結果

問題 No.1073 無限すごろく
ユーザー Keroru
提出日時 2021-04-26 23:44:49
言語 Python3
(3.13.1 + numpy 2.2.1 + scipy 1.14.1)
結果
AC  
実行時間 51 ms / 2,000 ms
コード長 11,920 bytes
コンパイル時間 91 ms
コンパイル使用メモリ 13,824 KB
実行使用メモリ 12,928 KB
最終ジャッジ日時 2024-07-05 16:01:50
合計ジャッジ時間 2,694 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 3
other AC * 30
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

diff #
プレゼンテーションモードにする

import sys
read=sys.stdin.buffer.read;readline=sys.stdin.buffer.readline;input=lambda:sys.stdin.readline().rstrip()
import bisect,string,math,time,functools,random,fractions
from bisect import*
from heapq import heappush,heappop,heapify
from collections import deque,defaultdict,Counter
from itertools import permutations,combinations,groupby
rep=range;R=range
def I():return int(input())
def LI():return [int(i) for i in input().split()]
def LI_():return [int(i)-1 for i in input().split()]
def AI():return map(int,open(0).read().split())
def S_():return input()
def IS():return input().split()
def LS():return [i for i in input().split()]
def NI(n):return [int(input()) for i in range(n)]
def NI_(n):return [int(input())-1 for i in range(n)]
def NLI(n):return [[int(i) for i in input().split()] for i in range(n)]
def NLI_(n):return [[int(i)-1 for i in input().split()] for i in range(n)]
def StoLI():return [ord(i)-97 for i in input()]
def ItoS(n):return chr(n+97)
def LtoS(ls):return ''.join([chr(i+97) for i in ls])
def RLI(n=8,a=1,b=10):return [random.randint(a,b)for i in range(n)]
def RI(a=1,b=10):return random.randint(a,b)
def INP():
    N=10
    n=random.randint(1,N)
    a=RLI(n,0,n-1)
    return n,a
def Rtest(T):
    case,err=0,0
    for i in range(T):
        inp=INP()
        a1=naive(*inp)
        a2=solve(*inp)
        if a1!=a2:
            print(inp)
            print('naive',a1)
            print('solve',a2)
            err+=1
        case+=1
    print('Tested',case,'case with',err,'errors')
def GI(V,E,ls=None,Directed=False,index=1):
    org_inp=[];g=[[] for i in range(V)]
    FromStdin=True if ls==None else False
    for i in range(E):
        if FromStdin:
            inp=LI()
            org_inp.append(inp)
        else:
            inp=ls[i]
        if len(inp)==2:a,b=inp;c=1
        else:a,b,c=inp
        if index==1:a-=1;b-=1
        aa=(a,c);bb=(b,c);g[a].append(bb)
        if not Directed:g[b].append(aa)
    return g,org_inp
def GGI(h,w,search=None,replacement_of_found='.',mp_def={'#':1,'.':0},boundary=1):
    #h,w,g,sg=GGI(h,w,search=['S','G'],replacement_of_found='.',mp_def={'#':1,'.':0},boundary=1) # sample usage
    mp=[boundary]*(w+2);found={}
    for i in R(h):
        s=input()
        for char in search:
            if char in s:
                found[char]=((i+1)*(w+2)+s.index(char)+1)
                mp_def[char]=mp_def[replacement_of_found]
        mp+=[boundary]+[mp_def[j] for j in s]+[boundary]
    mp+=[boundary]*(w+2)
    return h+2,w+2,mp,found
def TI(n):return GI(n,n-1)
def accum(ls):
    rt=[0]
    for i in ls:rt+=[rt[-1]+i]
    return rt
def bit_combination(n,base=2):
    rt=[]
    for tb in R(base**n):s=[tb//(base**bt)%base for bt in R(n)];rt+=[s]
    return rt
def gcd(x,y):
    if y==0:return x
    if x%y==0:return y
    while x%y!=0:x,y=y,x%y
    return y
def YN(x):print(['NO','YES'][x])
def Yn(x):print(['No','Yes'][x])
def show(*inp,end='\n'):
    if show_flg:print(*inp,end=end)
mo=10**9+7
#mo=998244353
inf=float('inf')
FourNb=[(-1,0),(1,0),(0,1),(0,-1)];EightNb=[(-1,0),(1,0),(0,1),(0,-1),(1,1),(-1,-1),(1,-1),(-1,1)];compas=dict(zip('WENS',FourNb));cursol=dict(zip
    ('LRUD',FourNb))
alp=[chr(ord('a')+i)for i in range(26)]
#sys.setrecursionlimit(10**7)
def gcj(c,x):
    print("Case #{0}:".format(c+1),x)
#####################################################################################################################################################
    ###################
# Verified by
# https://yukicoder.me/problems/no/979
# https://atcoder.jp/contests/abc152/tasks/abc152_e
## return prime factors of N as dictionary {prime p:power of p}
## within 2 sec for N = 2*10**20+7
def primeFactor(N):
    i,n=2,N
    ret={}
    d,sq=2,99
    while i<=sq:
        k=0
        while n%i==0:
            n,k,ret[i]=n//i,k+1,k+1
        if k>0 or i==97:
            sq=int(n**(1/2)+0.5)
        if i<4:
            i=i*2-1
        else:
            i,d=i+d,d^6
    if n>1:
        ret[n]=1
    return ret
## return divisors of n as list
def divisor(n):
    div=[1]
    for i,j in primeFactor(n).items():
        div=[(i**k)*d for d in div for k in range(j+1)]
    return div
## return the list of prime numbers in [2,N], using eratosthenes sieve
## around 800 ms for N = 10**6  by PyPy3 (7.3.0) @ AtCoder
def PrimeNumSet(N):
    M=int(N**0.5)
    seachList=[i for i in range(2,N+1)]
    primes=[]
    while seachList:
        if seachList[0]>M:
            break
        primes.append(seachList[0])
        tmp=seachList[0]
        seachList=[i for i in seachList if i%tmp!=0]
    return primes+seachList
## retrun LCM of numbers in list b
## within 2sec for no of B = 10*5  and  Bi < 10**6
def LCM(b,mo=10**9+7):
    prs=PrimeNumSet(max(b))
    M=dict(zip(prs,[0]*len(prs)))
    for i in b:
        dc=primeFactor(i)
        for j,k in dc.items():
            M[j]=max(M[j],k)
    
