結果

問題 No.1750 ラムドスウイルスの感染拡大-hard
ユーザー 👑 KazunKazun
提出日時 2021-11-19 21:41:55
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,424 ms / 2,000 ms
コード長 8,764 bytes
コンパイル時間 212 ms
コンパイル使用メモリ 82,432 KB
実行使用メモリ 81,440 KB
最終ジャッジ日時 2024-06-10 08:19:32
合計ジャッジ時間 17,166 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
このコードへのチャレンジ
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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 39 ms
54,144 KB
testcase_01 AC 39 ms
54,528 KB
testcase_02 AC 43 ms
60,032 KB
testcase_03 AC 46 ms
61,824 KB
testcase_04 AC 100 ms
72,704 KB
testcase_05 AC 41 ms
54,528 KB
testcase_06 AC 39 ms
54,148 KB
testcase_07 AC 38 ms
54,016 KB
testcase_08 AC 291 ms
76,416 KB
testcase_09 AC 285 ms
76,840 KB
testcase_10 AC 284 ms
76,672 KB
testcase_11 AC 250 ms
76,736 KB
testcase_12 AC 317 ms
76,752 KB
testcase_13 AC 299 ms
76,440 KB
testcase_14 AC 1,355 ms
81,272 KB
testcase_15 AC 1,386 ms
81,280 KB
testcase_16 AC 1,424 ms
81,440 KB
testcase_17 AC 1,383 ms
80,772 KB
testcase_18 AC 1,420 ms
80,768 KB
testcase_19 AC 1,354 ms
79,996 KB
testcase_20 AC 953 ms
78,992 KB
testcase_21 AC 1,111 ms
79,276 KB
testcase_22 AC 257 ms
76,408 KB
testcase_23 AC 1,297 ms
79,916 KB
testcase_24 AC 202 ms
77,404 KB
testcase_25 AC 403 ms
77,124 KB
testcase_26 AC 172 ms
76,672 KB
testcase_27 AC 55 ms
66,176 KB
testcase_28 AC 63 ms
71,936 KB
testcase_29 AC 53 ms
66,048 KB
testcase_30 AC 257 ms
76,796 KB
testcase_31 AC 243 ms
76,500 KB
testcase_32 AC 240 ms
76,604 KB
testcase_33 AC 237 ms
76,684 KB
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ソースコード

diff # 

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):
        if self.row!=self.col:
            raise Modulo_Matrix_Error("正方行列ではありません.")

        def __mat_mul(A,B,r,Mod):
            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

        def __mat_pow(A,n,r,Mod):
            if n==0:
                return [[1 if i==j else 0 for j in range(r)] for i in range(r)]
            else:
                return __mat_mul(__mat_pow(A,n-1,r,Mod),A,r,Mod) if n&1 else __mat_pow(__mat_mul(A,A,r,Mod),n>>1,r,Mod)

        S=__mat_pow(self.ele,abs(n),self.col,self.Mod)
        if n>=0:
            return Modulo_Matrix(S,self.Mod)
        else:
            return Modulo_Matrix(S,self.Mod).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,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
#==================================================
N,M,T=map(int,input().split())

Mod=998244353
A=Modulo_Matrix([[0]*N for _ in range(N)],Mod)
for _ in range(M):
    s,t=map(int,input().split())
    A[s,t]=A[t,s]=1

print(pow(A,T)[0,0])
0