結果
| 問題 | No.1333 Squared Sum |
| ユーザー |
 vwxyz
|
| 提出日時 | 2023-02-22 18:26:13 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 919 ms / 2,000 ms |
| コード長 | 22,304 bytes |
| コンパイル時間 | 2,476 ms |
| コンパイル使用メモリ | 86,924 KB |
| 実行使用メモリ | 186,760 KB |
| 最終ジャッジ日時 | 2023-09-30 01:44:16 |
| 合計ジャッジ時間 | 28,330 ms |
|
ジャッジサーバーID （参考情報） |
judge13 / judge11 |
（要ログイン）
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 | 73 ms
71,232 KB |
| testcase_01 | AC | 74 ms
71,220 KB |
| testcase_02 | AC | 75 ms
71,024 KB |
| testcase_03 | AC | 872 ms
169,556 KB |
| testcase_04 | AC | 835 ms
170,132 KB |
| testcase_05 | AC | 835 ms
169,224 KB |
| testcase_06 | AC | 793 ms
170,412 KB |
| testcase_07 | AC | 793 ms
169,360 KB |
| testcase_08 | AC | 780 ms
168,720 KB |
| testcase_09 | AC | 781 ms
170,628 KB |
| testcase_10 | AC | 759 ms
167,908 KB |
| testcase_11 | AC | 866 ms
169,056 KB |
| testcase_12 | AC | 829 ms
170,820 KB |
| testcase_13 | AC | 641 ms
186,244 KB |
| testcase_14 | AC | 842 ms
179,360 KB |
| testcase_15 | AC | 919 ms
186,576 KB |
| testcase_16 | AC | 74 ms
71,368 KB |
| testcase_17 | AC | 74 ms
71,328 KB |
| testcase_18 | AC | 75 ms
71,264 KB |
| testcase_19 | AC | 74 ms
71,328 KB |
| testcase_20 | AC | 75 ms
71,404 KB |
| testcase_21 | AC | 73 ms
71,496 KB |
| testcase_22 | AC | 74 ms
70,996 KB |
| testcase_23 | AC | 73 ms
71,340 KB |
| testcase_24 | AC | 75 ms
71,344 KB |
| testcase_25 | AC | 76 ms
71,000 KB |
| testcase_26 | AC | 906 ms
184,080 KB |
| testcase_27 | AC | 903 ms
182,320 KB |
| testcase_28 | AC | 897 ms
184,688 KB |
| testcase_29 | AC | 668 ms
186,760 KB |
| testcase_30 | AC | 407 ms
115,508 KB |
| testcase_31 | AC | 292 ms
100,076 KB |
| testcase_32 | AC | 555 ms
133,116 KB |
| testcase_33 | AC | 446 ms
120,676 KB |
| testcase_34 | AC | 672 ms
150,336 KB |
| testcase_35 | AC | 537 ms
132,524 KB |
| testcase_36 | AC | 347 ms
109,028 KB |
| testcase_37 | AC | 383 ms
110,564 KB |
| testcase_38 | AC | 398 ms
114,484 KB |
| testcase_39 | AC | 590 ms
139,316 KB |
| testcase_40 | AC | 538 ms
168,792 KB |
| testcase_41 | AC | 543 ms
169,288 KB |
| testcase_42 | AC | 526 ms
168,932 KB |
| testcase_43 | AC | 514 ms
170,036 KB |
ソースコード
import sys
readline=sys.stdin.readline
class Graph:
def __init__(self,V,edges=False,graph=False,directed=False,weighted=False,inf=float("inf")):
self.V=V
self.directed=directed
self.weighted=weighted
self.inf=inf
if graph:
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
def MIV_DFS(self,initial_vertices=None,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):
if initial_vertices==None:
initial_vertices=[s for s in range(self.V)]
seen=[False]*self.V
finished=[False]*self.V
if bipartite_graph:
bg=[None]*self.V
cnt=-1
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 bipartite_graph or unweighted_dist:
uwd=[self.inf]*self.V
if weighted_dist:
wd=[self.inf]*self.V
for s in initial_vertices:
if seen[s]:
continue
if bipartite_graph:
cnt+=1
bg[s]=(cnt,0)
if linked_components:
lc.append([])
if bipartite_graph or unweighted_dist:
uwd[s]=0
if weighted_dist:
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[-1].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 bipartite_graph:
bg[y]=(cnt,bg[x][1]^1)
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 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_=bg
bg=[[[],[]] for i in range(cnt+1)]
for tpl in self.edges:
i,j=tpl[:2] if self.weighted else tpl
if not bg_[i][1]^bg_[j][1]:
bg[bg_[i][0]]=False
for x in range(self.V):
if bg[bg_[x][0]]:
bg[bg_[x][0]][bg_[x][1]].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
