#495209 (Python3) No.1073 無限すごろく

• 問題: No.1073 無限すごろく
• ユーザー: Keroru
• 提出日時: 2020-06-11 21:53:02
• 言語: Python3 (3.12.2 + numpy 1.26.4 + scipy 1.12.0)
• 結果: AC
• 実行時間: 22 ms / 2,000 ms
• コード長: 5,156 bytes
• コンパイル時間: 103 ms
• コンパイル使用メモリ: 11,500 KB
• 実行使用メモリ: 8,512 KB
• 最終ジャッジ日時: 2023-09-06 08:38:06
• 合計ジャッジ時間: 3,197 ms
• ジャッジサーバーID （参考情報）: judge13 / judge12

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	19 ms; 8,416 KB
testcase_01	AC	19 ms; 8,356 KB
testcase_02	AC	19 ms; 8,400 KB
testcase_03	AC	18 ms; 8,460 KB
testcase_04	AC	17 ms; 8,364 KB
testcase_05	AC	18 ms; 8,284 KB
testcase_06	AC	17 ms; 8,288 KB
testcase_07	AC	18 ms; 8,364 KB
testcase_08	AC	18 ms; 8,324 KB
testcase_09	AC	17 ms; 8,416 KB
testcase_10	AC	17 ms; 8,416 KB
testcase_11	AC	17 ms; 8,356 KB
testcase_12	AC	18 ms; 8,328 KB
testcase_13	AC	18 ms; 8,284 KB
testcase_14	AC	19 ms; 8,356 KB
testcase_15	AC	18 ms; 8,416 KB
testcase_16	AC	19 ms; 8,344 KB
testcase_17	AC	19 ms; 8,348 KB
testcase_18	AC	19 ms; 8,512 KB
testcase_19	AC	19 ms; 8,360 KB
testcase_20	AC	20 ms; 8,368 KB
testcase_21	AC	19 ms; 8,320 KB
testcase_22	AC	19 ms; 8,284 KB
testcase_23	AC	20 ms; 8,344 KB
testcase_24	AC	20 ms; 8,308 KB
testcase_25	AC	20 ms; 8,284 KB
testcase_26	AC	20 ms; 8,288 KB
testcase_27	AC	20 ms; 8,344 KB
testcase_28	AC	22 ms; 8,332 KB
testcase_29	AC	21 ms; 8,304 KB
testcase_30	AC	21 ms; 8,464 KB
testcase_31	AC	21 ms; 8,368 KB
testcase_32	AC	20 ms; 8,296 KB

ソースコード

## Verified by Yukicoder 1073
## https://yukicoder.me/problems/no/1073
##
## Matrix Class supporting operators +, -, *, %, +=, -=, *=, %=
## *, *= allows int/float/complex
## ** or pow(self,p,mod) for the size N*N matrix is implemented by Repeated squaring. O(N^3*log(p))
##
## Constructor: matrix(array), where array is 1D or 2D array. 1-dimensional array X is modified as 2D array of [X].
##
## methods
## T(): returns transposed matrix
## resize((n,m),fill=0): changes the matrix instance into the new shape (n * m), missing entries are filled with "fill" (default value is zero).


class matrix:
    class MulShapeError(Exception):
        "mult is not applicable between the two matrices given"
        pass

    def __init__(self,arr_input):
        if hasattr(arr_input[0],"__getitem__"):
            self.arr=arr_input
        else:
            self.arr=[arr_input]
        self.shape=(len(self.arr),len(self.arr[0]))

    def __getitem__(self,key):
        return self.arr[key]

    def __setitem__(self,key,value):
        self.arr[key]=value

    def __iter__(self):
        return iter(self.arr)
        
    def __add__(self,B):
        if type(B)!=matrix:
            return NotImplemented
        if B.shape!=self.shape:
            return NotImplemented
        rt=[[0]*self.shape[1] for i in range(self.shape[0])]
        for i in range(self.shape[0]):
            for j in range(self.shape[1]):
                rt[i][j]=self.arr[i][j]+B.arr[i][j]
        return matrix(rt)

