結果
| 問題 |
No.1442 I-wate Shortest Path Problem
|
| コンテスト | |
| ユーザー |
 vwxyz
|
| 提出日時 | 2023-10-20 23:47:49 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 2,623 ms / 3,000 ms |
| コード長 | 11,557 bytes |
| コンパイル時間 | 282 ms |
| コンパイル使用メモリ | 82,536 KB |
| 実行使用メモリ | 191,216 KB |
| 最終ジャッジ日時 | 2024-09-20 23:57:30 |
| 合計ジャッジ時間 | 29,430 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 25 |
ソースコード
import sys
readline=sys.stdin.readline
import heapq
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=[[None]*self.N for k in range(self.k)]
for n in range(self.N):
self.permutation_doubling[0][n]=self.permutation[n]
if self.lst!=None:
self.doubling=[[None]*self.N for k in range(self.k)]
for n in range(self.N):
self.doubling[0][n]=self.lst[n]
for k in range(1,self.k):
for n in range(self.N):
if self.permutation_doubling[k-1][n]!=None:
self.permutation_doubling[k][n]=self.permutation_doubling[k-1][self.permutation_doubling[k-1][n]]
if self.f!=None:
self.doubling[k][n]=self.f(self.doubling[n][k-1],self.doubling[k-1][self.permutation_doubling[k-1][n]])
def Permutation_Doubling(self,N,K):
if K<0 or 1<<self.k<=K:
return None
for k in range(self.k):
if K>>k&1 and N!=None:
N=self.permutation_doubling[k][N]
return N
def Doubling(self,N,K):
if K<0:
return self.e
retu=self.e
for k in range(self.k):
if K>>k&1:
if self.permutation_doubling[k][N]==None:
return None
retu=self.f(retu,self.doubling[k][N])
N=self.permutation_doubling[k][N]
return N,retu
def Bisect(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.permutation_doubling[k][x]):
K|=1<<k
x=self.permutation_doubling[k][x]
return K,x
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 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,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)
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.Permutation_Doubling(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.permutation_doubling[k][a]!=self.lca_PD.permutation_doubling[k][b]:
a,b=self.lca_PD.permutation_doubling[k][a],self.lca_PD.permutation_doubling[k][b]
a,b=self.lca_PD.permutation_doubling[0][a],self.lca_PD.permutation_doubling[0][b]
lca=a
return lca
def Dijkstra(self,s,route_restoration=False):
dist=[self.inf]*self.V
dist[s]=0
queue=[(0,s)]
if route_restoration:
parents=[None]*self.V
while queue:
dx,x=heapq.heappop(queue)
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(queue,(dist[y],y))
if route_restoration:
return dist,parents
else:
return dist
N,K=map(int,readline().split())
graph=[[] for x in range(N+K)]
for _ in range(N-1):
A,B,C=map(int,readline().split())
A-=1;B-=1
graph[A].append((B,2*C))
graph[B].append((A,2*C))
G=Graph(N+K,graph=graph,directed=True,weighted=True)
dist_T=G.SIV_DFS(0,weighted_dist=True)
G.Build_LCA(0)
for k in range(N,N+K):
M,P=map(int,readline().split())
X=list(map(int,readline().split()))
for m in range(M):
X[m]-=1
graph[X[m]].append((k,P))
graph[k].append((X[m],P))
dist=[G.Dijkstra(k) for k in range(N,N+K)]
Q=int(readline())
for q in range(Q):
U,V=map(int,readline().split())
U-=1;V-=1
lca=G.LCA(U,V)
ans=dist_T[U]+dist_T[V]-2*dist_T[lca]
for k in range(K):
ans=min(ans,dist[k][V]+dist[k][U])
ans//=2
print(ans)