NetworkX系列教程(10)-算法之三:关键路径问题

小书匠Graph图论

重头戏部分来了,写到这里我感觉得仔细认真点了,可能在NetworkX中,实现某些算法就一句话的事,但是这个算法是做什么的,用在什么地方,原理是怎么样的,不清除,所以,我决定先把图论中常用算法弄个明白在写这部分.

图论常用算法看我的博客:

下面我将使用NetworkX实现上面的算法,建议不清楚的部分打开两篇博客对照理解.

我将图论的经典问题及常用算法的总结写在下面两篇博客中:

图论---问题篇

图论---算法篇

目录:

* 11.3关键路径算法(CPA)

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注意:如果代码出现找不库,请返回第一个教程,把库文件导入.

11.3关键路径算法(CPA)

以下代码从这里复制,由于版本问题,将代码中的:nx.topological_sort(self, reverse=True)改为list(reversed(list(nx.topological_sort(self))))

1. import networkx as nx 
   

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2. import matplotlib.pyplot as plt 
   

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3. from matplotlib.font_manager import *  
   

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4. ---

5. #定义自定义字体，文件名从1.b查看系统中文字体中来  
   

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6. myfont = FontProperties(fname='/usr/share/fonts/truetype/wqy/wqy-zenhei.ttc')  
   

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7. #解决负号'-'显示为方块的问题  
   

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8. matplotlib.rcParams['axes.unicode_minus']=False  
   

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9. ---

10. class CPM(nx.DiGraph): 
    

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11. ---

12. def __init__(self): 
    

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13. super().__init__() 
    

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14. self._dirty = True 
    

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15. self._critical_path_length = -1 
    

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16. self._criticalPath = None 
    

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17. ---

18. def add_node(self, *args, **kwargs): 
    

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19. self._dirty = True 
    

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20. super().add_node(*args, **kwargs) 
    

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21. ---

22. def add_nodes_from(self, *args, **kwargs): 
    

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23. self._dirty = True 
    

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24. super().add_nodes_from(*args, **kwargs) 
    

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25. ---

26. def add_edge(self, *args): # , **kwargs): 
    

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27. self._dirty = True 
    

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28. super().add_edge(*args) # , **kwargs) 
    

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29. ---

30. def add_edges_from(self, *args, **kwargs): 
    

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31. self._dirty = True 
    

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32. super().add_edges_from(*args, **kwargs) 
    

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33. ---

34. def remove_node(self, *args, **kwargs): 
    

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35. self._dirty = True 
    

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36. super().remove_node(*args, **kwargs) 
    

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37. ---

38. def remove_nodes_from(self, *args, **kwargs): 
    

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39. self._dirty = True 
    

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40. super().remove_nodes_from(*args, **kwargs) 
    

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41. ---

42. def remove_edge(self, *args): # , **kwargs): 
    

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43. self._dirty = True 
    

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44. super().remove_edge(*args) # , **kwargs) 
    

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45. ---

46. def remove_edges_from(self, *args, **kwargs): 
    

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47. self._dirty = True 
    

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48. super().remove_edges_from(*args, **kwargs) 
    

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49. ---

50. #根据前向拓扑排序算弧的最早发生时间 
    

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51. def _forward(self): 
    

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52. for n in nx.topological_sort(self): 
    

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53. es = max([self.node[j]['EF'] for j in self.predecessors(n)], default=0) 
    

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54. self.add_node(n, ES=es, EF=es + self.node[n]['duration']) 
    

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55. ---

56. #根据前向拓扑排序算弧的最迟发生时间 
    

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57. def _backward(self): 
    

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58. #for n in nx.topological_sort(self, reverse=True): 
    

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59. for n in list(reversed(list(nx.topological_sort(self)))): 
    

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60. lf = min([self.node[j]['LS'] for j in self.successors(n)], default=self._critical_path_length) 
    

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61. self.add_node(n, LS=lf - self.node[n]['duration'], LF=lf) 
    

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62. ---

63. #最早发生时间=最迟发生时间,则判断该节点为关键路径上的关键活动 
    

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64. def _compute_critical_path(self): 
    

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65. graph = set() 
    

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66. for n in self: 
    

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67. if self.node[n]['EF'] == self.node[n]['LF']: 
    

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68. graph.add(n) 
    

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69. self._criticalPath = self.subgraph(graph) 
    

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70. ---

71. @property 
    

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72. def critical_path_length(self): 
    

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73. if self._dirty: 
    

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74. self._update() 
    

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75. return self._critical_path_length 
    

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76. ---

77. @property 
    

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78. def critical_path(self): 
    

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79. if self._dirty: 
    

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80. self._update() 
    

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81. return sorted(self._criticalPath, key=lambda x: self.node[x]['ES']) 
    

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82. ---

83. def _update(self): 
    

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84. self._forward() 
    

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85. self._critical_path_length = max(nx.get_node_attributes(self, 'EF').values()) 
    

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86. self._backward() 
    

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87. self._compute_critical_path() 
    

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88. self._dirty = False 
    

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89. ---

90. if __name__ == "__main__": 
    

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91. ---

92. #构建graph 
    

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93. G = CPM() 
    

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94. G.add_node('A', duration=5) 
    

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95. G.add_node('B', duration=2) 
    

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96. G.add_node('C', duration=4) 
    

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97. G.add_node('D', duration=4) 
    

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98. G.add_node('E', duration=3) 
    

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99. G.add_node('F', duration=7) 
    

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100. G.add_node('G', duration=4) 
     

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101. ---

102. G.add_edges_from([ 
     

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103. ('A', 'B'), 
     

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104. ('A', 'C'), 
     

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105. ('C','D'), 
     

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106. ('C','E'), 
     

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107. ('C','G'), 
     

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108. ('B','D'), 
     

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109. ('D','F'), 
     

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110. ('E','F'), 
     

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111. ('G','F'), 
     

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112. ])  
     

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113. ---

114. #显示graph 
     

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115. nx.draw_spring(G,with_labels=True) 
     

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116. plt.title('AOE网络',fontproperties=myfont) 
     

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117. plt.axis('on') 
     

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118. plt.xticks([]) 
     

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119. plt.yticks([]) 
     

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120. plt.show() 
     

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121. ---

122. ---

123. print('关键活动为:') 
     

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124. print(G.critical_path_length, G.critical_path) 
     

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125. ---

126. G.add_node('D', duration=2) 
     

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127. print('\n修改D活动持续时间4为2后的关键活动为:') 
     

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128. print(G.critical_path_length, G.critical_path) 
     

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关键路径示例(该图非黑色线为手工绘制,数字手工添加)

从graph中可以知道,有两条关键路径,分别是:A->C->G->F和A->C->D->F,长度都是20.

输出:

关键活动为: 20 ['A', 'C', 'D', 'G', 'F']

修改D活动持续时间4为2后的关键活动为: 20 ['A', 'C', 'G', 'F']

关键活动为: ['A', 'C', 'D', 'G', 'F'],可以构成两条边.D活动持续时间4为2后,关键路径变化.