結果
| 問題 | No.1547 [Cherry 2nd Tune *] 偶然の勝利の確率 |
| ユーザー |
👑  Kazun
|
| 提出日時 | 2022-01-12 01:46:43 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 285 ms / 2,000 ms |
| コード長 | 9,706 bytes |
| コンパイル時間 | 481 ms |
| コンパイル使用メモリ | 82,252 KB |
| 実行使用メモリ | 77,808 KB |
| 最終ジャッジ日時 | 2024-11-14 12:38:12 |
| 合計ジャッジ時間 | 6,874 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge2 |
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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 | 44 ms
56,568 KB |
| testcase_01 | AC | 51 ms
64,480 KB |
| testcase_02 | AC | 68 ms
73,488 KB |
| testcase_03 | AC | 49 ms
64,640 KB |
| testcase_04 | AC | 58 ms
65,952 KB |
| testcase_05 | AC | 50 ms
65,452 KB |
| testcase_06 | AC | 51 ms
64,440 KB |
| testcase_07 | AC | 52 ms
64,716 KB |
| testcase_08 | AC | 51 ms
65,228 KB |
| testcase_09 | AC | 52 ms
66,112 KB |
| testcase_10 | AC | 52 ms
64,580 KB |
| testcase_11 | AC | 53 ms
65,280 KB |
| testcase_12 | AC | 51 ms
63,940 KB |
| testcase_13 | AC | 122 ms
77,364 KB |
| testcase_14 | AC | 104 ms
77,068 KB |
| testcase_15 | AC | 86 ms
77,224 KB |
| testcase_16 | AC | 90 ms
76,732 KB |
| testcase_17 | AC | 93 ms
77,320 KB |
| testcase_18 | AC | 89 ms
76,912 KB |
| testcase_19 | AC | 68 ms
71,192 KB |
| testcase_20 | AC | 187 ms
77,760 KB |
| testcase_21 | AC | 83 ms
76,988 KB |
| testcase_22 | AC | 50 ms
64,020 KB |
| testcase_23 | AC | 270 ms
77,628 KB |
| testcase_24 | AC | 276 ms
77,508 KB |
| testcase_25 | AC | 282 ms
77,808 KB |
| testcase_26 | AC | 285 ms
77,620 KB |
| testcase_27 | AC | 273 ms
77,568 KB |
| testcase_28 | AC | 273 ms
77,620 KB |
| testcase_29 | AC | 273 ms
77,508 KB |
| testcase_30 | AC | 272 ms
77,728 KB |
| testcase_31 | AC | 278 ms
77,648 KB |
| testcase_32 | AC | 277 ms
77,520 KB |
| testcase_33 | AC | 275 ms
77,712 KB |
| testcase_34 | AC | 89 ms
77,168 KB |
| testcase_35 | AC | 92 ms
77,456 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
#========================
#===入力
MA,NA,S=map(int,input().split())
MB,NB,T=map(int,input().split())
K=int(input())
#===定数の設定
Mod=998244353
rho_A=(MA*pow(NA,Mod-2,Mod))%Mod
rho_B=(MB*pow(NB,Mod-2,Mod))%Mod
#===Aについての行列
U=[[0]*(S+T+1) for _ in range(S+T+1)]
for y in range(S+T+1):
for x in range(S+T+1):
if x==0:
U[y][x]=1 if y==0 else 0
elif x==S+T:
U[y][x]=1 if y==S+T else 0
else:
if y<x:
U[y][x]=0
else:
if y==S+T:
U[y][x]=pow(rho_A,y-x,Mod)
else:
U[y][x]=(pow(rho_A,y-x,Mod)*(1-rho_A))%Mod
#===Bについての行列
V=[[0]*(S+T+1) for _ in range(S+T+1)]
for y in range(S+T+1):
for x in range(S+T+1):
if x==0:
V[y][x]=1 if y==0 else 0
elif x==S+T:
V[y][x]=1 if y==S+T else 0
else:
if y>x:
V[y][x]=0
else:
if y==0:
V[y][x]=pow(rho_B,x-y,Mod)
else:
V[y][x]=(pow(rho_B,x-y,Mod)*(1-rho_B))%Mod
#===行列の計算
E=pow(Modulo_Matrix(V)*Modulo_Matrix(U),K)
#===結果の出力
print(E[S+T,T])
print(E[0,T])