def SIV_BFS(self,s,bfs_tour=False,bipartite_graph=False,linked_components=False,parents=False,unweighted_dist=False,weighted_dist=False):
seen=[False]*self.V
seen[s]=True
if bfs_tour:
bt=[s]
if linked_components:
lc=[s]
if parents:
ps=[None]*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
queue=deque([s])
while queue:
x=queue.popleft()
for y in self.graph[x]:
if self.weighted:
y,d=y
if not seen[y]:
seen[y]=True
queue.append(y)
if bfs_tour:
bt.append(y)
if linked_components:
lc.append(y)
if parents:
ps[y]=x
if unweighted_dist or bipartite_graph:
uwd[y]=uwd[x]+1
if weighted_dist:
wd[y]=wd[x]+d
if bipartite_graph:
bg=[[],[]]
for tpl in self.edges:
i,j=tpl[:2] if self.weighted else tpl
if uwd[i]==self.inf or uwd[j]==self.inf:
continue
if not uwd[i]%2^uwd[j]%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 bfs_tour:
retu+=(bt,)
if bipartite_graph:
retu+=(bg,)
if linked_components:
retu+=(lc,)
if parents:
retu+=(ps,)
if unweighted_dist:
retu+=(uwd,)
if weighted_dist:
retu+=(wd,)
if len(retu)==1:
retu=retu[0]
return retu
def MIV_BFS(self,initial_vertices=None,bipartite_graph=False,linked_components=False,parents=False,unweighted_dist=False,weighted_dist=False):
if initial_vertices==None:
initial_vertices=[i for i in range(self.V)]
seen=[False]*self.V
if bipartite_graph:
bg=[None]*self.V
cnt=-1
if linked_components:
lc=[]
if parents:
ps=[None]*self.V
if unweighted_dist:
uwd=[self.inf]*self.V
if weighted_dist:
wd=[self.inf]*self.V
for s in initial_vertices:
if seen[s]:
continue
seen[s]=True
if bipartite_graph:
cnt+=1
bg[s]=(cnt,0)
if linked_components:
lc.append([s])
if unweighted_dist:
uwd[s]=0
if weighted_dist:
wd[s]=0
queue=deque([s])
while queue:
x=queue.popleft()
for y in self.graph[x]:
if self.weighted:
y,d=y
if not seen[y]:
seen[y]=True
queue.append(y)
if bipartite_graph:
bg[y]=(cnt,bg[x][1]^1)
if linked_components:
lc[-1].append(y)
if parents:
ps[y]=x
if unweighted_dist:
uwd[y]=uwd[x]+1
if weighted_dist:
wd[y]=wd[x]+d
if bipartite_graph:
bg_=bg
bg=[[[],[]] for i in range(cnt+1)]
for tpl in self.edges:
i,j=tpl[:2] if self.weighted else tpl
if not bg_[i][1]^bg_[j][1]:
bg[bg_[i][0]]=False
for x in range(self.V):
if bg[bg_[x][0]]:
bg[bg_[x][0]][bg_[x][1]].append(x)
retu=()
if bipartite_graph:
retu+=(bg,)
if linked_components:
retu+=(lc,)
if parents:
retu=(ps,)
if unweighted_dist:
retu+=(uwd,)
if weighted_dist:
retu+=(wd,)
if len(retu)==1:
retu=retu[0]
return retu
def Build_Approach(self,s):
self.approach_parents,self.approach_depth=self.SIV_DFS(s,parents=True,unweighted_dist=True)
self.approach_parents[s]=s
self.approach_PD=Path_Doubling(self.V,self.approach_parents)
self.approach_PD.Build_Next()
def Approach(self,x,y):
if x==y:
return None
if self.approach_depth[x]>=self.approach_depth[y]:
return self.approach_parents[x]
retu=self.approach_PD.Permutation_Doubling(y,self.approach_depth[y]-self.approach_depth[x]-1)
if self.approach_parents[retu]==x:
return retu
else:
return self.approach_parents[x]
def Build_Rerooting(self,s,f,f_merge,subtree=False):
self.rerooting_s=s
self.rerooting_f=f
self.rerooting_f_merge=f_merge
self.subtree=subtree
if self.subtree:
parents,postorder,preorder,self.rerooting_depth=self.SIV_DFS(s,parents=True,postorder=True,preorder=True,unweighted_dist=True)
parents[s]=s
self.rerooting_PD=Path_Doubling(self.V,parents)
self.rerooting_PD.Build_Next()
parents[s]=None
else:
parents,postorder,preorder=self.SIV_DFS(s,parents=True,postorder=True,preorder=True)
self.rerooting_lower_dp=[None]*self.V
for x in postorder:
children=[y[0] if self.weighted else y for y in self.graph[x] if (y[0] if self.weighted else y)!=parents[x]]
self.rerooting_lower_dp[x]=self.rerooting_f_merge(x,[self.rerooting_f(y,self.rerooting_lower_dp[y]) for y in children])
