結果
| 問題 | No.1418 Sum of Sum of Subtree Size |
| ユーザー |
 vwxyz
|
| 提出日時 | 2021-11-25 15:06:10 |
| 言語 | Python3 (3.12.2 + numpy 1.26.4 + scipy 1.12.0) |
| 結果 |
AC
|
| 実行時間 | 687 ms / 2,000 ms |
| コード長 | 37,452 bytes |
| コンパイル時間 | 107 ms |
| コンパイル使用メモリ | 16,640 KB |
| 実行使用メモリ | 43,016 KB |
| 最終ジャッジ日時 | 2024-06-28 06:23:42 |
| 合計ジャッジ時間 | 12,160 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge5 |
（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 | 44 ms
14,336 KB |
| testcase_01 | AC | 45 ms
14,336 KB |
| testcase_02 | AC | 45 ms
14,464 KB |
| testcase_03 | AC | 687 ms
40,448 KB |
| testcase_04 | AC | 683 ms
40,320 KB |
| testcase_05 | AC | 682 ms
40,448 KB |
| testcase_06 | AC | 681 ms
40,448 KB |
| testcase_07 | AC | 671 ms
40,320 KB |
| testcase_08 | AC | 445 ms
31,488 KB |
| testcase_09 | AC | 213 ms
22,144 KB |
| testcase_10 | AC | 229 ms
22,656 KB |
| testcase_11 | AC | 139 ms
18,688 KB |
| testcase_12 | AC | 344 ms
27,904 KB |
| testcase_13 | AC | 409 ms
30,336 KB |
| testcase_14 | AC | 418 ms
31,104 KB |
| testcase_15 | AC | 325 ms
26,752 KB |
| testcase_16 | AC | 73 ms
15,104 KB |
| testcase_17 | AC | 75 ms
15,104 KB |
| testcase_18 | AC | 612 ms
37,760 KB |
| testcase_19 | AC | 133 ms
18,176 KB |
| testcase_20 | AC | 58 ms
14,592 KB |
| testcase_21 | AC | 311 ms
26,368 KB |
| testcase_22 | AC | 269 ms
24,576 KB |
| testcase_23 | AC | 61 ms
14,592 KB |
| testcase_24 | AC | 62 ms
14,464 KB |
| testcase_25 | AC | 57 ms
14,464 KB |
| testcase_26 | AC | 62 ms
14,464 KB |
| testcase_27 | AC | 47 ms
14,336 KB |
| testcase_28 | AC | 50 ms
14,464 KB |
| testcase_29 | AC | 67 ms
14,592 KB |
| testcase_30 | AC | 64 ms
14,720 KB |
| testcase_31 | AC | 55 ms
14,592 KB |
| testcase_32 | AC | 59 ms
14,464 KB |
| testcase_33 | AC | 153 ms
20,224 KB |
| testcase_34 | AC | 652 ms
43,016 KB |
| testcase_35 | AC | 263 ms
25,856 KB |
| testcase_36 | AC | 101 ms
16,384 KB |
| testcase_37 | AC | 517 ms
37,120 KB |
| testcase_38 | AC | 459 ms
35,328 KB |
| testcase_39 | AC | 44 ms
14,464 KB |
| testcase_40 | AC | 45 ms
14,464 KB |
| testcase_41 | AC | 45 ms
14,464 KB |
| testcase_42 | AC | 45 ms
14,464 KB |
| testcase_43 | AC | 45 ms
14,464 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 not graph:
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)
else:
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))
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=False,bipartite_graph=False,linked_components=False,parents=False):
if not initial_vertices:
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
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])
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 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 len(retu)==1:
retu=retu[0]
return retu
def SIV_DFS(self,s,bipartite_graph=False,cycle_detection=False,directed_acyclic=False,euler_tour=False,linked_components=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 parents or cycle_detection 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 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 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 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:
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 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 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=False,bipartite_graph=False,cycle_detection=False,directed_acyclic=False,euler_tour=False,linked_components=False,parents=False,postorder=False,preorder=False,subtree_size=False,topological_sort=False,unweighted_dist=False,weighted_dist=False):
if not initial_vertices:
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 parents or cycle_detection 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:
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 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 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 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 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 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 Tree_Diameter(self,weighted=False):
def Farthest_Point(u):
dist=self.SIV_BFS(u,weighted_dist=True) if weighted else self.SIV_BFS(u,unweighted_dist=True)
fp=0
for i in range(self.V):
if dist[fp]<dist[i]:
fp=i
return fp,dist[fp]
u,d=Farthest_Point(0)
v,d=Farthest_Point(u)
return u,v,d
def SCC(self):
reverse_graph=[[] for i in range(self.V)]
for tpl in self.edges:
i,j=tpl[:2] if self.weighted else tpl
reverse_graph[j].append(i)
postorder=self.MIV_DFS(postorder=True)
scc=[]
seen=[False]*self.V
for s in postorder[::-1]:
if seen[s]:
continue
queue=deque([s])
seen[s]=True
lst=[]
while queue:
x=queue.popleft()
lst.append(x)
for y in reverse_graph[x]:
if self.weighted:
y,d=y
if not seen[y]:
seen[y]=True
queue.append(y)
scc.append(lst)
return scc
def Build_LCA(self,s):
self.lca_euler_tour,self.lca_parents,depth=self.SIV_DFS(s,euler_tour=True,parents=True,unweighted_dist=True)
self.lca_dfs_in_index=[None]*self.V
self.lca_dfs_out_index=[None]*self.V
for i,x in enumerate(self.lca_euler_tour):
if x>=0:
self.lca_dfs_in_index[x]=i
else:
self.lca_dfs_out_index[~x]=i
self.ST=Segment_Tree(2*self.V,lambda x,y:min(x,y),self.V)
lst=[None]*(2*self.V)
for i in range(2*self.V-1):
if self.lca_euler_tour[i]>=0:
lst[i]=depth[self.lca_euler_tour[i]]
else:
lst[i]=depth[self.lca_parents[~self.lca_euler_tour[i]]]
lst[2*self.V-1]=-1
self.ST.Build(lst)
def LCA(self,a,b):
m=min(self.lca_dfs_in_index[a],self.lca_dfs_in_index[b])
M=max(self.lca_dfs_in_index[a],self.lca_dfs_in_index[b])
x=self.lca_euler_tour[self.ST.Fold_Index(m,M+1)]
if x>=0:
return x
else:
return self.lca_parents[~x]
def Build_HLD(self,s):
self.hld_parents,size,self.hld_depth=self.SIV_DFS(s,parents=True,subtree_size=True,unweighted_dist=True)
stack=[s]
self.hld_tour=[]
self.hld_path_parents=[None]*self.V
self.hld_path_parents[s]=s
while stack:
x=stack.pop()
self.hld_tour.append(x)
max_size=0
max_size_y=None
for y in self.graph[x]:
if self.weighted:
y,d=y
if y==self.hld_parents[x]:
continue
if max_size<size[y]:
max_size=size[y]
max_size_y=y
for y in self.graph[x]:
if self.weighted:
y,d=y
if y==self.hld_parents[x]:
continue
if y!=max_size_y:
stack.append(y)
self.hld_path_parents[y]=y
if max_size_y!=None:
stack.append(max_size_y)
self.hld_path_parents[max_size_y]=self.hld_path_parents[x]
self.hld_tour_idx=[None]*self.V
for i in range(self.V):
self.hld_tour_idx[self.hld_tour[i]]=i
def HLD(self,a,b,edge=False):
L,R=[],[]
while self.hld_path_parents[a]!=self.hld_path_parents[b]:
if self.hld_depth[self.hld_path_parents[a]]<self.hld_depth[self.hld_path_parents[b]]:
R.append((self.hld_tour_idx[self.hld_path_parents[b]],self.hld_tour_idx[b]+1))
b=self.hld_parents[self.hld_path_parents[b]]
else:
L.append((self.hld_tour_idx[a]+1,self.hld_tour_idx[self.hld_path_parents[a]]))
a=self.hld_parents[self.hld_path_parents[a]]
if edge:
if self.hld_depth[a]!=self.hld_depth[b]:
retu=L+[(self.hld_tour_idx[a]+1,self.hld_tour_idx[b]+1)]+R[::-1]
else:
retu=L+R[::-1]
else:
if self.hld_depth[a]<self.hld_depth[b]:
retu=L+[(self.hld_tour_idx[a],self.hld_tour_idx[b]+1)]+R[::-1]
else:
retu=L+[(self.hld_tour_idx[a]+1,self.hld_tour_idx[b])]+R[::-1]
return retu
def Build_Hash(self,s,random_number=False,mod=(1<<61)-1,rerooting=False):
self.bottom_hash=[None]*self.V
if random_number:
self.hash_random_number=random_number
else:
self.hash_random_number=[random.randint(1,10**10) for i in range(self.V)]
self.hash_mod=mod
parents,postorder,preorder=self.SIV_DFS(s,parents=True,postorder=True,preorder=True)
for x in postorder:
level=0
for y in self.graph[x]:
if self.weighted:
y,d=y
if y==parents[x]:
continue
h,l=self.bottom_hash[y]
level=max(level,l+1)
ha=1
for y in self.graph[x]:
if self.weighted:
y,d=y
if y==parents[x]:
continue
h,l=self.bottom_hash[y]
ha*=h+self.hash_random_number[l]
ha%=self.hash_mod
self.bottom_hash[x]=(ha,level)
if rerooting:
self.top_hash=[None]*self.V
self.top_hash[s]=(1,-1)
for x in preorder:
children=[y for y,d in self.graph[x] if y!=parents[x]] if self.weighted else [y for y in self.graph[x] if y!=parents[x]]
if children:
l=len(children)
l_lst,r_lst=[None]*(l+1),[None]*(l+1)
l_lst[0],r_lst[l]=(1,-1),(1,-1)
for i in range(1,l+1):
h0,l0=l_lst[i-1]
h1,l1=self.bottom_hash[children[i-1]]
l_lst[i]=(h0*(h1+self.hash_random_number[l1])%self.hash_mod,max(l0,l1))
for i in range(l-1,-1,-1):
h0,l0=r_lst[i+1]
h1,l1=self.bottom_hash[children[i]]
r_lst[i]=(h0*(h1+self.hash_random_number[l1])%self.hash_mod,max(l0,l1))
for i in range(l):
if x==s:
ha,level=1,0
else:
ha,level=self.top_hash[x]
h0,l0=l_lst[i]
h1,l1=r_lst[i+1]
ha*=h0*h1
level=max(level,l0+1,l1+1)
ha+=self.hash_random_number[level]
ha%=self.hash_mod
level+=1
self.top_hash[children[i]]=(ha,level)
return
def Hash(self,root,subtree=False):
if subtree:
ha,level=self.bottom_hash[root]
ha+=self.hash_random_number[level]
ha%=self.hash_mod
else:
h0,l0=self.bottom_hash[root]
h1,l1=self.top_hash[root]
ha=(h0*h1+self.hash_random_number[max(l0,l1)])%self.hash_mod
level=max(l0,l1)
return ha,level
def Centroid(self,root=0):
x=root
parents,size=self.SIV_DFS(x,parents=True,subtree_size=True)
while True:
for y in self.graph[x]:
if self.weighted:
y,d=y
if y==parents[x]:
continue
if size[y]*2>size[root]:
x=y
break
else:
for y in self.graph[x]:
if y==parents[x]:
