結果
問題 | No.718 行列のできるフィボナッチ数列道場 (1) |
ユーザー | vwxyz |
提出日時 | 2021-08-20 21:54:26 |
言語 | PyPy3 (7.3.15) |
結果 |
AC
|
実行時間 | 167 ms / 2,000 ms |
コード長 | 25,269 bytes |
コンパイル時間 | 210 ms |
コンパイル使用メモリ | 82,048 KB |
実行使用メモリ | 88,704 KB |
最終ジャッジ日時 | 2024-10-14 03:27:52 |
合計ジャッジ時間 | 5,195 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge2 |
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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 | 163 ms
88,320 KB |
testcase_01 | AC | 166 ms
88,320 KB |
testcase_02 | AC | 161 ms
88,320 KB |
testcase_03 | AC | 159 ms
88,576 KB |
testcase_04 | AC | 159 ms
88,704 KB |
testcase_05 | AC | 164 ms
88,704 KB |
testcase_06 | AC | 162 ms
88,320 KB |
testcase_07 | AC | 158 ms
88,448 KB |
testcase_08 | AC | 158 ms
88,448 KB |
testcase_09 | AC | 158 ms
88,576 KB |
testcase_10 | AC | 159 ms
88,448 KB |
testcase_11 | AC | 158 ms
88,448 KB |
testcase_12 | AC | 160 ms
88,576 KB |
testcase_13 | AC | 160 ms
88,320 KB |
testcase_14 | AC | 162 ms
88,448 KB |
testcase_15 | AC | 157 ms
88,448 KB |
testcase_16 | AC | 159 ms
88,448 KB |
testcase_17 | AC | 167 ms
88,448 KB |
testcase_18 | AC | 164 ms
88,576 KB |
testcase_19 | AC | 160 ms
88,320 KB |
testcase_20 | AC | 163 ms
88,704 KB |
testcase_21 | AC | 159 ms
88,576 KB |
testcase_22 | AC | 161 ms
88,576 KB |
ソースコード
import bisect import copy import decimal import fractions import functools import heapq import itertools import math import random import sys from collections import Counter,deque,defaultdict from functools import lru_cache,reduce from heapq import heappush,heappop,heapify,heappushpop,_heappop_max,_heapify_max def _heappush_max(heap,item): heap.append(item) heapq._siftdown_max(heap, 0, len(heap)-1) def _heappushpop_max(heap, item): if heap and item < heap[0]: item, heap[0] = heap[0], item heapq._siftup_max(heap, 0) return item from math import degrees, gcd as GCD read=sys.stdin.read readline=sys.stdin.readline readlines=sys.stdin.readlines def Extended_Euclid(n,m): stack=[] while m: stack.append((n,m)) n,m=m,n%m if n>=0: x,y=1,0 else: x,y=-1,0 for i in range(len(stack)-1,-1,-1): n,m=stack[i] x,y=y,x-(n//m)*y return x,y class MOD: def __init__(self,mod): self.mod=mod def Pow(self,a,n): a%=self.mod if n>=0: return pow(a,n,self.mod) else: assert math.gcd(a,self.mod)==1 x=Extended_Euclid(a,self.mod)[0] return pow(x,-n,self.mod) def Build_Fact(self,N): assert N>=0 self.factorial=[1] for i in range(1,N+1): self.factorial.append((self.factorial[-1]*i)%self.mod) self.factorial_inv=[None]*(N+1) self.factorial_inv[-1]=self.Pow(self.factorial[-1],-1) for i in range(N-1,-1,-1): self.factorial_inv[i]=(self.factorial_inv[i+1]*(i+1))%self.mod return self.factorial_inv def Fact(self,N): return self.factorial[N] def Fact_Inv(self,N): return self.factorial_inv[N] def Comb(self,N,K): if K<0 or K>N: return 0 s=self.factorial[N] s=(s*self.factorial_inv[K])%self.mod s=(s*self.factorial_inv[N-K])%self.mod return s class Matrix: def __init__(self,H=0,W=0,matrix=False,eps=1e-12,mod=0,identity=0): if identity: if H: self.H=H self.W=H else: self.H=W self.W=W self.matrix=[[0]*self.W for i in range(self.H)] for i in range(self.H): self.matrix[i][i]=identity elif matrix: self.matrix=matrix self.H=len(self.matrix) self.W=len(self.matrix[0]) if self.matrix else 0 else: self.H=H self.W=W self.matrix=[[0]*self.W for i in range(self.H)] self.mod=mod self.eps=eps def __eq__(self,other): if type(other)!=Matrix: return False if self.H!=other.H: return False if self.mod: for i in range(self.H): for j in range(self.W): if self.matrix[i][j]%self.mod!