排课表软件的设计是一项复杂的任务，需要考虑多个因素，包括教师的时间安排、教室的可用性、课程的需求等。为了实现高效合理的排课表，可以采用科学的方法和先进的算法来解决。
首先，我们来看一个简单的贪心算法应用：
def greedy_schedule(courses, rooms, teachers):
schedule = {}
for course in courses:
available_rooms = [room for room in rooms if room['capacity'] >= course['students']]
available_teachers = [teacher for teacher in teachers if teacher['availability'][course['time']] == 'free']
if available_rooms and available_teachers:
room = min(available_rooms, key=lambda x: x['cost'])
teacher = min(available_teachers, key=lambda x: x['cost'])
schedule[course['name']] = {'room': room['name'], 'teacher': teacher['name']}
room['availability'][course['time']] = 'occupied'
teacher['availability'][course['time']] = 'occupied'
return schedule
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该算法按照房间成本和教师成本最小化的原则进行分配，虽然简单但可能不是最优解。
为了优化解决方案，我们可以使用模拟退火算法：
import random
import math
def simulated_annealing(courses, rooms, teachers, initial_temp=1000, cooling_rate=0.003):
current_solution = greedy_schedule(courses, rooms, teachers)
best_solution = current_solution
current_energy = evaluate_energy(current_solution)
best_energy = current_energy
temperature = initial_temp
while temperature > 1:
new_solution = generate_neighbor(current_solution, courses, rooms, teachers)
new_energy = evaluate_energy(new_solution)
delta_energy = new_energy - current_energy
if delta_energy < 0 or random.uniform(0, 1) < math.exp(-delta_energy / temperature):
current_solution = new_solution
current_energy = new_energy
if new_energy < best_energy:
best_solution = new_solution
best_energy = new_energy
temperature *= (1 - cooling_rate)
return best_solution
def evaluate_energy(solution):
# 实现评估函数
pass
def generate_neighbor(solution, courses, rooms, teachers):
# 实现生成邻居解的函数
pass
]]>
以上代码展示了如何利用贪心算法和模拟退火算法来优化排课表。实际应用中，还需要根据具体情况调整参数和优化细节。
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