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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#780702#5088. Two ChoreographiesvwxyzWA 15ms10752kbPython320.9kb2024-11-25 12:35:492024-11-25 12:35:50

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  • [2024-11-25 12:35:50]
  • 评测
  • 测评结果:WA
  • 用时:15ms
  • 内存:10752kb
  • [2024-11-25 12:35:49]
  • 提交

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

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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]