結果

問題 No.828 全方位神童数
ユーザー vwxyz
提出日時 2024-04-08 08:39:28
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 841 ms / 2,000 ms
コード長 10,493 bytes
コンパイル時間 373 ms
コンパイル使用メモリ 82,304 KB
実行使用メモリ 174,356 KB
最終ジャッジ日時 2024-10-01 04:59:42
合計ジャッジ時間 23,212 ms
ジャッジサーバーID
(参考情報)
judge4 / judge3
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 * 43
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

from collections import defaultdict
class UnionFind:
def __init__(self,N,label=None,f=None,weighted=False,rollback=False):
self.N=N
self.parents=[None]*self.N
self.size=[1]*self.N
self.roots={i for i in range(self.N)}
self.label=label
if self.label!=None:
self.label=[x for x in label]
self.f=f
self.weighted=weighted
if self.weighted:
self.weight=[0]*self.N
self.rollback=rollback
if self.rollback:
self.operate_list=[]
self.operate_set=[]
def Find(self,x):
stack=[]
while self.parents[x]!=None:
stack.append(x)
x=self.parents[x]
if not self.rollback:
if self.weighted:
w=0
for y in stack[::-1]:
self.parents[y]=x
w+=self.weight[y]
self.weight[y]=w
else:
for y in stack[::-1]:
self.parents[y]=x
return x
def Union(self,x,y,w=None):
root_x=self.Find(x)
root_y=self.Find(y)
if self.rollback:
self.operate_list.append([])
self.operate_set.append([])
if root_x==root_y:
if self.weighted:
if self.weight[y]-self.weight[x]==w:
return True
else:
return False
else:
if self.size[root_x]<self.size[root_y]:
x,y=y,x
root_x,root_y=root_y,root_x
if self.weighted:
w=-w
if self.rollback:
self.operate_list[-1].append((self.parents,root_y,self.parents[root_y]))
self.operate_list[-1].append((self.size,root_x,self.size[root_x]))
self.operate_set[-1].append(root_y)
if self.label!=None:
self.operate_list[-1]((self.label,root_x,self.label[root_x]))
if self.weighted:
self.operate_list[-1].append((self.weight,root_y,self.weight[root_y]))
self.parents[root_y]=root_x
self.size[root_x]+=self.size[root_y]
self.roots.remove(root_y)
if self.label!=None:
self.label[root_x]=self.f(self.label[root_x],self.label[root_y])
if self.weighted:
self.weight[root_y]=w+self.weight[x]-self.weight[y]
def Size(self,x):
return self.size[self.Find(x)]
def Same(self,x,y):
return self.Find(x)==self.Find(y)
def Label(self,x):
return self.label[self.Find(x)]
def Weight(self,x,y):
root_x=self.Find(x)
root_y=self.Find(y)
if root_x!=root_y:
return None
return self.weight[y]-self.weight[x]
def Roots(self):
return list(self.roots)
def Linked_Components_Count(self):
return len(self.roots)
def Linked_Components(self):
linked_components=defaultdict(list)
for x in range(self.N):
linked_components[self.Find(x)].append(x)
return linked_components
def Rollback(self):
assert self.rollback
if self.operate_list:
for lst,x,v in self.operate_list.pop():
lst[x]=v
for x in self.operate_set.pop():
self.roots.add(x)
return True
else:
return False
def __str__(self):
linked_components=defaultdict(list)
for x in range(self.N):
linked_components[self.Find(x)].append(x)
return "\n".join(f"{r}: {linked_components[r]}" for r in sorted(list(linked_components.keys())))
class Graph:
def __init__(self,V,edges=None,graph=None,directed=False,weighted=False,inf=float("inf")):
self.V=V
self.directed=directed
self.weighted=weighted
self.inf=inf
if graph!=None:
self.graph=graph
"""
self.edges=[]
for i in range(self.V):
if self.weighted:
for j,d in self.graph[i]:
if self.directed or not self.directed and i<=j:
self.edges.append((i,j,d))
else:
for j in self.graph[i]:
if self.directed or not self.directed and i<=j:
self.edges.append((i,j))
"""
else:
self.edges=edges
self.graph=[[] for i in range(self.V)]
