結果
| 問題 |
No.1073 無限すごろく
|
| コンテスト | |
| ユーザー |
 Keroru
|
| 提出日時 | 2020-06-07 16:03:40 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 186 ms / 2,000 ms |
| コード長 | 12,514 bytes |
| コンパイル時間 | 155 ms |
| コンパイル使用メモリ | 82,268 KB |
| 実行使用メモリ | 92,160 KB |
| 最終ジャッジ日時 | 2024-12-23 17:36:35 |
| 合計ジャッジ時間 | 6,319 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 30 |
ソースコード
import sys,bisect,string,math,time,functools,random,fractions
from heapq import heappush,heappop,heapify
from collections import deque,defaultdict,Counter
from itertools import permutations,combinations,groupby
rep=range
def Golf():n,*t=map(int,open(0).read().split())
def I():return int(input())
def S_():return input()
def IS():return input().split()
def LS():return [i for i in input().split()]
def LI():return [int(i) for i in input().split()]
def LI_():return [int(i)-1 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 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 RA():return map(int,open(0).read().split())
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 range(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 range(base**n):s=[tb//(base**bt)%base for bt in range(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 show(*inp,end='\n'):
if show_flg:print(*inp,end=end)
YN=['YES','NO'];Yn=['Yes','No']
mo=10**9+7
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))
l_alp=string.ascii_lowercase
#sys.setrecursionlimit(10**7)
read=sys.stdin.buffer.read
readline=sys.stdin.buffer.readline
input=lambda: sys.stdin.readline().rstrip()
class Tree:
def __init__(self,inp_size=None,ls=None,init=True,index=1):
self.LCA_init_stat=False
self.ETtable=[]
if init:
if ls==None:
self.stdin(inp_size,index=index)
else:
self.size=len(ls)+1
self.edges,_=GI(self.size,self.size-1,ls,index=index)
return
def stdin(self,inp_size=None,index=1):
if inp_size==None:
self.size=int(input())
else:
self.size=inp_size
self.edges,_=GI(self.size,self.size-1,index=index)
return
def listin(self,ls,index=0):
self.size=len(ls)+1
self.edges,_=GI(self.size,self.size-1,ls,index=index)
return
def dfs(self,x,func=lambda pr,prv,nx,dist:prv+dist,root_v=0):
q=deque([x])
v=[None]*self.size
v[x]=root_v
while q:
c=q.pop()
for nb,d in self.edges[c]:
if v[nb]==None:
q.append(nb)
v[nb]=func(c,v[c],nb,d)
return v
def bfs(self,x,func=lambda pr,prv,nx,dist:prv+dist,root_v=0):
q=deque([x])
v=[None]*self.size
v[x]=root_v
while q:
c=q.popleft()
for nb,d in self.edges[c]:
if v[nb]==None:
q.append(nb)
v[nb]=func(c,v[c],nb,d)
return v
def parent(self,x):
return self.dfs(0,func=lambda pr,prv,nx,dist:pr,root_v=-1)
def topological_sort(self,x): # return topological sort of the tree
tps=[]
q=deque([x])
v=[None]*self.size
v[x]=0
while q:
c=q.popleft()
tps.append(c)
for nb,d in self.edges[c]:
if v[nb]==None:
q.append(nb)
v[nb]=0
return tps
def EulerTour(self,x):
q=deque()
q.append(x)
self.depth=[None]*self.size
self.depth[x]=0
self.ETtable=[]
self.ETdepth=[]
self.ETin=[-1]*self.size
self.ETout=[-1]*self.size
cnt=0
while q:
c=q.pop()
if c<0:
ce=~c
else:
ce=c
for nb,d in self.edges[ce]:
if self.depth[nb]==None:
q.append(~ce)
q.append(nb)
self.depth[nb]=self.depth[ce]+1
self.ETtable.append(ce)