self.rerooting_upper_dp=[None]*self.V
for x in preorder:
children=[y[0] if self.weighted else y for y in self.graph[x] if (y[0] if self.weighted else y)!=parents[x]]
left_accumule_f=[None]*(len(children)+1)
right_accumule_f=[None]*(len(children)+1)
left_accumule_f[0]=self.rerooting_f_merge(x,[])
for i in range(1,len(children)+1):
left_accumule_f[i]=self.rerooting_f_merge(x,[left_accumule_f[i-1],self.rerooting_f(children[i-1],self.rerooting_lower_dp[children[i-1]])])
right_accumule_f[len(children)]=self.rerooting_f_merge(x,[])
for i in range(len(children)-1,-1,-1):
right_accumule_f[i]=self.rerooting_f_merge(x,[right_accumule_f[i+1],self.rerooting_f(children[i],self.rerooting_lower_dp[children[i]])])
for i in range(len(children)):
if parents[x]==None:
self.rerooting_upper_dp[children[i]]=self.rerooting_f(x,self.rerooting_f_merge(x,[left_accumule_f[i],right_accumule_f[i+1]]))
else:
self.rerooting_upper_dp[children[i]]=self.rerooting_f(x,self.rerooting_f_merge(x,[left_accumule_f[i],right_accumule_f[i+1],self.rerooting_upper_dp[x]]))
if self.subtree:
self.rerooting_parents=parents
def Rerooting(self,root,subtree=None):
if self.subtree and root!=subtree:
if self.rerooting_depth[subtree]>=self.rerooting_depth[root]:
x=self.rerooting_parents[subtree]
else:
x=self.rerooting_PD.Permutation_Doubling(root,self.rerooting_depth[root]-self.rerooting_depth[subtree]-1)
if self.rerooting_parents[x]!=subtree:
x=self.rerooting_parents[subtree]
if self.rerooting_parents[subtree]==x:
retu=self.rerooting_f(subtree,self.rerooting_lower_dp[subtree])
else:
retu=self.rerooting_upper_dp[x]
else:
if root==self.rerooting_s:
retu=self.rerooting_f(root,self.rerooting_lower_dp[root])
else:
retu=self.rerooting_f(root,self.rerooting_f_merge(root,[self.rerooting_lower_dp[root],self.rerooting_upper_dp[root]]))
return retu
def XOR_Basis(lst):
xor_basis=[]
triangulation=[]
for i,x in enumerate(lst):
xx=x
for j,xb in enumerate(triangulation):
if xx>xx^xb:
xx=xx^xb
if xx:
xor_basis.append(x)
for j in range(len(triangulation)):
if triangulation[j]^xx<triangulation[j]:
triangulation[j]^=xx
triangulation.append(xx)
return xor_basis,triangulation
class Path_Doubling:
def __init__(self,N,permutation,lst=None,f=None,e=None):
self.N=N
self.permutation=permutation
self.lst=lst
self.f=f
self.e=e
def Build_Next(self,K=None):
if K==None:
K=self.N
self.k=K.bit_length()
self.permutation_doubling=[[self.permutation[n]] for n in range(self.N)]
if self.lst!=None:
self.doubling=[[self.lst[n]] for n in range(self.N)]
for i in range(1,self.k):
for n in range(self.N):
self.permutation_doubling[n].append(self.permutation_doubling[self.permutation_doubling[n][i-1]][i-1])
if self.f!=None:
self.doubling[n].append(self.f(self.doubling[n][i-1],self.doubling[self.permutation_doubling[n][i-1]][i-1]))
def Permutation_Doubling(self,N,K):
if K<0:
return N
for i in range(self.k):
if K>>i&1:
N=self.permutation_doubling[N][i]
return N
def Doubling(self,N,K):
if K<0:
return self.e
retu=self.e
for i in range(self.k):
if K>>i&1:
retu=self.f(retu,self.doubling[N][i])
N=self.permutation_doubling[N][i]
return retu
N=int(readline())
edges=[]
for n in range(N-1):
u,v,w=map(int,readline().split())
u-=1;v-=1
edges.append((u,v,w))
mod=10**9+7
G=Graph(N,edges=edges,weighted=True)
parents,tour=G.SIV_DFS(0,parents=True,postorder=True)
dp=[None]*N
ans=0
for x in tour:
DP0,DP1,DP2=0,0,0
for y,d in G.graph[x]:
if y==parents[x]:
continue
dp0,dp1,dp2=dp[y]
dp1,dp2=dp1+dp0*d,dp2+2*dp1*d+d*d*dp0
DP0+=dp0
DP1+=dp1
DP2+=dp2
ans-=dp1*dp1-dp2+dp0*dp2
ans+=DP2
ans+=DP1*DP1-DP2+DP0*DP2
DP0+=1
dp[x]=(DP0,DP1,DP2)
ans%=mod
print(ans)