if weighted:
for i,j,d in self.edges:
self.graph[i].append((j,d))
if not self.directed:
self.graph[j].append((i,d))
else:
for i,j in self.edges:
self.graph[i].append(j)
if not self.directed:
self.graph[j].append(i)
def SIV_DFS(self,s,bipartite_graph=False,cycle_detection=False,directed_acyclic=False,euler_tour=False,linked_components=False,lowlink=False
        ,parents=False,postorder=False,preorder=False,subtree_size=False,topological_sort=False,unweighted_dist=False,weighted_dist=False):
seen=[False]*self.V
finished=[False]*self.V
if directed_acyclic or cycle_detection or topological_sort:
dag=True
if euler_tour:
et=[]
if linked_components:
lc=[]
if lowlink:
order=[None]*self.V
ll=[None]*self.V
idx=0
if parents or cycle_detection or lowlink or subtree_size:
ps=[None]*self.V
if postorder or topological_sort:
post=[]
if preorder:
pre=[]
if subtree_size:
ss=[1]*self.V
if unweighted_dist or bipartite_graph:
uwd=[self.inf]*self.V
uwd[s]=0
if weighted_dist:
wd=[self.inf]*self.V
wd[s]=0
stack=[(s,0)] if self.weighted else [s]
while stack:
if self.weighted:
x,d=stack.pop()
else:
x=stack.pop()
if not seen[x]:
seen[x]=True
stack.append((x,d) if self.weighted else x)
if euler_tour:
et.append(x)
if linked_components:
lc.append(x)
if lowlink:
order[x]=idx
ll[x]=idx
idx+=1
if preorder:
pre.append(x)
for y in self.graph[x]:
if self.weighted:
y,d=y
if not seen[y]:
stack.append((y,d) if self.weighted else y)
if parents or cycle_detection or lowlink or subtree_size:
ps[y]=x
if unweighted_dist or bipartite_graph:
uwd[y]=uwd[x]+1
if weighted_dist:
wd[y]=wd[x]+d
elif not finished[y]:
if (directed_acyclic or cycle_detection or topological_sort) and dag:
dag=False
if cycle_detection:
cd=(y,x)
elif not finished[x]:
finished[x]=True
if euler_tour:
et.append(~x)
if lowlink:
bl=True
for y in self.graph[x]:
if self.weighted:
y,d=y
if ps[x]==y and bl:
bl=False
continue
ll[x]=min(ll[x],order[y])
if x!=s:
ll[ps[x]]=min(ll[ps[x]],ll[x])
if postorder or topological_sort:
post.append(x)
if subtree_size:
for y in self.graph[x]:
if self.weighted:
y,d=y
if y==ps[x]:
continue
ss[x]+=ss[y]
if bipartite_graph:
bg=[[],[]]
for tpl in self.edges:
x,y=tpl[:2] if self.weighted else tpl
if uwd[x]==self.inf or uwd[y]==self.inf:
continue
if not uwd[x]%2^uwd[y]%2:
bg=False
break
else:
for x in range(self.V):
if uwd[x]==self.inf:
continue
bg[uwd[x]%2].append(x)
retu=()
if bipartite_graph:
retu+=(bg,)
if cycle_detection:
if dag:
cd=[]
else:
y,x=cd
cd=self.Route_Restoration(y,x,ps)
retu+=(cd,)
if directed_acyclic:
retu+=(dag,)
if euler_tour:
retu+=(et,)
if linked_components:
retu+=(lc,)
if lowlink:
retu=(ll,)
if parents:
retu+=(ps,)
if postorder:
retu+=(post,)
if preorder:
retu+=(pre,)
if subtree_size:
retu+=(ss,)
if topological_sort:
if dag:
tp_sort=post[::-1]
else:
tp_sort=[]
retu+=(tp_sort,)
if unweighted_dist:
retu+=(uwd,)
if weighted_dist:
retu+=(wd,)
if len(retu)==1:
retu=retu[0]
return retu
N=int(input())
R=list(map(int,input().split()))
graph=[[] for x in range(N)]
for i in range(N-1):
u,v=map(int,input().split())
u-=1;v-=1
if u>v:
u,v=v,u
graph[v].append(u)
cnt=[0]*N
UF=UnionFind(N,label=[x for x in range(N)],f=max)
edges=[]
for x in range(N):
for y in graph[x]:
edges.append((UF.Label(x),UF.Label(y)))
UF.Union(x,y)
cnt[UF.Label(x)]+=1
G=Graph(N,edges=edges)
parents,tour=G.SIV_DFS(UF.Label(N-1),parents=True,preorder=True)
for x in tour:
for y in G.graph[x]:
if y==parents[x]:
continue
cnt[y]+=cnt[x]
ans=1
mod=10**9+7
for x in range(N):
ans*=R[x]+cnt[x]
ans%=mod
print(ans)
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0