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QOJ
| ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
|---|---|---|---|---|---|---|---|---|---|
| #731150 | #2517. Critical Structures | vwxyz | AC ✓ | 1423ms | 127900kb | Python3 | 14.3kb | 2024-11-10 00:10:30 | 2024-11-10 00:10:31 |
Judging History
answer
import math
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 Bridges(self):
lowlink,preorder=self.MIV_DFS(lowlink=True,preorder=True)
order=[None]*self.V
for x in range(self.V):
order[preorder[x]]=x
bridges=[]
for e in self.edges:
if self.weighted:
x,y,d=e
else:
x,y=e
if order[x]<lowlink[y] or order[y]<lowlink[x]:
bridges.append(e)
return bridges
def Articulation_Points(self):
lowlink,parents,preorder=self.MIV_DFS(lowlink=True,parents=True,preorder=True)
order=[None]*self.V
for x in range(self.V):
order[preorder[x]]=x
articulation_points=[]
for x in range(self.V):
if parents[x]==None:
if len({y for y in self.graph[x] if parents[y]==x})>=2:
articulation_points.append(x)
else:
for y in self.graph[x]:
if parents[y]!=x:
continue
if order[x]<=lowlink[y]:
articulation_points.append(x)
break
return articulation_points
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 TECCD(self):
lowlink,preorder=self.MIV_DFS(lowlink=True,preorder=True)
order=[None]*self.V
for x in range(self.V):
order[preorder[x]]=x
edges=[]
for e in self.edges:
if self.weighted:
x,y,d=e
else:
x,y=e
if order[x]>=lowlink[y] and order[y]>=lowlink[x]:
edges.append((x,y))
teccd=Graph(self.V,edges=edges).MIV_DFS(linked_components=True)
idx=[None]*self.V
for i,lst in enumerate(teccd):
for x in lst:
idx[x]=i
teccd_edges=[(idx[a],idx[b]) for a,b in self.edges if idx[a]!=idx[b]]
return teccd,teccd_edges
T=int(input())
for t in range(T):
N,M=map(int,input().split())
edges=[]
for m in range(M):
a,b=map(int,input().split())
a-=1;b-=1
edges.append((a,b))
G=Graph(N,edges=edges)
P,E=G.TECCD()
le=len(P)
idx=[None]*N
for i in range(le):
for x in P[i]:
idx[x]=i
cnt=[0]*le
for a,b in edges:
if idx[a]==idx[b]:
cnt[idx[a]]+=1
ans_lst=[]
ans_lst.append(len(G.Articulation_Points()))
ans_lst.append(len(G.Bridges()))
ans_lst.append(sum(1 for p in P if len(p)>=2)+ans_lst[1])
ans_lst.append(max(max(cnt),1))
g=math.gcd(ans_lst[2],ans_lst[3])
ans_lst[2]//=g
ans_lst[3]//=g
print(*ans_lst)
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 15ms
memory: 10772kb
input:
1 6 6 1 2 2 3 3 4 4 5 5 6 6 1
output:
0 0 1 6
result:
ok single line: '0 0 1 6'
Test #2:
score: 0
Accepted
time: 12ms
memory: 10764kb
input:
1 6 7 1 2 2 3 3 1 4 5 5 6 6 4 1 4
output:
2 1 1 1
result:
ok single line: '2 1 1 1'
Test #3:
score: 0
Accepted
time: 1423ms
memory: 127900kb
input:
10 6 6 1 2 2 3 3 4 4 5 5 6 6 1 5 4 1 2 2 3 3 4 4 5 5 7 1 2 1 3 3 4 4 5 5 3 1 4 1 5 13 16 1 2 1 6 1 3 1 7 3 7 4 6 4 5 5 6 5 7 7 8 8 9 7 10 10 11 12 13 10 12 10 13 10 11 1 2 2 3 2 4 3 5 4 5 4 6 6 7 7 8 6 8 8 9 8 10 3 3 1 2 2 3 3 1 44 66 1 5 1 12 1 33 2 27 2 31 2 32 2 35 2 37 2 40 3 6 3 30 3 44 4 20 4 ...
output:
0 0 1 6 3 4 4 1 1 1 1 3 4 5 7 8 4 4 3 2 0 0 1 3 8 9 10 57 0 0 1 499500 2 2 3 1777 108 112 113 1531
result:
ok 10 lines