library_for_python
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Segment_Tree/Lazy_Evaluation_Proportion_Tree.py
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- Last update: 2023-03-20 03:47:37+09:00
Code
class Lazy_Evaluation_Proportion_Tree():
def __init__(self,L,calc,unit,act,comp,id,prop,index=1):
"""calcを演算,actを作用とするリストLのSegment Treeを作成
calc:演算
unit:モノイドcalcの単位元 (xe=ex=xを満たすe)
act:作用素
comp:作用素の合成
id:恒等写像
prop:比例の仕方
[条件] M:Monoid,F={f:F x M→ M:作用素},prop:F x N →Fに対して,以下が成立する.
・Fは恒等写像 id を含む.つまり,任意の x in M に対して id(x)=x
・Fは写像の合成に閉じている.つまり,任意の f,g in F に対して, comp(f,g) in F
・任意の f in F, x,y in M に対して,f(x*y)=f(x)*f(y)である.
・prop(f,2n)(x,y)=prop(f,n)(x)*prop(f,n)(y)
[注記]
作用素は左から掛ける.更新も左から.
calc(a,b,l,r):a,b:計算に用いる値,l,r:a,bが格納されているIndex (lがa,rがb)
prop(a,l,r):lからrまでのブロックがaであるときの比例の仕方.
"""
self.calc=calc
self.unit=unit
self.act=act
self.comp=comp
self.id=id
self.prop=prop
self.index=index
N=len(L)
d=max(1,(N-1).bit_length())
k=1<<d
self.data=[unit]*k+L+[unit]*(k-len(L))
self.lazy=[self.id]*(2*k)
self.N=k
self.depth=d
self.len=[0]*(2*k)
for i in range(k-1,0,-1):
self.data[i]=calc(self.data[i<<1],self.data[i<<1|1],i<<1,i<<1|1)
self.Left=[0]*k+[x for x in range(1,k+1)]
self.Right=[0]*k+[x for x in range(1,k+1)]
for i in range(k-1,0,-1):
self.Left[i]=self.Left[i<<1]
self.Right[i]=self.Right[i<<1|1]
def _eval_at(self,m):
if self.lazy[m]==self.id:
return self.data[m]
return self.act(self.prop(self.lazy[m],self.Left[m],self.Right[m]),self.data[m])
#配列の第m要素を下に伝搬
def _propagate_at(self,m):
self.data[m]=self._eval_at(m)
if m<self.N and self.lazy[m]!=self.id:
self.lazy[m<<1]=self.comp(
self.lazy[m],
self.lazy[m<<1]
)
self.lazy[m<<1|1]=self.comp(
self.lazy[m],
self.lazy[m<<1|1]
)
self.lazy[m]=self.id
#配列の第m要素より上を全て伝搬
def _propagate_above(self,m):
H=m.bit_length()
for h in range(H-1,0,-1):
self._propagate_at(m>>h)
#配列の第m要素より上を全て再計算
def _recalc_above(self,m):
l=1<<(self.depth+1-m.bit_length())
while m>1:
m>>=1
l<<=1
self.data[m]=self.calc(
self._eval_at(m<<1),
self._eval_at(m<<1|1)
)
def get(self,k):
m=k-self.index+self.N
self._propagate_above(m)
self.data[m]=self._eval_at(m)
self.lazy[m]=self.id
return self.data[m]
#作用
def action(self,From,To,alpha,left_closed=True,right_closed=True):
L=(From-self.index)+self.N+(not left_closed)
R=(To-self.index)+self.N+(right_closed)
L0=R0=-1
X,Y=L,R-1
while X<Y:
if X&1:
L0=max(L0,X)
X+=1
if Y&1==0:
R0=max(R0,Y)
Y-=1
X>>=1
Y>>=1
L0=max(L0,X)
R0=max(R0,Y)
self._propagate_above(L0)
self._propagate_above(R0)
while L<R:
if L&1:
self.lazy[L]=self.comp(alpha,self.lazy[L])
L+=1
if R&1:
R-=1
self.lazy[R]=self.comp(alpha,self.lazy[R])
L>>=1
R>>=1
self._recalc_above(L0)
self._recalc_above(R0)
def update(self,k,x):
""" 第k要素をxに変更する.
"""
m=k-self.index+self.N
self._propagate_above(m)
self.data[m]=x
self.lazy[m]=self.id
self._recalc_above(m)
def product(self,From,To,left_closed=True,right_closed=True):
L=(From-self.index)+self.N+(not left_closed)
R=(To-self.index)+self.N+(right_closed)
L0=R0=-1
X,Y=L,R-1
while X<Y:
if X&1:
L0=max(L0,X)
X+=1
if Y&1==0:
R0=max(R0,Y)
Y-=1
X>>=1
Y>>=1
L0=max(L0,X)
R0=max(R0,Y)
self._propagate_above(L0)
self._propagate_above(R0)
vL=vR=self.unit
while L<R:
if L&1:
#vL=self.calc(vL,self._eval_at(L))
L+=1
if R&1:
R-=1
#vR=self.calc(self._eval_at(R),vR)
L>>=1
R>>=1
print(L,R)
return self.calc(vL,vR)
def all_product(self):
return self.product(self.index,self.N+(self.index-1))
#リフレッシュ
def refresh(self):
for m in range(1,2*self.N):
self.data[m]=self._eval_at(m)
if m<self.N and self.lazy[m]!=self.id:
self.lazy[m<<1]=self.comp(
self.lazy[m],
self.lazy[m<<1]
)
self.lazy[m<<1|1]=self.comp(
self.lazy[m],
self.lazy[m<<1|1]
)
self.lazy[m]=self.idTraceback (most recent call last):
File "/opt/hostedtoolcache/Python/3.13.3/x64/lib/python3.13/site-packages/onlinejudge_verify/documentation/build.py", line 71, in _render_source_code_stat
bundled_code = language.bundle(stat.path, basedir=basedir, options={'include_paths': [basedir]}).decode()
~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/opt/hostedtoolcache/Python/3.13.3/x64/lib/python3.13/site-packages/onlinejudge_verify/languages/python.py", line 96, in bundle
raise NotImplementedError
NotImplementedError