tinyEWG_txt = """
{
0:[(6,0.58),(2,0.26),(4,0.38),(7,0.16)],
1:[(3,0.29),(2,0.36),(7,0.19),(5,0.32)],
2:[(6,0.40),(7,0.34),(1,0.36),(0,0.26),(3,0.17)],
3:[(6,0.52),(1,0.29),(2,0.17)],
4:[(6,0.93),(0,0.38),(7,0.37),(5,0.35)],
5:[(1,0.32),(7,0.28),(4,0.35)],
6:[(4,0.93),(0,0.58),(3,0.52),(2,0.40)],
7:[(2,0.34),(1,0.19),(0,0.16),(5,0.28)]
}
"""
## 模拟优先队列
class Min_PQ_:
def __init__(self,f,reversed= False):
self.data = []
self.f = f
self.__reversed = reversed
def remove(self):
return self.data.pop(0)
def insert(self,item):
self.data.append(item)
self.data.sort(key=self.f,reverse=self.__reversed)
def __len__(self):
return len(self.data)
def __str__(self):
return str(self.data)
# 补全edge
def fill(g):
for v in g:
for i in range(0,len(g[v])):
g[v][i] = (v,)+g[v][i]
def mst_prim(g):
visited = set()
pq = Min_PQ_(lambda x:x[-1])
mst = []
def visit(v):
visited.add(v)
for edge in g.get(v,[]):
pq.insert(edge)
visit(0)
while pq:
min_edge = pq.remove()
x,y = min_edge[0],min_edge[1]
if x in visited and y in visited:continue
else:
mst.append(min_edge)
if x not in visited:visit(x)
if y not in visited:visit(y)
return mst
def get_edges_set(g):
s = set()
for v in g:
for e in g.get(v,[]):
a,b,weight = e[0],e[1],e[-1]
if a<b:
s.add((a,b,weight))
else:
s.add((b,a,weight))
return s
def add_edge(g,x,y):
if x in g:
(g[x]).append(y)
else:
g[x]=[]
add_edge(g,x,y)
def has_connected(g,x,y):
has_connected__ = False
visited = set()
def __dfs(__x):
visited.add(__x)
for v in g.get(__x,[]):
if v == y :
nonlocal has_connected__
has_connected__ = True
return
elif v not in visited:
__dfs(v)
__dfs(x)
return has_connected__
def mst_kruskal(g):
sorted_edges = list(get_edges_set(g))
sorted_edges.sort(key = lambda x:x[-1])
mst = []
g_temp = dict()
while sorted_edges:
min_edge = sorted_edges.pop(0)
x,y = min_edge[0],min_edge[1]
if has_connected(g_temp,x,y): continue
else:
mst.append(min_edge)
add_edge(g_temp,x,y)
add_edge(g_temp,y,x)
return mst
if __name__ == '__main__':
g = eval(tinyEWG_txt)
fill(g)
print(mst_kruskal(g))