=other.matrix[i][j]%self.mod: return False else: for i in range(self.H): for j in range(self.W): if abs(self.matrix[i][j]-other.matrix[i][j])>self.eps: return False return True def __ne__(self,other): if type(other)!=Matrix: return True if self.H!=other.H: return True if self.mod: for i in range(self.H): for j in range(self.W): if self.matrix[i][j]%self.mod!=other.matrix[i][j]%self.mod: return True else: for i in range(self.H): for j in range(self.W): if abs(self.matrix[i][j]-other.matrix[i][j])>self.eps: return True return False def __add__(self,other): if type(other)==Matrix: assert self.H==other.H assert self.W==other.W if self.mod: summ=Matrix(matrix=[[(self.matrix[i][j]+other.matrix[i][j])%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) else: summ=Matrix(matrix=[[self.matrix[i][j]+other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) else: if self.mod: summ=Matrix(matrix=[[(self.matrix[i][j]+other)%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) else: summ=Matrix(matrix=[[self.matrix[i][j]+other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) return summ def __sub__(self,other): if type(other)==Matrix: assert self.H==other.H assert self.W==other.W if self.mod: diff=Matrix(matrix=[[(self.matrix[i][j]-other.matrix[i][j])%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) else: diff=Matrix(matrix=[[self.matrix[i][j]-other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) else: if self.mod: diff=Matrix(matrix=[[(self.matrix[i][j]-other)%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) else: diff=Matrix(matrix=[[self.matrix[i][j]-other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) return diff def __mul__(self,other): if type(other)==Matrix: assert self.H==other.H assert self.W==other.W if self.mod: prod=Matrix(matrix=[[(self.matrix[i][j]*other.matrix[i][j])%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) else: prod=Matrix(matrix=[[self.matrix[i][j]*other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) else: if self.mod: prod=Matrix(matrix=[[(self.matrix[i][j]*other)%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) else: prod=Matrix(matrix=[[self.matrix[i][j]*other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) return prod def __matmul__(self,other): if type(other)==Matrix: assert self.W==other.H prod=Matrix(H=self.H,W=other.W,eps=self.eps,mod=self.mod) for i in range(self.H): for j in range(other.W): for k in range(self.W): prod.matrix[i][j]+=self.matrix[i][k]*other.matrix[k][j] if self.mod: prod.matrix[i][j]%=self.mod elif type(other)==int: assert self.H==self.W if other==0: prod=Matrix(H=self.H,eps=self.eps,mod=self.mod,identity=1) elif other==1: prod=Matrix(matrix=[[self.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) else: prod=Matrix(H=self.H,eps=self.eps,mod=self.mod,identity=1) doub=Matrix(matrix=[[self.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) while other>=2: if other&1: prod@=doub doub@=doub other>>=1 prod@=doub return prod def __truediv__(self,other): if type(other)==Matrix: assert self.H==other.H assert self.W==other.W if self.mod: quot=Matrix(matrix=[[(self.matrix[i][j]*MOD(self.mod).Pow(other.matrix[i][j],-1))%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) else: quot=Matrix(matrix=[[self.matrix[i][j]/other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) else: if self.mod: inve=MOD(self.mod).Pow(other,-1) quot=Matrix(matrix=[[(self.matrix[i][j]*inve)%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) else: quot=Matrix(matrix=[[self.matrix[i][j]/other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) return quot def __floordiv__(self,other): if type(other)==Matrix: assert self.H==other.H assert self.W==other.W