結果

問題 No.1958 Bit Game
ユーザー 👑 Kazun
提出日時 2022-05-27 22:19:09
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 203 ms / 2,000 ms
コード長 8,680 bytes
コンパイル時間 238 ms
コンパイル使用メモリ 82,088 KB
実行使用メモリ 145,944 KB
最終ジャッジ日時 2024-09-20 16:03:17
合計ジャッジ時間 6,660 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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 * 3
other AC * 30
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ソースコード

diff #
プレゼンテーションモードにする

from copy import deepcopy
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):
            assert self.col==other.row, "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):
        assert self.row==self.col,"正方行列ではありません."
        M=self
        N=M.row
        R=[[1 if i==j else 0 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:
                    assert 0, "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
        r%=Mod
        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):
        assert self.row==self.col, "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):
        return self.ele==other.ele
    #不等号
    def __neq__(self,other):
        return not(self==other)
    #転置
    def transpose(self):
        return Modulo_Matrix(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
        rnk=0
        for i in range(R):
            f=False
            for j in range(C):
                if T[i][j]!=0:
                    f=True
                    break
            if f:
                rnk+=1
            else:
                break
        return rnk
    #行の結合
    def row_union(self,other):
        return Modulo_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 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
def solve(N,X,Y,A,B):
    mu=max(max(A), max(B)).bit_length()
    Ans=0
    for d in range(mu):
        S=[0,0]; T=[0,0]
        for i in range(X):
            S[A[i]&1]+=1
            A[i]>>=1
        for j in range(Y):
            T[B[j]&1]+=1
            B[j]>>=1
        M=[[0,0],[0,0]]
        for r in [0,1]:
            for p,q in [[0,0], [0,1], [1,0], [1,1]]:
                M[(r|p)&q][r]+=(S[p]*T[q])%Mod
        M=Modulo_Matrix(M)
        Ans+=pow(M,N)[1,0]*(1<<d)
    return Ans%Mod
N,X,Y=map(int,input().split())
A=list(map(int,input().split()))
B=list(map(int,input().split()))
Mod=998244353
print(solve(N,X,Y,A,B))
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