continue
if size[root]<=2*size[y]:
return x,y
return x,None
def Centroid_Decomposition(self,edge=False,linked_point=False,point=False,tree=False):
if edge:
cd_edges_lst=[None]*self.V
if linked_point:
cd_linked_points=[None]*self.V
if point:
cd_points_lst=[None]*self.V
if tree:
cd_tree=[]*self.V
if self.weighted:
edges=[(i,j) for i,j,d in self.edges]
else:
edges=self.edges
points=[i for i in range(self.V)]
prev_centroid=None
stack=[(edges,points,None,prev_centroid)] if linked_point else [(edges,points,prev_centroid)]
while stack:
if linked_point:
edges,points,lp,prev_centroid=stack.pop()
else:
edges,points,prev_centroid=stack.pop()
if len(points)==1:
centroid=points[0]
if edge:
cd_edges_lst[centroid]=[]
if linked_point:
cd_linked_points[centroid]=lp
if point:
cd_points_lst[centroid]=[centroid]
if tree and prev_centroid!=None:
cd_tree.append((prev_centroid,centroid))
continue
G=Graph(len(points),edges=edges)
centroid,_=G.Centroid()
if tree and prev_centroid!=None:
cd_tree.append((prev_centroid,points[centroid]))
parents,tour=G.SIV_DFS(centroid,parents=True,preorder=True)
dp=[None]*len(points)
edges_lst=[]
points_lst=[]
if linked_point:
linked_points=[]
for i,x in enumerate(G.graph[centroid]):
dp[x]=(i,0)
edges_lst.append([])
points_lst.append([points[x]])
if linked_point:
linked_points.append(points[x])
for x in tour[1:]:
for y in G.graph[x]:
if y==parents[x]:
continue
i,j=dp[x]
jj=len(points_lst[i])
edges_lst[i].append((j,jj))
points_lst[i].append(points[y])
dp[y]=(i,jj)
centroid=points[centroid]
if edge:
cd_edges_lst[centroid]=edges
if linked_point:
cd_linked_points[centroid]=lp
if point:
cd_points_lst[centroid]=points
if linked_point:
for edges,points,lp in zip(edges_lst,points_lst,linked_points):
stack.append((edges,points,lp,centroid))
else:
for edges,points in zip(edges_lst,points_lst):
stack.append((edges,points,centroid))
retu=()
if edge:
retu+=(cd_edges_lst,)
if linked_point:
retu+=(cd_linked_points,)
if point:
retu+=(cd_points_lst,)
if tree:
retu+=(cd_tree,)
if len(retu)==1:
retu=retu[0]
return retu
def Distance_Frequency(self):
mod=206158430209
cnt=[0]*N
cd_edges,cd_lp,cd_points,cd_tree=self.Centroid_Decomposition(edge=True,linked_point=True,point=True,tree=True)
CD=Graph(N,edges=cd_tree)
parents,tour=CD.SIV_DFS(cd_tree[0][0],parents=True,postorder=True)
for x in tour:
C=[0]*(len(cd_points[x])+1)
for y in CD.graph[x]:
if y==parents[x]:
continue
depth=Graph(len(cd_points[y]),edges=cd_edges[y]).SIV_DFS(0,unweighted_dist=True)
CC=[0]*(max(depth)+2)
for d in depth:
CC[d+1]+=1
cnt[d+1]+=2
C[d+1]+=1
poly=NTT_Pow(CC,2)
for d,c in enumerate(poly):
if d<N:
cnt[d]-=c
while C and C[-1]==0:
C.pop()
poly=NTT_Pow(C,2)
for d,c in enumerate(poly):
if d<N:
cnt[d]+=c
for i in range(N):
cnt[i]//=2
return cnt
def Dijkstra(self,s,route_restoration=False):
dist=[self.inf]*self.V
dist[s]=0
hq=[(0,s)]
if route_restoration:
parents=[None]*self.V
while hq:
dx,x=heapq.heappop(hq)
if dist[x]<dx:
continue
for y,dy in self.graph[x]:
if dist[y]>dx+dy:
dist[y]=dx+dy
if route_restoration:
parents[y]=x
heapq.heappush(hq,(dist[y],y))
if route_restoration:
return dist,parents
else:
return dist
def Bellman_Ford(self,s,route_restoration=False):
dist=[self.inf]*self.V
dist[s]=0
if route_restoration:
parents=[None]*self.V
for _ in range(self.V-1):
for i,j,d in self.edges:
if dist[j]>dist[i]+d:
dist[j]=dist[i]+d
if route_restoration:
parents[j]=i
if not self.directed and dist[i]>dist[j]+d:
dist[i]=dist[j]+d
if route_restoration:
parents[i]=j
negative_cycle=[]
for i,j,d in self.edges:
if dist[j]>dist[i]+d:
negative_cycle.append(j)
if not self.directed and dist[i]>dist[j]+d:
negative_cycle.append(i)
if negative_cycle:
is_negative_cycle=[False]*self.V
for i in negative_cycle:
if is_negative_cycle[i]:
continue
else:
queue=deque([i])
is_negative_cycle[i]=True
while queue:
x=queue.popleft()
for y,d in self.graph[x]:
if not is_negative_cycle[y]:
queue.append(y)
is_negative_cycle[y]=True
if route_restoration:
parents[y]=x
for i in range(self.V):
if is_negative_cycle[i]:
dist[i]=-self.inf
if route_restoration:
return dist,parents
else:
return dist
def Warshall_Floyd(self,route_restoration=False):
dist=[[self.inf]*self.V for i in range(self.V)]
for i in range(self.V):
dist[i][i]=0
if route_restoration:
parents=[[j for j in range(self.V)] for i in range(self.V)]
for i,j,d in self.edges:
if i==j:
continue
if dist[i][j]>d:
dist[i][j]=d
if route_restoration:
parents[i][j]=i
if not self.directed and dist[j][i]>d:
dist[j][i]=d
if route_restoration:
parents[j][i]=j
for k in range(self.V):
for i in range(self.V):
for j in range(self.V):
if dist[i][j]>dist[i][k]+dist[k][j]:
dist[i][j]=dist[i][k]+dist[k][j]
if route_restoration:
parents[i][j]=parents[k][j]
for i in range(self.V):
if dist[i][i]<0:
for j in range(self.V):
if dist[i][j]!=self.inf:
dist[i][j]=-self.inf
if route_restoration:
for i in range(self.V):
if dist[i][i]==0:
parents[i][i]=None
return dist,parents
else:
return dist
def Route_Restoration(self,s,g,parents):
route=[g]
while s!=g:
if parents[g]==None:
route=[]
break
g=parents[g]
route.append(g)
route=route[::-1]
return route
def Kruskal(self):
UF=UnionFind(self.V)
sorted_edges=sorted(self.edges,key=lambda x:x[2])
minimum_spnning_tree=[]
for i,j,d in sorted_edges:
if not UF.Same(i,j):
UF.Union(i,j)
minimum_spnning_tree.append((i,j,d))
return minimum_spnning_tree
def Ford_Fulkerson(self,s,t):
max_flow=0
residual_graph=[defaultdict(int) for i in range(self.V)]
if self.weighted:
for i,j,d in self.edges:
if not d:
continue
residual_graph[i][j]+=d
if not self.directed:
residual_graph[j][i]+=d
else:
for i,j in self.edges:
residual_graph[i][j]+=1
if not self.directed:
residual_graph[j][i]+=1
while True:
parents=[None]*self.V
parents[s]=s
seen=[False]*self.V
seen[s]=True
queue=deque([s])
while queue:
x=queue.popleft()
for y in residual_graph[x].keys():
if not seen[y]:
seen[y]=True
queue.append(y)
parents[y]=x
if y==t:
tt=t
while tt!=s:
residual_graph[parents[tt]][tt]-=1
residual_graph[tt][parents[tt]]+=1
if not residual_graph[parents[tt]][tt]:
residual_graph[parents[tt]].pop(tt)
tt=parents[tt]
max_flow+=1
break
else:
continue
break
else:
break
return max_flow
def BFS(self,s):
seen=[False]*self.V
seen[s]=True
