結果
| 問題 |
No.19 ステージの選択
|
| ユーザー |
 vwxyz
|
| 提出日時 | 2021-07-17 11:22:41 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 134 ms / 5,000 ms |
| コード長 | 22,612 bytes |
| コンパイル時間 | 232 ms |
| コンパイル使用メモリ | 82,304 KB |
| 実行使用メモリ | 89,216 KB |
| 最終ジャッジ日時 | 2024-07-06 22:53:58 |
| 合計ジャッジ時間 | 4,601 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 24 |
ソースコード
import bisect
import copy
import decimal
import fractions
import heapq
import itertools
import math
import random
import sys
from collections import Counter, deque,defaultdict
from functools import lru_cache,reduce
from heapq import heappush,heappop,heapify,heappushpop,_heappop_max,_heapify_max
def _heappush_max(heap,item):
heap.append(item)
heapq._siftdown_max(heap, 0, len(heap)-1)
def _heappushpop_max(heap, item):
if heap and item < heap[0]:
item, heap[0] = heap[0], item
heapq._siftup_max(heap, 0)
return item
from math import gcd as GCD
read=sys.stdin.read
readline=sys.stdin.readline
readlines=sys.stdin.readlines
class Graph:
def __init__(self,V,edges=False,graph=False,directed=False,weighted=False):
self.V=V
self.directed=directed
self.weighted=weighted
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 SS_BFS(self,s,bipartite_graph=False,linked_components=False,parents=False,unweighted_dist=False,weighted_dist=False):
seen=[False]*self.V
seen[s]=True
if linked_components:
lc=[s]
if parents:
ps=[None]*self.V
ps[s]=s
if unweighted_dist or bipartite_graph:
uwd=[float('inf')]*self.V
uwd[s]=0
if weighted_dist:
wd=[float('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 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 type(uwd[i])==float or type(uwd[j])==float:
continue
if not uwd[i]%2^uwd[j]%2:
bg=False
break
else:
for x in range(self.V):
if type(uwd[x])==float:
continue
bg[uwd[x]%2].append(x)
tpl=()
if bipartite_graph:
tpl+=(bg,)
if linked_components:
tpl+=(lc,)
if parents:
tpl+=(ps,)
if unweighted_dist:
tpl+=(uwd,)
if weighted_dist:
tpl+=(wd,)
if len(tpl)==1:
tpl=tpl[0]
return tpl
def AP_BFS(self,bipartite_graph=False,linked_components=False,parents=False):
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 range(self.V):
if seen[s]:
continue
seen[s]=True
if bipartite_graph:
cnt+=1
bg[s]=(cnt,s&1)
if linked_components:
lc.append([s])
if parents:
ps[s]=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
print(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]]:
print(bg_[x][0])
print(bg_[x][1])
bg[bg_[x][0]][bg_[x][1]].append(x)
tpl=()
if bipartite_graph:
tpl+=(bg,)
if linked_components:
tpl+=(lc,)
if parents:
tpl+=(ps,)
if len(tpl)==1:
tpl=tpl[0]
return tpl
def SS_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
ps[s]=s
if postorder or topological_sort:
post=[]
if preorder:
pre=[]
if subtree_size:
ss=[1]*self.V
if unweighted_dist or bipartite_graph:
uwd=[float('inf')]*self.V
uwd[s]=0
if weighted_dist:
wd=[float('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 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 type(uwd[i])==float or type(uwd[j])==float:
continue
if not uwd[i]%2^uwd[j]%2:
bg=False
break
else:
for x in range(self.V):
if type(uwd[x])==float:
continue
bg[uwd[x]%2].append(x)
tpl=()
if bipartite_graph:
tpl+=(bg,)
if cycle_detection:
if dag:
cd=[]
else:
y,x=cd
cd=self.Route_Restoration(y,x,ps)
tpl+=(cd,)
if directed_acyclic:
tpl+=(dag,)
if euler_tour:
tpl+=(et,)
if linked_components:
tpl+=(lc,)
if parents:
tpl+=(ps,)
if postorder:
tpl+=(post,)
if preorder:
tpl+=(pre,)
if subtree_size:
tpl+=(ss,)
