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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#780702 | #5088. Two Choreographies | vwxyz | WA | 15ms | 10752kb | Python3 | 20.9kb | 2024-11-25 12:35:49 | 2024-11-25 12:35:50 |
Judging History
answer
from collections import deque
class Path_Doubling:
def __init__(self,N,permutation,V=None,f=None,e=None):
self.N=N
self.permutation=permutation
self.V=V
self.f=f
self.e=e
def Build_Next(self,K=None):
if K==None:
K=self.N
K=max(K,1)
self.k=K.bit_length()
self.doubling_permutation=[[None]*self.N for k in range(self.k)]
for n in range(self.N):
self.doubling_permutation[0][n]=self.permutation[n]
if self.V!=None:
self.doubling=[[self.e]*self.N for k in range(self.k)]
for n in range(self.N):
self.doubling[0][n]=self.V[n]
for k in range(1,self.k):
for n in range(self.N):
if self.doubling_permutation[k-1][n]!=None:
self.doubling_permutation[k][n]=self.doubling_permutation[k-1][self.doubling_permutation[k-1][n]]
if self.f!=None:
self.doubling[k][n]=self.f(self.doubling[k-1][n],self.doubling[k-1][self.doubling_permutation[k-1][n]])
def Doubling_Permutation(self,x,K):
if K<0 or 1<<self.k<=K:
return None
for k in range(self.k):
if K>>k&1 and x!=None:
x=self.doubling_permutation[k][x]
return x
def Doubling(self,x,K,edge=False):
if K<0:
return self.e
retu=self.e
for k in range(self.k):
if K>>k&1:
if self.doubling_permutation[k][x]==None:
return None
retu=self.f(retu,self.doubling[k][x])
x=self.doubling_permutation[k][x]
if not edge:
retu=self.f(retu,self.V[x])
return x,retu
def Bisect_Permutation(self,x,is_ok):
if not is_ok(x):
return -1,None
K=0
for k in range(self.k-1,-1,-1):
if is_ok(self.doubling_permutation[k][x]):
K|=1<<k
x=self.doubling_permutation[k][x]
return K,x
def Bisect(self,x,is_ok,edge=False):
if edge:
if not is_ok(x,self.e):
return -1,None,None
v=self.e
K=0
for k in range(self.k-1,-1,-1):
xx=self.doubling_permutation[k][x]
vv=self.f(v,self.doubling[k][x])
if is_ok(xx,vv):
K|=1<<k
x,v=xx,vv
else:
if not is_ok(x,self.V[x]):
return -1,None,None
v=self.V[x]
K=0
for k in range(self.k-1,-1,-1):
xx=self.doubling_permutation[k][x]
vv=self.f(v,self.doubling[k][self.permutation[x]])
if is_ok(xx,vv):
K|=1<<k
x,v=xx,vv
return K,x,v
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
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_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 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_=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 Build_LCA(self,s,segment_tree=False):
self.lca_segment_tree=segment_tree
if self.lca_segment_tree:
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,min,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)
else:
self.lca_parents,self.lca_depth=self.SIV_DFS(s,parents=True,unweighted_dist=True)
self.lca_PD=Path_Doubling(self.V,self.lca_parents)
self.lca_PD.Build_Next(self.V)
def LCA(self,a,b):
if self.lca_segment_tree:
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:
lca=x
else:
lca=self.lca_parents[~x]
else:
if self.lca_depth[a]>self.lca_depth[b]:
a,b=b,a
b=self.lca_PD.Doubling_Permutation(b,self.lca_depth[b]-self.lca_depth[a])
if a!=b:
for k in range(self.lca_PD.k-1,-1,-1):
if self.lca_PD.doubling_permutation[k][a]!=self.lca_PD.doubling_permutation[k][b]:
a,b=self.lca_PD.doubling_permutation[k][a],self.lca_PD.doubling_permutation[k][b]
a,b=self.lca_PD.doubling_permutation[0][a],self.lca_PD.doubling_permutation[0][b]
lca=a
return lca
def LCD(self):
lcd_points=self.MIV_DFS(linked_components=True)
lcd_edges=[[] for i in range(len(lcd_points))]
idx=[None]*self.V
for i in range(len(lcd_points)):
for j in range(len(lcd_points[i])):
idx[lcd_points[i][j]]=(i,j)
for tpl in self.edges:
if self.weighted:
x,y,d=tpl
else:
x,y=tpl
i,j0=idx[x]
i,j1=idx[y]
if self.weighted:
lcd_edges[i].append((j0,j1,d))
else:
lcd_edges[i].append((j0,j1))
return lcd_points,lcd_edges
N=int(input())
edges=[]
for i in range(2*N-3):
a,b=map(int,input().split())
a-=1;b-=1
edges.append((a,b))
G=Graph(N,edges=edges)
for P,E in zip(*G.LCD()):
le=len(P)
if le>3 and 2*le-3<=len(E):
GG=Graph(le,edges=E)
for x in range(le):
if len(GG.graph[x])>=3:
s=x
break
parents=GG.SIV_BFS(s,parents=True)
tree=[]
for x in range(le):
if parents[x]!=None:
tree.append((parents[x],x))
ST=Graph(le,edges=tree)
ST.Build_LCA(s)
parents,depth=ST.lca_parents,ST.lca_depth
D=[[] for d in range(le)]
for a,b in E:
if parents[a]!=b and parents[b]!=a:
lca=ST.LCA(a,b)
d=depth[a]+depth[b]-2*depth[lca]
D[d].append((a,b,lca))
for d in range(le):
if len(D[d])>=2:
def cycle(a,b,lca):
cycle0=[]
while a!=lca:
cycle0.append(a)
a=parents[a]
cycle1=[]
while b!=lca:
cycle1.append(b)
b=parents[b]
return cycle0+[lca]+cycle1[::-1]
A=cycle(*D[d].pop())
B=cycle(*D[d].pop())
print(d)
print(*[P[a]+1 for a in A])
print(*[P[b]+1 for b in B])
exit()
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 0
Wrong Answer
time: 15ms
memory: 10752kb
input:
4 1 2 1 3 1 4 2 3 2 4
output:
2 2 1 4 2 1 3
result:
wrong answer Integer 2 violates the range [3, 4]