python求解关键路径

关键路径是项目管理中的一个重要概念，可以帮助确定项目的最短完成时间和关键活动。下面是一个使用Python求解关键路径的例子：
class Project:
def __init__(self, activities, durations, dependencies):
self.activities = activities
self.durations = durations
self.dependencies = dependencies
self.early_start = [0] * len(activities)
self.early_finish = [0] * len(activities)
self.late_start = [0] * len(activities)
self.late_finish = [0] * len(activities)
self.total_float = [0] * len(activities)
self.free_float = [0] * len(activities)
self.critical_path = []

def calculate_early_start(self):
for i in range(len(self.activities)):
if not self.dependencies[i]:
self.early_start[i] = 0
else:
self.early_start[i] = max([self.early_finish[j] for j in self.dependencies[i]])

def calculate_early_finish(self):
for i in range(len(self.activities)):
self.early_finish[i] = self.early_start[i] + self.durations[i]

def calculate_late_finish(self):
self.late_finish[-1] = self.early_finish[-1]
for i in range(len(self.activities) - 2, -1, -1):
self.late_finish[i] = min([self.late_start[j] for j in self.dependencies[i]]) - self.durations[i]

def calculate_late_start(self):
for i in range(len(self.activities)):
self.late_start[i] = self.late_finish[i] - self.durations[i]

def calculate_total_float(self):
for i in range(len(self.activities)):
self.total_float[i] = self.late_finish[i] - self.early_finish[i]

def calculate_free_float(self):
for i in range(len(self.activities)):
successors = [j for j in range(len(self.activities)) if i in self.dependencies[j]]
self.free_float[i] = min([self.early_start[j] - self.early_finish[i] for j in successors]) - self.durations[i]

def calculate_critical_path(self):
self.critical_path = [self.activities[i] for i in range(len(self.activities)) if self.total_float[i] == 0]

# 创建项目对象
activities = ['A', 'B', 'C', 'D', 'E', 'F', 'G']
durations = [3, 2, 4, 5, 6, 2, 3]
dependencies = [[], [0], [0], [1], [2, 3], [4], [5]]
project = Project(activities, durations, dependencies)

# 计算关键路径
project.calculate_early_start()
project.calculate_early_finish()
project.calculate_late_finish()
project.calculate_late_start()
project.calculate_total_float()
project.calculate_free_float()
project.calculate_critical_path()

# 输出关键路径
print("Critical Path:", project.critical_path)
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这个例子中，我们创建了一个Project类，包含了活动列表、持续时间和依赖关系。然后，我们使用该类的方法计算每个活动的最早开始时间、最晚开始时间等数据，并计算关键路径。最后，我们输出关键路径。