self.ETdepth.append(self.depth[ce])
if self.ETin[ce]==-1:
self.ETin[ce]=cnt
else:
self.ETout[ce]=cnt
cnt+=1
return
def LCA_init(self,root):
self.EulerTour(root)
self.st=SparseTable(self.ETdepth,init_func=min,init_idl=inf)
#self.st=SegTree(self.size*2-1,self.ETdepth,function=min,ide=inf)
self.LCA_init_stat=True
return
def LCA(self,root,x,y):
if self.LCA_init_stat==False:
self.LCA_init(root)
xin,xout=self.ETin[x],self.ETout[x]
yin,yout=self.ETin[y],self.ETout[y]
a=min(xin,yin)
b=max(xout,yout,xin,yin)
id_of_min_dep_in_et=self.st.query_id(a,b+1)
return self.ETtable[id_of_min_dep_in_et]
def __str__(self):
return str(self.edges)
def show(self):
if all([all([d==1 for nd,d in edge]) for edge in self.edges]):
print( [[nd for nd,d in edge] for edge in self.edges] )
else:
print(self)
class SparseTable: # O(N log N) for init, O(1) for query(l,r)
def __init__(self,ls,init_func=min,init_idl=float('inf')):
self.func=init_func
self.idl=init_idl
self.size=len(ls)
self.N0=self.size.bit_length()
self.table=[ls[:]]
self.index=[list(range(self.size))]
self.lg=[0]*(self.size+1)
for i in range(2,self.size+1):
self.lg[i]=self.lg[i>>1]+1
for i in range(self.N0):
tmp=[self.func(self.table[i][j],self.table[i][min(j+(1<<i),self.size-1)]) for j in range(self.size)]
tmp_id=[self.index[i][j] if self.table[i][j]==self.func(self.table[i][j],self.table[i][min(j+(1<<i),self.size-1)]) else self.index[i][min(j+(1<<i),self.size-1)] for j in range(self.size)]
self.table+=[tmp]
self.index+=[tmp_id]
# return func of [l,r)
def query(self,l,r):
if r>self.size:r=self.size
#N=(r-l).bit_length()-1
N=self.lg[r-l]
return self.func(self.table[N][l],self.table[N][max(0,r-(1<<N))])
# return index of which val[i] = func of v among [l,r)
def query_id(self,l,r):
if r>self.size:r=self.size
#N=(r-l).bit_length()-1
N=self.lg[r-l]
a,b=self.index[N][l],self.index[N][max(0,r-(1<<N))]
if self.table[0][a]==self.func(self.table[N][l],self.table[N][max(0,r-(1<<N))]):
b=a
return b
# return boundary index of r such that func({table[i]} =< x , i in [pos,r]
def right_bound(self,pos,x):
k=(self.size-pos).bit_length()
for j in range(k)[::-1]:
nx=pos+(1<<j)
if nx<n and self.query(pos,nx+1)<=x:
pos+=(1<<j)
return pos
# return boundary index of l such that func({table[i]} =< x , i in [l,pos]
def left_bound(self,pos,x):
k=pos.bit_length()
for j in range(k)[::-1]:
nx=pos-(1<<j)
if 0<=nx and self.query(nx,pos+1)<=x:
pos-=(1<<j)
return pos
def __str__(self):
return str(self.table[0])
def print(self):
for i in self.table:
print(*i)
show_flg=False
show_flg=True
ans=0
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 __str__(self):
return str(self.arr)
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 matrix 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)
n=I()
b=pow(6,mo-2,mo)
ls=[[b]*6]
for i in range(5):
t=[0]*6
t[i]=1
ls+=[t]
X=matrix([[1*(i==0)] for i in range(6)])
M=matrix(ls)
M**=n
ans=M*X
print(ans[0][0])
exit()
def prob(a,b):
return a*pow(b,mo-2,mo)%mo
mp=[None]*(n+1)
mp[0]=1
b=pow(6,mo-2,mo)
def p(n):
if n<0:
return 0
else:
if mp[n]!=None:
return mp[n]
else:
mp[n]=(p(n-1)*1*b+p(n-2)*1*b+p(n-3)*1*b+p(n-4)*1*b+p(n-5)*b+p(n-6)*b)%mo
return mp[n]
ans=prob(7,36)
ans=p(n)