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)
return
def DFS(self,s):
seen=[False]*self.V
finished=[False]*self.V
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)
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)
elif not finished[x]:
finished[x]=True
return
class Cumsum:
def __init__(self,lst,mod=0):
self.N=len(lst)
self.mod=mod
self.cumsum=[0]*(self.N+1)
self.cumsum[0]=0
for i in range(1,self.N+1):
self.cumsum[i]=self.cumsum[i-1]+lst[i-1]
if self.mod:
self.cumsum[i]%=self.mod
def __getitem__(self,i):
if type(i)==int:
if 0<=i<self.N:
a,b=i,i+1
elif -self.N<=i<0:
a,b=i+self.N,i+self.N+1
else:
raise IndexError('list index out of range')
else:
a,b=i.start,i.stop
if a==None or a<-self.N:
a=0
elif self.N<=a:
a=self.N
elif a<0:
a+=self.N
if b==None or self.N<=b:
b=self.N
elif b<-self.N:
b=0
elif b<0:
b+=self.N
s=self.cumsum[b]-self.cumsum[a]
if self.mod:
s%=self.mod
return s
def __setitem__(self,i,x):
if -self.N<=i<0:
i+=self.N
elif not 0<=i<self.N:
raise IndexError('list index out of range')
self.cumsum[i+1]=self.cumsum[i]+x
if self.mod:
self.cumsum[i+1]%=self.mod
def __str__(self):
lst=[self.cumsum[i+1]-self.cumsum[i] for i in range(self.N)]
if self.mod:
for i in range(self.N):
lst[i]%=self.mod
return "["+", ".join(map(str,lst))+"]"
class Prime:
def __init__(self,N):
assert N<=10**8
self.smallest_prime_factor=[None]*(N+1)
for i in range(2,N+1,2):
self.smallest_prime_factor[i]=2
n=int(N**.5)+1
for p in range(3,n,2):
if self.smallest_prime_factor[p]==None:
self.smallest_prime_factor[p]=p
for i in range(p**2,N+1,2*p):
if self.smallest_prime_factor[i]==None:
self.smallest_prime_factor[i]=p
for p in range(n,N+1):
if self.smallest_prime_factor[p]==None:
self.smallest_prime_factor[p]=p
self.primes=[p for p in range(N+1) if p==self.smallest_prime_factor[p]]
def Factorize(self,N):
assert N>=1
factors=defaultdict(int)
if N<=len(self.smallest_prime_factor)-1:
while N!=1:
factors[self.smallest_prime_factor[N]]+=1
N//=self.smallest_prime_factor[N]
else:
for p in self.primes:
while N%p==0:
N//=p
factors[p]+=1
if N<p*p:
if N!=1:
factors[N]+=1
break
if N<=len(self.smallest_prime_factor)-1:
while N!=1:
factors[self.smallest_prime_factor[N]]+=1
N//=self.smallest_prime_factor[N]
break
else:
if N!=1:
factors[N]+=1
return factors
def Divisors(self,N):
assert N>0
divisors=[1]
for p,e in self.Factorize(N).items():
A=[1]
for _ in range(e):
A.append(A[-1]*p)
divisors=[i*j for i in divisors for j in A]
return divisors
def Is_Prime(self,N):
return N==self.smallest_prime_factor[N]
def Totient(self,N):
for p in self.Factorize(N).keys():
N*=p-1
N//=p
return N
def Mebius(self,N):
fact=self.Factorize(N)
for e in fact.values():
if e>=2:
return 0
else:
if len(fact)%2==0:
return 1
else:
return -1
N=int(readline())
edges=[]
for _ in range(N-1):
A,B=map(int,readline().split())
A-=1;B-=1
edges.append((A,B))
G=Graph(N,edges=edges)
parents,size=G.SIV_DFS(0,parents=True,subtree_size=True)
ans=0
for x in range(N):
ans+=N**2
lst=[]
for y in G.graph[x]:
if y==parents[x]:
continue
lst.append(size[y])
if x:
lst.append(N-1-sum(lst))
for s in lst:
ans-=s**2
print(ans)