quot=Matrix(matrix=[[self.matrix[i][j]//other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) else: quot=Matrix(matrix=[[self.matrix[i][j]//other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) return quot def __mod__(self,other): if type(other)==Matrix: assert self.H==other.H assert self.W==other.W rema=Matrix(matrix=[[self.matrix[i][j]%other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) else: rema=Matrix(matrix=[[self.matrix[i][j]%other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) return rema def __pow__(self,other): if type(other)==Matrix: assert self.H==other.H assert self.W==other.W if self.mod: powe=Matrix(matrix=[[pow(self.matrix[i][j],other.matrix[i][j],self.mod) for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) else: powe=Matrix(matrix=[[pow(self.matrix[i][j],other.matrix[i][j]) for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) else: if self.mod: powe=Matrix(matrix=[[pow(self.matrix[i][j],other,self.mod) for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) else: powe=Matrix(matrix=[[pow(self.matrix[i][j],other) for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) return powe def __lshift__(self,other): if type(other)==Matrix: assert self.H==other.H assert self.W==other.W lshi=Matrix(matrix=[[self.matrix[i][j]<<other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) else: lshi=Matrix(matrix=[[self.matrix[i][j]<<other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) return lshi def __rshift__(self,other): if type(other)==Matrix: assert self.H==other.H assert self.W==other.W rshi=Matrix(matrix=[[self.matrix[i][j]>>other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) else: rshi=Matrix(matrix=[[self.matrix[i][j]>>other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) return rshi def __and__(self,other): if type(other)==Matrix: assert self.H==other.H assert self.W==other.W conj=Matrix(matrix=[[self.matrix[i][j]&other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) else: conj=Matrix(matrix=[[self.matrix[i][j]&other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) return conj def __or__(self,other): if type(other)==Matrix: assert self.H==other.H assert self.W==other.W disj=Matrix(matrix=[[self.matrix[i][j]|other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) else: disj=Matrix(matrix=[[self.matrix[i][j]|other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) return disj def __xor__(self,other): if type(other)==Matrix: assert self.H==other.H assert self.W==other.W excl=Matrix(matrix=[[self.matrix[i][j]^other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) else: excl=Matrix(matrix=[[self.matrix[i][j]^other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) return excl def __iadd__(self,other): if type(other)==Matrix: assert self.H==other.H assert self.W==other.W for i in range(self.H): for j in range(self.W): self.matrix[i][j]+=other.matrix[i][j] if self.mod: self.matrix[i][j]%=self.mod else: for i in range(self.H): for j in range(self.W): self.matrix[i][j]+=other if self.mod: self.matrix[i][j]%=self.mod return self def __isub__(self,other): if type(other)==Matrix: assert self.H==other.H assert self.W==other.W for i in range(self.H): for j in range(self.W): self.matrix[i][j]-=other.matrix[i][j] if self.mod: self.matrix[i][j]%=self.mod else: for i in range(self.H): for j in range(self.W): self.matrix[i][j]-=other if self.mod: self.matrix[i][j]%=self.mod return self def __imul__(self,other): if type(other)==Matrix: assert self.H==other.H assert self.W==other.W for i in range(self.H): for j in range(self.W): self.matrix[i][j]*=other.matrix[i][j] if self.mod: self.matrix[i][j]%=self.mod else: for i in range(self.H): for