結果

問題 No.1521 Playing Musical Chairs Alone
ユーザー 👑 KazunKazun
提出日時 2021-05-31 04:29:30
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 773 ms / 2,000 ms
コード長 7,840 bytes
コンパイル時間 300 ms
コンパイル使用メモリ 81,920 KB
実行使用メモリ 77,056 KB
最終ジャッジ日時 2024-11-08 21:06:43
合計ジャッジ時間 9,280 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
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 45 ms
54,144 KB
testcase_01 AC 52 ms
61,312 KB
testcase_02 AC 62 ms
64,640 KB
testcase_03 AC 45 ms
53,888 KB
testcase_04 AC 45 ms
54,144 KB
testcase_05 AC 245 ms
76,544 KB
testcase_06 AC 210 ms
76,544 KB
testcase_07 AC 281 ms
76,416 KB
testcase_08 AC 81 ms
67,840 KB
testcase_09 AC 70 ms
67,328 KB
testcase_10 AC 54 ms
63,232 KB
testcase_11 AC 476 ms
76,288 KB
testcase_12 AC 44 ms
54,016 KB
testcase_13 AC 57 ms
63,488 KB
testcase_14 AC 62 ms
64,384 KB
testcase_15 AC 528 ms
76,416 KB
testcase_16 AC 618 ms
77,056 KB
testcase_17 AC 597 ms
76,800 KB
testcase_18 AC 526 ms
76,544 KB
testcase_19 AC 512 ms
76,928 KB
testcase_20 AC 622 ms
76,800 KB
testcase_21 AC 565 ms
76,928 KB
testcase_22 AC 522 ms
76,416 KB
testcase_23 AC 498 ms
76,160 KB
testcase_24 AC 525 ms
76,544 KB
testcase_25 AC 773 ms
77,056 KB
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ソースコード

diff # 

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):
        A=self
        B=other
        if A.size!=B.size:
            raise Modulo_Matrix_Error("2つの行列のサイズが異なります.({},{})".format(A.size,B.size))
        M=A.ele
        N=B.ele

        L=[0]*self.row
        for i in range(A.row):
            E,F=M[i],N[i]
            L[i]=[(E[j]+F[j])%self.Mod for j in range(self.col)]
        return Modulo_Matrix(L,self.Mod)

    #減法
    def __sub__(self,other):
        return self+(-other)

    #乗法
    def __mul__(self,other):
        A=self
        B=other
        if isinstance(B,Modulo_Matrix):
            R=A.row
            C=B.col

            if A.col!=B.row:
                raise Modulo_Matrix_Error("左側の列と右側の行が一致しません.({},{})".format(A.size,B.size))
            G=A.col

            M=A.ele
            N=B.ele

            E=[[0]*other.col for _ in range(self.row)]
            for i in range(R):
                e=E[i]; F=M[i]
                for k in range(G):
                    n=N[k]
                    for j in range(C):
                        e[j]+=F[k]*n[j]
                        e[j]%=self.Mod

            return Modulo_Matrix(E,self.Mod)

        elif isinstance(B,int):
            return A.__scale__(B)

    def __rmul__(self,other):
        if isinstance(other,int):
            return self*other

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

        R=M.row
        I=[[1*(i==j) for j in range(R)] for i in range(R)]
        G=M.Column_Union(Modulo_Matrix(I,self.Mod))
        G=G.Row_Reduce()

        A,B=[None]*R,[None]*R
        for i in range(R):
            A[i]=G.ele[i][:R]
            B[i]=G.ele[i][R:]

        if A==I:
            return Modulo_Matrix(B,self.Mod)
        else:
            raise Modulo_Matrix_Error("正則ではありません.")

    #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.")

        if n<0:
            return pow(self,-n).Inverse()

        m=self.row
        Mod=self.Mod
        R=[[1 if i==j else 0 for j in range(m)] for i in range(m)]
        D=[[] for _ in range(m)]
        for i in range(m): D[i]=self.ele[i][:]

        while n>0:
            if n%2==1:
                S=[[0]*m for _ in range(m)]

                for i in range(m):
                    s=S[i]; r=R[i]
                    for k in range(m):
                        d=D[k]
                        for j in range(m):
                            s[j]+=r[k]*d[j]
                            s[j]%=Mod

                for i in range(m): R[i]=S[i][:]

            E=[[0]*m for _ in range(m)]
            for i in range(m):
                e=E[i]; d=D[i]
                for k in range(m):
                    d2=D[k]
                    for j in range(m):
                        e[j]+=d[k]*d2[j]
                        e[j]%=Mod

            for i in range(m): D[i]=E[i][:]
            n=n>>1

        return Modulo_Matrix(R,Mod)

    #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,K,L=map(int,input().split())
Mod=10**9+7

M=[[0]*N for _ in range(N)]
for i in range(0,N):
    for j in range(1,L+1):
        M[i][(i+j)%N]=1

M=Modulo_Matrix(M,Mod)
M**=K


for i in range(N): print(M[0,i])
0