    def __iadd__(self,B):
        return self.__add__(B)

    def __sub__(self,B):
        if type(B)!=matrix:
            return NotImplemented
        if B.shape!=self.shape:
            return NotImplemented
        rt=[[0]*self.shape[1] for i in range(self.shape[0])]
        for i in range(self.shape[0]):
            for j in range(self.shape[1]):
                rt[i][j]=self.arr[i][j]-B.arr[i][j]
        return matrix(rt)

    def __isub__(self,B):
        return self.__sub__(B)

    def __mul__(self,M):
        if type(M) in [int,float,complex]:
            M=matrix([[M*(i==j) for j in range(self.shape[1])] for i in range(self.shape[1])])
        if type(M)!=matrix:
            return NotImplemented
        if M.shape[0]!=self.shape[1]:
            raise matrix.MulShapeError("mult is not applicable between the matrices of shape "+str(self.shape)+" and "+str(M.shape))
        ra,ca=self.shape
        rb,cb=M.shape
        c=[[0]*cb for i in range(ra)]
        for i in range(ra):
            for j in range(cb):
                for k in range(ca):
                    c[i][j]+=self.arr[i][k]*M.arr[k][j]
        return matrix(c)

    def __imul__(self,M):
        return self.__mul__(M)

    def __rmul__(self,M):
        if type(M) in [int,float,complex]:
            M=matrix([[M*(i==j) for j in range(self.shape[1])] for i in range(self.shape[1])])
        if type(M)!=matrix:
            return NotImplemented
        if M.shape[0]!=self.shape[1]:
            raise matrix.MulShapeError("mult is not applicable between the matrix shape "+str(self.shape)+" and "+str(M.shape))
        ra,ca=M.shape
        rb,cb=self.shape
        c=[[0]*cb for i in range(ra)]
        for i in range(ra):
            for j in range(cb):
                for k in range(ca):
                    c[i][j]+=M.arr[i][k]*self.arr[k][j]
        return matrix(c)

    def __mod__(self,p):
        if type(p)!=int:
            return NotImplemented
        c=[[0]*self.shape[1] for i in range(self.shape[0])]
        for i in range(self.shape[0]):
            for j in range(self.shape[1]):
                c[i][j]=self.arr[i][j]%p
        return matrix(c)

    def __imod__(self,p):
        return self.__mod__(p)

    def __pow__(self,p,mod=10**9+7):
        if type(p)!=int or self.shape[0]!=self.shape[1]:
            return NotImplemented
        A=matrix(self.arr)
        R=matrix([[1*(i==j) for j in range(self.shape[0])] for i in range(self.shape[0])])
        while p>0:
            if p&1:
                R*=A
                R%=mod
            A*=A
            A%=mod
            p>>=1
        return R

    def __neg__(self):
        return self.__mul__(-1)

    def __str__(self):
        rt='['
        for i in self.arr:
            rt=rt+str(i)+",\n"
        return rt[:-2]+']'

    def T(self):
        rt=[[0]*self.shape[0] for i in range(self.shape[1])]
        for i in range(self.shape[0]):
            for j in range(self.shape[1]):
                rt[j][i]=self.arr[i][j]
        return matrix(rt)

    def resize(self,new_shape,fill=0):
        t_arr=[]
        for i in self.arr:
            t_arr+=i
        t_arr.reverse()
        n,m=new_shape
        self.shape=(n,m)
        self.arr=[[fill]*m for i in range(n)]

        for i in range(self.shape[0]):
            for j in range(self.shape[1]):
                if t_arr:
                    self.arr[i][j]=t_arr.pop()
        return

    def view(self):
        for i in self.arr:
            print(i)


mo=10**9+7
n=int(input())
b=pow(6,mo-2,mo)

M=matrix([b]*6)
M.resize((6,6))
for i in range(5):
    M[i+1][i]=1

X=matrix([1]+[0]*5)
X.resize((6,1))

M**=n
ans=M*X
print(ans[0][0])