j in range(self.W): self.matrix[i][j]*=other if self.mod: self.matrix[i][j]%=self.mod return self def __imatmul__(self,other): if type(other)==Matrix: assert self.W==other.H prod=Matrix(H=self.H,W=other.W,eps=self.eps,mod=self.mod) for i in range(self.H): for j in range(other.W): for k in range(self.W): prod.matrix[i][j]+=self.matrix[i][k]*other.matrix[k][j] if self.mod: prod.matrix[i][j]%=self.mod elif type(other)==int: assert self.H==self.W if other==0: return Matrix(H=self.H,eps=self.eps,mod=self.mod,identity=1) elif other==1: prod=Matrix(matrix=[[self.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) else: prod=Matrix(H=self.H,eps=self.eps,mod=self.mod,identity=1) doub=self while other>=2: if other&1: prod@=doub doub@=doub other>>=1 prod@=doub return prod def __itruediv__(self,other): if type(other)==Matrix: assert self.H==other.H assert self.W==other.W for i in range(self.H): for j in range(self.W): if self.mod: self.matrix[i][j]=self.matrix[i][j]*MOD(self.mod).Pow(other.matrix[i][j],-1)%self.mod else: self.matrix[i][j]/=other.matrix[i][j] else: if self.mod: inve=MOD(self.mod).Pow(other,-1) for i in range(self.H): for j in range(self.W): if self.mod: self.matrix[i][j]=self.matrix[i][j]*inve%self.mod else: self.matrix[i][j]/=other return self def __ifloordiv__(self,other): if type(other)==Matrix: assert self.H==other.H assert self.W==other.W for i in range(self.H): for j in range(self.W): self.matrix[i][j]//=other.matrix[i][j] else: for i in range(self.H): for j in range(self.W): self.matrix[i][j]//=other return self def __imod__(self,other): if type(other)==Matrix: assert self.H==other.H assert self.W==other.W for i in range(self.H): for j in range(self.W): self.matrix[i][j]%=other.matrix[i][j] else: for i in range(self.H): for j in range(self.W): self.matrix[i][j]%=other return self def __ipow__(self,other): if type(other)==Matrix: assert self.H==other.H assert self.W==other.W for i in range(self.H): for j in range(self.W): if self.mod: self.matrix[i][j]=pow(self.matrix[i][j],other.matrix[i][j],self.mod) else: self.matrix[i][j]=pow(self.matrix[i][j],other.matrix[i][j]) else: for i in range(self.H): for j in range(self.W): if self.mod: self.matrix[i][j]=pow(self.matrix[i][j],other,self.mod) else: self.matrix[i][j]=pow(self.matrix[i][j],other) return self def __ilshift__(self,other): if type(other)==Matrix: assert self.H==other.H assert self.W==other.W for i in range(self.H): for j in range(self.W): self.matrix[i][j]<<=other.matrix[i][j] else: for i in range(self.H): for j in range(self.W): self.matrix[i][j]<<=other return self def __irshift__(self,other): if type(other)==Matrix: assert self.H==other.H assert self.W==other.W for i in range(self.H): for j in range(self.W): self.matrix[i][j]>>=other.matrix[i][j] else: for i in range(self.H): for j in range(self.W): self.matrix[i][j]>>=other return self def __iand__(self,other): if type(other)==Matrix: assert self.H==other.H assert self.W==other.W for i in range(self.H): for j in range(self.W): self.matrix[i][j]&=other.matrix[i][j] else: for i in range(self.H): for j in range(self.W): self.matrix[i][j]&=other return self def __ior__(self,other): if type(other)==Matrix: assert self.H==other.H assert self.W==other.W for i in range(self.H): for j in range(self.W): self.matrix[i][j]|=other.matrix[i][j] else: for i in range(self.H): for j in range(self.W): self.matrix[i][j]|=other return self def __ixor__(self,other): if type(other)==Matrix: assert self.H==other.H assert self.W==other.W for i in range(self.H): for j in range(self.W): self.matrix[i][j]^=other.matrix[i][j] else: for i in range(self.H): for j in range(self.W): self.matrix[i][j]^=other return self def __neg__(self): if self.mod: nega=Matrix(matrix=[[(-self.matrix[i][j])%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) else: nega=Matrix(matrix=[[-self.