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python最小生成樹(shù)kruskal與prim算法詳解

更新時(shí)間：2019年01月17日 14:15:05 作者：風(fēng)云pgg

這篇文章主要為大家詳細(xì)介紹了python最小生成樹(shù)kruskal與prim算法，具有一定的參考價(jià)值，感興趣的小伙伴們可以參考一下

kruskal算法基本思路：先對(duì)邊按權(quán)重從小到大排序，先選取權(quán)重最小的一條邊，如果該邊的兩個(gè)節(jié)點(diǎn)均為不同的分量，則加入到最小生成樹(shù)，否則計(jì)算下一條邊，直到遍歷完所有的邊。

prim算法基本思路：所有節(jié)點(diǎn)分成兩個(gè)group，一個(gè)為已經(jīng)選取的selected_node（為list類(lèi)型），一個(gè)為candidate_node，首先任取一個(gè)節(jié)點(diǎn)加入到selected_node，然后遍歷頭節(jié)點(diǎn)在selected_node，尾節(jié)點(diǎn)在candidate_node的邊，選取符合這個(gè)條件的邊里面權(quán)重最小的邊，加入到最小生成樹(shù)，選出的邊的尾節(jié)點(diǎn)加入到selected_node，并從candidate_node刪除。直到candidate_node中沒(méi)有備選節(jié)點(diǎn)（這個(gè)循環(huán)條件要求所有節(jié)點(diǎn)都有邊連接，即邊數(shù)要大于等于節(jié)點(diǎn)數(shù)-1，循環(huán)開(kāi)始前要加入這個(gè)條件判斷，否則可能會(huì)有節(jié)點(diǎn)一直在candidate中，導(dǎo)致死循環(huán)）。

#coding=utf-8
class 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])#已經(jīng)排好序的邊集合
    
    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 = 9999
row0 = [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('鄰接矩陣為\n%s'%graph.maps)
print('節(jié)點(diǎn)數(shù)據(jù)為%d，邊數(shù)為%d\n'%(graph.nodenum, graph.edgenum))
print('------最小生成樹(shù)kruskal算法------')
print(graph.kruskal())
print('------最小生成樹(shù)prim算法')
print(graph.prim())

初始的圖如下。