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GSpanTree.py
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executable file
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""" classes and functions for binary trees
"""
from 队列的实现方式.PrioQueue import PrioQueue
from 图.Graph import *
# Kruskal 算法 最小生成树问题
def Kruskal(graph):
vnum = graph.vertex_num()
reps = [i for i in range(vnum)]
mst, edges = [], []
for vi in range(vnum): # put all edges into a list
for v, w in graph.out_edges(vi):
edges.append((w, (vi, v)))
edges.sort() # sort, O(n log n) time
for w, e in edges:
if reps[e[0]] != reps[e[1]]:
mst.append((e, w))
if len(mst) == vnum - 1: break
rep, orep = reps[e[0]], reps[e[1]]
for i in range(vnum):
if reps[i] == orep: reps[i] = rep
return mst
# Prim 算法 最小生成树问题
def Prim(graph):
""" Assume that graph is a network, a connected undirect
graph. This function implements Prim algorithm to build its
minimal span tree. A list mst to store the resulting
span tree, where each element takes the form ((i, j), w).
A representing array reps is used to record the representive
vertics of each of the connective parts.
"""
vnum = graph.vertex_num()
mst = [None] * vnum
cands = PrioQueue([(0, 0, 0)]) # record cand-edges (w, vi, wj)
count = 0
while count < vnum and not cands.is_empty():
w, u, vmin = cands.dequeue() # take minimal candidate edge
if mst[vmin]: continue # vmin is already in mst
mst[vmin] = ((u, vmin), w) # record new MST edge and vertex
count += 1
for v, w in graph.out_edges(vmin): # for adjacents of vmin
if not mst[v]: # when v is not in mst yet
cands.enqueue((w, vmin, v))
return mst
# def Prim2(graph):
# vnum = graph.vertex_num()
# wv_seq = [[graph.get_edge(0, v), v, 0] for v in range(vnum)]
# connects = DecPrioHeap(wv_seq) # 最近连接的顶点堆， |V| 个元素
# mst = [None]*vnum
# while not connects.is_empty():
# w, mv, u = connects.getmin() # 取得最近顶点和连接边
# if w == infinity: break # 最近顶点已不连通，说明该图没有生成树
# mst[mv] = ((u, mv), w) # 这就是新的 MST 边
# for v, w in graph.out_edges(mv): # 检查 mv 的邻接边
# if not mst[v] and w < connects.weight(v): # 如果更短就修改
# connects.dec_weight(v, w, mv)
# return mst
inf = float("inf")
if __name__ == '__main__':
gmat3 = [[0, 10, inf, inf, 19, 21],
[10, 0, 5, 6, inf, 11],
[inf, 5, 0, 6, inf, inf],
[inf, 6, 6, 0, 18, 14],
[19, inf, inf, 18, 0, 7],
[21, 11, inf, 14, 7, 0]]
gmat4 = [[0, 10, inf, inf, 19, 21],
[10, 0, 5, 6, inf, 11],
[inf, 5, 0, 6, inf, inf],
[inf, 6, 6, 0, 18, 14],
[19, inf, inf, 18, 0, 33],
[21, 11, inf, 14, 33, 0]]
g3 = GraphA(gmat3, inf)
g4 = GraphA(gmat4, inf)
spt1 = Kruskal(g3)
print(spt1)
spt2 = Prim(g3)
print(spt2)
spt3 = Kruskal(g4)
print(spt3)
spt4 = Prim(g4)
print(spt4)