#706015 (PyPy3) No.1706 Many Bus Stops (hard)

提出ソース

結果

問題	No.1706 Many Bus Stops (hard)
ユーザー	👑 Kazun
提出日時	2021-10-08 22:59:30
言語	PyPy3 (7.3.15)
結果	AC
実行時間	75 ms / 2,000 ms
コード長	8,459 bytes
コンパイル時間	581 ms
コンパイル使用メモリ	82,388 KB
実行使用メモリ	75,212 KB
最終ジャッジ日時	2024-07-23 06:15:41
合計ジャッジ時間	4,744 ms
ジャッジサーバーID （参考情報）	judge3 / judge1

このコードへのチャレンジ
（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	65 ms 69,424 KB
testcase_01	AC	64 ms 69,476 KB
testcase_02	AC	72 ms 74,608 KB
testcase_03	AC	73 ms 74,096 KB
testcase_04	AC	74 ms 73,292 KB
testcase_05	AC	72 ms 74,672 KB
testcase_06	AC	74 ms 74,188 KB
testcase_07	AC	73 ms 73,760 KB
testcase_08	AC	72 ms 73,900 KB
testcase_09	AC	74 ms 73,636 KB
testcase_10	AC	72 ms 74,284 KB
testcase_11	AC	71 ms 73,096 KB
testcase_12	AC	74 ms 73,760 KB
testcase_13	AC	72 ms 74,756 KB
testcase_14	AC	72 ms 73,688 KB
testcase_15	AC	73 ms 74,692 KB
testcase_16	AC	73 ms 73,820 KB
testcase_17	AC	74 ms 73,424 KB
testcase_18	AC	73 ms 75,212 KB
testcase_19	AC	74 ms 74,480 KB
testcase_20	AC	72 ms 74,020 KB
testcase_21	AC	73 ms 73,368 KB
testcase_22	AC	74 ms 74,788 KB
testcase_23	AC	72 ms 73,892 KB
testcase_24	AC	73 ms 73,452 KB
testcase_25	AC	73 ms 73,432 KB
testcase_26	AC	73 ms 74,384 KB
testcase_27	AC	72 ms 74,260 KB
testcase_28	AC	73 ms 74,252 KB
testcase_29	AC	72 ms 73,564 KB
testcase_30	AC	73 ms 73,708 KB
testcase_31	AC	73 ms 74,344 KB
testcase_32	AC	73 ms 73,100 KB
testcase_33	AC	74 ms 74,584 KB
testcase_34	AC	74 ms 74,076 KB
testcase_35	AC	75 ms 73,976 KB
testcase_36	AC	73 ms 73,228 KB
testcase_37	AC	73 ms 74,092 KB
testcase_38	AC	71 ms 74,112 KB
testcase_39	AC	73 ms 74,436 KB
testcase_40	AC	72 ms 73,632 KB
testcase_41	AC	72 ms 74,508 KB
testcase_42	AC	71 ms 74,880 KB

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

raw source code

from copy import copy,deepcopy
from typing import Match

class Modulo_Matrix_Error(Exception):
    pass

class Modulo_Matrix():
    #入力
    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)

    #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):
        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

    #減法
    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

    #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]%=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("正方行列ではありません.")

        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("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,Mod)

    #スカラー倍
    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)

    #累乗
    def __pow__(self,n):
        A=self
        if A.row!=A.col:
            raise Modulo_Matrix_Error("正方行列ではありません.")

        if n<0:
            return (A**(-n)).Inverse()

        R=Modulo_Matrix([[1*(i==j) for j in range(A.row)] for i in range(A.row)],self.Mod)
        D=A

        while n>0:
            if n%2==1:
                R*=D
            D*=D
            n=n>>1

        return R

    #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,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)

    #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,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)

    #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,self.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,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
#==================================================
C,N,M=map(int,input().split())
Mod=10**9+7

S=pow(C,Mod-2,Mod)
X=Modulo_Matrix([[0]*4 for _ in range(4)],Mod)
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

Prob=(X**N)[0,0]

print((1-pow(1-Prob,M,Mod))%Mod)

yukicoder

結果

テストケース

ソースコード