
79,152 KB |
| testcase_41 | AC | 340 ms
78,428 KB |
ソースコード
from copy import deepcopy
class Modulo_Matrix_Error(Exception):
pass
class Modulo_Matrix():
__slots__=("ele","row","col","size")
#入力
def __init__(self,M):
""" 行列 M の定義
M: 行列
※ Mod: 法はグローバル変数から指定
"""
self.ele=[[x%Mod for x in X] for X in M]
R=len(M)
if R!=0:
C=len(M[0])
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 __repr__(self):
return str(self)
#+,-
def __pos__(self):
return self
def __neg__(self):
return self.__scale__(-1)
#加法
def __add__(self,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)
def __iadd__(self,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]%=Mod
return self
#減法
def __sub__(self,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)
def __isub__(self,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]%=Mod
return self
#乗法
def __mul__(self,other):
if isinstance(other,Modulo_Matrix):
if self.col!=other.row:
raise Modulo_Matrix_Error("左側の列と右側の行が一致しません.({},{})".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]%=Mod
return Modulo_Matrix(E)
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("正方行列ではありません.")
M=self
N=M.row
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("正則行列ではありません")
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)
#スカラー倍
def __scale__(self,r):
M=self.ele
L=[[(r*M[i][j])%Mod for j in range(self.col)] for i in range(self.row)]
return Modulo_Matrix(L)
#累乗
def __pow__(self,n):
if self.row!=self.col:
raise Modulo_Matrix_Error("正方行列ではありません.")
r=self.col
def __mat_mul(A,B):
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
X=deepcopy(self.ele)
E=[[1 if i==j else 0 for j in range(r)] for i in range(r)]
sgn=1 if n>=0 else -1
n=abs(n)
while True:
if n&1:
E=__mat_mul(E,X)
n>>=1
if n:
X=__mat_mul(X,X)
else:
break
if sgn==1:
return Modulo_Matrix(E)
else:
return Modulo_Matrix(E).Inverse()
#等号
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
#不等号
def __neq__(self,other):
return not(self==other)
#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(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,Mod-2,Mod)
for j in range(C):
T[I][j]*=u_inv
T[I][j]%=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]%=Mod
I+=1
if I==R:
break
return Modulo_Matrix(T)
#列基本変形
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,Mod-2,Mod)
for i in range(R):
T[i][J]*=u_inv
T[i][J]%=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]%=Mod
J+=1
if J==C:
break
return Modulo_Matrix(T)
#行列の階数
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
#行の結合
def Row_Union(self,other):
return Modulo_Matrix(self.ele+other.ele,Mod)
#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 Modulo_Matrix(E)
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
#==================================================
import sys
input=sys.stdin.readline
write=sys.stdout.write
Mod=10**9+7
M=3
S=pow(M,Mod-2,Mod)
X=Modulo_Matrix([[0]*4 for _ in range(4)])
Data=[
(0,0,S), (0,3,1-S),
(1,1,S), (1,2,S), (1,3,1-2*S),
(2,0,1), (3,1,1)
]
for a,b,p in Data:
X[a,b]=p
T=int(input())
Ans=[0]*T
for t in range(T):
N=int(input())
Ans[t]=(X**N)[0,0]
write("\n".join(map(str,Ans)))