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) return nega def __pos__(self): posi=Matrix(matrix=[[self.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) return posi def __invert__(self): inve=Matrix(matrix=[[~self.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) return inve def __abs__(self): abso=Matrix(matrix=[[abs(self.matrix[i][j]) for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) return abso def __getitem__(self,i): if type(i)==int: return self.matrix[i] elif type(i)==tuple: i,j=i if type(i)==int: i=slice(i,i+1) if type(j)==int: j=slice(j,j+1) return Matrix(matrix=[lst[j] for lst in self.matrix[i]],eps=self.eps,mod=self.mod) def __contains__(self,x): for i in range(self.H): if x in self.matrix[i]: return True return False def __str__(self): digit=[max(len(str(self.matrix[i][j])) for i in range(self.H)) for j in range(self.W)] return "\n".join([(" [" if i else "[[")+", ".join([str(self.matrix[i][j]).rjust(digit[j]," ") for j in range(self.W)])+"]" for i in range(self.H)])+"]" def __bool__(self): return True def Transpose(self): return Matrix(matrix=[[self.matrix[i][j] for i in range(self.H)] for j in range(self.W)]) def Trace(self): assert self.H==self.W trace=sum(self.matrix[i][i] for i in range(self.H)) if self.mod: trace%=self.mod return trace def Elem_Raw_Operate_1(self,i1,i2): self.matrix[i1],self.matrix[i2]=self.matrix[i2],self.matrix[i1] def Elem_Raw_Operate_2(self,i,c): if self.mod: self.matrix[i]=[self.matrix[i][j]*c%self.mod for j in range(self.W)] else: self.matrix[i]=[self.matrix[i][j]*c for j in range(self.W)] def Elem_Raw_Operate_3(self,i1,i2,c): if self.mod: self.matrix[i1]=[(self.matrix[i1][j]+c*self.matrix[i2][j])%self.mod for j in range(self.H)] else: self.matrix[i1]=[self.matrix[i1][j]+c*self.matrix[i2][j] for j in range(self.H)] def Elimination(self,determinant=False,inverse_matrix=False,linear_equation=False,rank=False,upper_triangular=False): h=0 ut=Matrix(matrix=[[self.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod) if determinant or inverse_matrix: assert self.H==self.W det=1 if inverse_matrix: assert self.H==self.W im=Matrix(H=self.H,eps=self.eps,mod=self.mod,identity=1) if linear_equation: assert self.H==linear_equation.H le=Matrix(matrix=[[linear_equation.matrix[i][j] for j in range(linear_equation.W)] for i in range(linear_equation.H)],eps=self.eps,mod=self.mod) for j in range(ut.W): for i in range(h,ut.H): if abs(ut.matrix[i][j])>ut.eps: if ut.mod: inve=MOD(ut.mod).Pow(ut.matrix[i][j],-1) else: inve=1/ut.matrix[i][j] ut.Elem_Raw_Operate_1(i,h) if determinant and h%2!=i%2: det=(-det)%self.mod if inverse_matrix: im.Elem_Raw_Operate_1(i,h) if linear_equation: le.Elem_Raw_Operate_1(i,h) ut.Elem_Raw_Operate_2(h,inve) if determinant or inverse_matrix: det*=inve if ut.mod: det%=ut.mod if inverse_matrix: im.Elem_Raw_Operate_2(h,inve) if linear_equation: le.Elem_Raw_Operate_2(h,inve) for ii in range(ut.H): if ii==h: continue x=-ut.matrix[ii][j] ut.Elem_Raw_Operate_3(ii,h,x) if inverse_matrix: im.Elem_Raw_Operate_3(ii,h,x) if linear_equation: le.Elem_Raw_Operate_3(ii,h,x) h+=1 break else: det=0 tpl=() if determinant: tpl+=(det,) if inverse_matrix: if det<=0: im=False tpl+=(im,) if linear_equation: tpl+=(le,) if rank: tpl+=(h,) if upper_triangular: tpl+=(ut,) if len(tpl)==1: tpl=tpl[0] return tpl N=int(readline()) mod=10**9+7 M=Matrix(matrix=[[1,1],[1,0]],mod=mod) Fi=Matrix(matrix=[[1],[0]]) Fi=M@N@Fi ans=Fi[0][0]*Fi[1][0]%mod print(ans)