python最小生成树kruskal与prim算法详解

2019-11-25 13:27:30

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kruskal算法基本思路：先对边按权重从小到大排序，先选取权重最小的一条边，如果该边的两个节点均为不同的分量，则加入到最小生成树，否则计算下一条边，直到遍历完所有的边。

prim算法基本思路：所有节点分成两个group，一个为已经选取的selected_node（为list类型），一个为candidate_node，首先任取一个节点加入到selected_node，然后遍历头节点在selected_node，尾节点在candidate_node的边，选取符合这个条件的边里面权重最小的边，加入到最小生成树，选出的边的尾节点加入到selected_node，并从candidate_node删除。直到candidate_node中没有备选节点（这个循环条件要求所有节点都有边连接，即边数要大于等于节点数-1，循环开始前要加入这个条件判断，否则可能会有节点一直在candidate中，导致死循环）。

#coding=utf-8class Graph(object):  def __init__(self, maps):    self.maps = maps    self.nodenum = self.get_nodenum()    self.edgenum = self.get_edgenum()   def get_nodenum(self):    return len(self.maps)   def get_edgenum(self):    count = 0    for i in range(self.nodenum):      for j in range(i):        if self.maps[i][j] > 0 and self.maps[i][j] < 9999:          count += 1    return count   def kruskal(self):    res = []    if self.nodenum <= 0 or self.edgenum < self.nodenum-1:      return res    edge_list = []    for i in range(self.nodenum):      for j in range(i,self.nodenum):        if self.maps[i][j] < 9999:          edge_list.append([i, j, self.maps[i][j]])#按[begin, end, weight]形式加入    edge_list.sort(key=lambda a:a[2])#已经排好序的边集合        group = [[i] for i in range(self.nodenum)]    for edge in edge_list:      for i in range(len(group)):        if edge[0] in group[i]:          m = i        if edge[1] in group[i]:          n = i      if m != n:        res.append(edge)        group[m] = group[m] + group[n]        group[n] = []    return res   def prim(self):    res = []    if self.nodenum <= 0 or self.edgenum < self.nodenum-1:      return res    res = []    seleted_node = [0]    candidate_node = [i for i in range(1, self.nodenum)]        while len(candidate_node) > 0:      begin, end, minweight = 0, 0, 9999      for i in seleted_node:        for j in candidate_node:          if self.maps[i][j] < minweight:            minweight = self.maps[i][j]            begin = i            end = j      res.append([begin, end, minweight])      seleted_node.append(end)      candidate_node.remove(end)    return res max_value = 9999row0 = [0,7,max_value,max_value,max_value,5]row1 = [7,0,9,max_value,3,max_value]row2 = [max_value,9,0,6,max_value,max_value]row3 = [max_value,max_value,6,0,8,10]row4 = [max_value,3,max_value,8,0,4]row5 = [5,max_value,max_value,10,4,0]maps = [row0, row1, row2,row3, row4, row5]graph = Graph(maps)print('邻接矩阵为/n%s'%graph.maps)print('节点数据为%d，边数为%d/n'%(graph.nodenum, graph.edgenum))print('------最小生成树kruskal算法------')print(graph.kruskal())print('------最小生成树prim算法')print(graph.prim())

初始的图如下。