    r=1
    for j,k in M.items():
        if k!=0:
            r*=pow(j,k,mo)
            r%=mo
    return r
## return (a,b,gcd(x,y)) s.t. a*x+b*y=gcd(x,y)
def extgcd(x,y):
    if y==0:
        return 1,0
    r0,r1,s0,s1 = x,y,1,0
    while r1!= 0:
        r0,r1,s0,s1=r1,r0%r1,s1,s0-r0//r1*s1
    return s0,(r0-s0*x)//y,x*s0+y*(r0-s0*x)//y
## return x,LCM(mods) s.t. x = rem_i (mod_i), x = -1 if such x doesn't exist
## verified by ABC193E
## https://atcoder.jp/contests/abc193/tasks/abc193_e
def crt(rems,mods):
    n=len(rems)
    if n!=len(mods):
        return NotImplemented
    x,d=0,1
    
    for r,m in zip(rems,mods):
        a,b,g=extgcd(d,m)
        x,d=(m*b*x+d*a*r)//g,d*(m//g)
        x%=d
    for r,m in zip(rems,mods):
        if r!=x%m:
            return -1,d
    return x,d
## returns the maximum integer rt s.t. rt*rt<=x
## verified by ABC191D
## https://atcoder.jp/contests/abc191/tasks/abc191_d
def intsqrt(x):
    if x<0:
        return NotImplemented
    rt=int(x**0.5)-1
    while (rt+1)**2<=x:
        rt+=1
    return rt
## 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=[]
            self.shape=(len(arr_input),len(arr_input[0]))
            for i in arr_input:
                self.arr+=i
        else:
            self.arr=arr_input
            self.shape=(1,len(arr_input))
        
    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]*self.shape[0])
        for i in range(self.shape[0]):
            for j in range(self.shape[1]):
                rt[i*self.shape[1]+j]=self.arr[i*self.shape[1]+j]+B.arr[i*self.shape[1]+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]*self.shape[0])
        for i in range(self.shape[0]):
            for j in range(self.shape[1]):
                rt[i*self.shape[1]+j]=self.arr[i*self.shape[1]+j]-B.arr[i*self.shape[1]+j]
        return matrix(rt)
    def __isub__(self,B):
        return self.__sub__(B)
    def __mul__(self,M,mod=10**9+7):
        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])])
            M.resize(self.shape)
        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*ra)
        for i in range(ra):
            for j in range(cb):
                for k in range(ca):
                    c[i*cb+j]+=self.arr[i*ca+k]*M.arr[k*cb+j]
                    if c[i*cb+j]>=mod:c[i*cb+j]%=mod
        c=matrix(c)
        c.resize((ra,cb))
        return c
    
    
    def __imul__(self,M):
        return self.__mul__(M)
    def __rmul__(self,M,mod=10**9+7):
        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*ra)
        for i in range(ra):
            for j in range(cb):
                for k in range(ca):
                    c[i*cb+j]+=self.arr[i*ca+k]*M.arr[k*cb+j]
                    if c[i*cb+j]>=mod:c[i*cb+j]%=mod
        c=matrix(c)
        c.resize((ra,cb))
        return c
    def __mod__(self,p):
        if type(p)!=int:
            return NotImplemented
        c=[0]*(self.shape[1]*self.shape[0])
        for i in range(self.shape[0]):
            for j in range(self.shape[1]):
                c[i*self.shape[1]+j]=self.arr[i*self.shape[1]+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)
        A.resize(self.shape)
        R=matrix([1*(i==j) for j in range(self.shape[0]) for i in range(self.shape[0])])
        R.resize(self.shape)
        while p>0:
            if p&1:
                R*=A
            A*=A
            p>>=1
        return R
    def __neg__(self):
        return self.__mul__(-1)
    def __str__(self):
        rt='['
        for i in range(self.shape[0]):
            row='['
            for j in range(self.shape[1]):
                row=row+str(self.arr[i*self.shape[1]+j])+","
            rt=rt+row[:-1]+"]\n"
        return rt[:-1]+']'
    def T(self):
        rt=[0]*(self.shape[0]*self.shape[1])
        for i in range(self.shape[0]):
            for j in range(self.shape[1]):
                rt[j*self.shape[0]+i]=self.arr[i*self.shape[1]+j]
        rt=matrix(rt)
        rt.resize((self.shape[1],self.shape[0]))
        return rt
    def resize(self,new_shape,fill=0):
        self.shape=new_shape
        if len(self.arr)<self.shape[0]*self.shape[1]:
            self.arr+=[fill]*(self.shape[0]*self.shape[1]-len(self.arr))
        '''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)
show_flg=False
show_flg=True
ans=0
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)*6+i]=1
X=matrix([1]+[0]*5)
X.resize((6,1))
M**=n
ans=M*X
print(ans[0])
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0