if topological_sort:
if dag:
tp_sort=post[::-1]
else:
tp_sort=[]
tpl+=(tp_sort,)
if unweighted_dist:
tpl+=(uwd,)
if weighted_dist:
tpl+=(wd,)
if len(tpl)==1:
tpl=tpl[0]
return tpl
def AP_DFS(self,bipartite_graph=False,cycle_detection=False,directed_acyclic=False,euler_tour=False,linked_components=False,parents=False,postorder=False,preorder=False,topological_sort=False):
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:
ps=[None]*self.V
if postorder or topological_sort:
post=[]
if preorder:
pre=[]
for s in range(self.V):
if seen[s]:
continue
if bipartite_graph:
cnt+=1
bg[s]=(cnt,s&1)
if linked_components:
lc.append([])
if parents:
ps[s]=s
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:
ps[y]=x
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 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)
tpl=()
if bipartite_graph:
tpl+=(bg,)
if cycle_detection:
if dag:
cd=[]
else:
y,x=cd
cd=self.Route_Restoration(y,x,ps)
tpl+=(cd,)
if directed_acyclic:
tpl+=(dag,)
if euler_tour:
tpl+=(et,)
if linked_components:
tpl+=(lc,)
if parents:
tpl+=(ps,)
if postorder:
tpl+=(post,)
if preorder:
tpl+=(pre,)
if topological_sort:
if dag:
tp_sort=post[::-1]
else:
tp_sort=[]
tpl+=(tp_sort,)
if len(tpl)==1:
tpl=tpl[0]
return tpl
def Tree_Diameter(self,weighted=False):
def Farthest_Point(u):
dist=self.SS_BFS(u,weighted_dist=True) if weighted else self.SS_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.AP_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=y[0]
if not seen[y]:
seen[y]=True
queue.append(y)
scc.append(lst)
return scc
def Build_LCA(self,s):
self.euler_tour,self.parents,depth=self.SS_DFS(s,euler_tour=True,parents=True,unweighted_dist=True)
self.dfs_in_index=[None]*self.V
self.dfs_out_index=[None]*self.V
for i,x in enumerate(self.euler_tour):
if x>=0:
self.dfs_in_index[x]=i
else:
self.dfs_out_index[~x]=i
self.ST=Segment_Tree(2*self.V,lambda x,y:min(x,y),float('inf'))
lst=[None]*2*self.V
for i in range(2*self.V):
if self.euler_tour[i]>=0:
lst[i]=depth[self.euler_tour[i]]
else:
lst[i]=depth[self.parents[~self.euler_tour[i]]]
self.ST.Build(lst)
def LCA(self,a,b):
m=min(self.dfs_in_index[a],self.dfs_in_index[b])
M=max(self.dfs_in_index[a],self.dfs_in_index[b])
x=self.euler_tour[self.ST.Fold_Index(m,M+1)]
if x>=0:
return x
else:
return self.parents[~x]
def Dijkstra(self,s,route_restoration=False):
dist=[float('inf')]*self.V
dist[s]=0
hq=[(0,s)]
if route_restoration:
parents=[None]*self.V
parents[s]=s
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=[float('inf')]*self.V
dist[s]=0
if route_restoration:
parents=[s]*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]=-float('inf')
if route_restoration:
return dist,parents
else:
return dist
def Warshall_Floyd(self,route_restoration=False):
dist=[[float('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 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]!=float('inf'):
dist[i][j]=-float('inf')
if route_restoration:
return dist,parents
else:
return dist
def Route_Restoration(self,s,g,parents):
route=[g]
while s!=g and parents[g]!=g:
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
N=int(readline())
edges=[]
L=[]
ans=0
for i in range(N):
l,s=map(int,readline().split())
s-=1
if s!=i:
edges.append((s,i))
else:
ans+=l
L.append(l)
G=Graph(N,edges=edges,directed=True)
ans+=sum(L)
scc=G.SCC()
for lst in scc:
if len(lst)==1:
continue
ans+=min(L[x] for x in lst)
if ans%2:
ans=str(ans//2)+'.5'
else:
ans=str(ans//2)+'.0'
print(ans)