結果
| 問題 |
No.1690 Power Grid
|
| コンテスト | |
| ユーザー |
 vwxyz
|
| 提出日時 | 2023-12-01 15:41:25 |
| 言語 | Python3 (3.13.1 + numpy 2.2.1 + scipy 1.14.1) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 7,579 bytes |
| コンパイル時間 | 244 ms |
| コンパイル使用メモリ | 13,440 KB |
| 実行使用メモリ | 17,024 KB |
| 最終ジャッジ日時 | 2024-09-26 15:41:38 |
| 合計ジャッジ時間 | 5,208 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge5 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 3 TLE * 1 -- * 21 |
ソースコード
import sys
readline=sys.stdin.readline
from collections import defaultdict
class UnionFind:
def __init__(self,N,label=None,f=None,weighted=False,rollback=False):
self.N=N
self.parents=[None]*self.N
self.size=[1]*self.N
self.roots={i for i in range(self.N)}
self.label=label
if self.label!=None:
self.label=[x for x in label]
self.f=f
self.weighted=weighted
if self.weighted:
self.weight=[0]*self.N
self.rollback=rollback
if self.rollback:
self.operate_list=[]
self.operate_set=[]
def Find(self,x):
stack=[]
while self.parents[x]!=None:
stack.append(x)
x=self.parents[x]
if not self.rollback:
if self.weighted:
w=0
for y in stack[::-1]:
self.parents[y]=x
w+=self.weight[y]
self.weight[y]=w
else:
for y in stack[::-1]:
self.parents[y]=x
return x
def Union(self,x,y,w=None):
root_x=self.Find(x)
root_y=self.Find(y)
if self.rollback:
self.operate_list.append([])
self.operate_set.append([])
if root_x==root_y:
if self.weighted:
if self.weight[y]-self.weight[x]==w:
return True
else:
return False
else:
if self.size[root_x]<self.size[root_y]:
x,y=y,x
root_x,root_y=root_y,root_x
if self.weighted:
w=-w
if self.rollback:
self.operate_list[-1].append((self.parents,root_y,self.parents[root_y]))
self.operate_list[-1].append((self.size,root_x,self.size[root_x]))
self.operate_set[-1].append(root_y)
if self.label!=None:
self.operate_list[-1]((self.label,root_x,self.label[root_x]))
if self.weighted:
self.operate_list[-1].append((self.weight,root_y,self.weight[root_y]))
self.parents[root_y]=root_x
self.size[root_x]+=self.size[root_y]
self.roots.remove(root_y)
if self.label!=None:
self.label[root_x]=self.f(self.label[root_x],self.label[root_y])
if self.weighted:
self.weight[root_y]=w+self.weight[x]-self.weight[y]
def Size(self,x):
return self.size[self.Find(x)]
def Same(self,x,y):
return self.Find(x)==self.Find(y)
def Label(self,x):
return self.label[self.Find(x)]
def Weight(self,x,y):
root_x=self.Find(x)
root_y=self.Find(y)
if root_x!=root_y:
return None
return self.weight[y]-self.weight[x]
def Roots(self):
return list(self.roots)
def Linked_Components_Count(self):
return len(self.roots)
def Linked_Components(self):
linked_components=defaultdict(list)
for x in range(self.N):
linked_components[self.Find(x)].append(x)
return linked_components
def Rollback(self):
assert self.rollback
if self.operate_list:
for lst,x,v in self.operate_list.pop():
lst[x]=v
for x in self.operate_set.pop():
self.roots.add(x)
return True
else:
return False
def __str__(self):
linked_components=defaultdict(list)
for x in range(self.N):
linked_components[self.Find(x)].append(x)
return "\n".join(f"{r}: {linked_components[r]}" for r in sorted(list(linked_components.keys())))
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 Warshall_Floyd(self,route_restoration=False):
dist=[[self.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 i==j:
continue
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]!=self.inf:
dist[i][j]=-self.inf
if route_restoration:
for i in range(self.V):
if dist[i][i]==0:
parents[i][i]=None
return dist,parents
else:
return dist
def Kruskal(self,maximize=False,spanning_tree=False):
UF=UnionFind(self.V)
sorted_edges=sorted(self.edges if self.weighted else [(x,y,1) for x,y in self.edges],key=lambda tpl:tpl[2],reverse=maximize)
if spanning_tree:
st=[]
else:
cost=0
for x,y,d in sorted_edges:
if not UF.Same(x,y):
UF.Union(x,y)
if spanning_tree:
st.append((x,y,d))
else:
cost+=d
return st if spanning_tree else cost
N,M,K=map(int,readline().split())
A=list(map(int,readline().split()))
edges=[]
for m in range(M):
x,y,z=map(int,readline().split())
x-=1;y-=1
edges.append((x,y,z))
G=Graph(N,edges=edges,weighted=True)
dist=G.Warshall_Floyd()
inf=1<<60
ans=inf
for bit in range(1<<N):
if sum(1 for i in range(N) if bit&1<<i)==K:
edges=[]
for i in range(N):
for j in range(i+1,N):
if bit&1<<i and bit&1<<j:
edges.append((i,j,dist[i][j]))
ans=min(ans,sum(A[i] for i in range(N) if bit&1<<i)+Graph(N,edges=edges,weighted=True).Kruskal())
print(ans)