求大神指点…关于怎么找最好的课程表安排

好像很复杂… 去他限制条件呢？比如每个人最多上几门课最少上几门？ 平均一个人只能上5门课啊才。

你这题目都没描述清楚啊，一会又说教室要空余位置少，一会又要学生选满5门。排课到底有多少限制？给原题或者按标准格式写。不然这做项目是完全没法下手的。这是描述能力的问题，不是算法性质难易问题。

原题在这：
CodeJam() 2016 Junior Challenge Problem Background
One of the prevalent problems in student life is the coordination of student schedules. Many schools remedy this problem by operating on a ‘first’ to register, first to enter basis. As fair as this method is, it often results in student programs being delayed due to inability to get into classes. It also results in long periods of downtime of the registration website due to the frenzy of students trying to register for courses on time. A new solution is required. The Challenge HCI College has 80 students to enroll in the fall. 10 classes will be offered; each class can receive a maximum of 20 students. For all students, each class is equal in terms of credits and prerequisites. The same class is given twice a week by the same teacher and a student can pick only one of the 2 scheduled choices. Each student should be taking 5 classes this semester. The class schedule looks like this (complete schedule of classes in the INPUT - in the following):
Class ID Class Name Class Time 101 Mathematics Monday: 8:30am-10:30am, Tuesday: 8:00am-10:00am 102 Physics Tuesday: 8:30am-10:30am, Wednesday: 8:00am-10:00am 103 Biology Wednesday: 8:30am-10:30am, Friday: 8:00am-10:00am ... ... ...
This semester the schedule needs to be put together efficiently and quickly. HCI College is looking to a group of intelligent students from another school (your team) to design a system that schedules each student based on a single input parameters - each student’s availability for each working day of the week (Monday: 8:30am - 5:30pm, Tuesday: 8:00am-2:30pm, Thursday: 8:30am-5:30pm, Friday: 9:30am-1:30pm). Note:
• Notice that some students are not available on some days (i.e. Saturday, Sunday and some week days – Availability: 0h) There are several schedules that can be generated. Your program should find the BEST scheduling of all students. (Hint: This is an optimization problem). An ideal solution should fill all classes to the maximum class size of 20 students/class.
Givens You will be given the following:
JSON file that contains the Classes data (classes.json ) and student data input for Availability (studentsWithAvailability.json )
Example of how your solutions should be formatted in the JSON output file ( codejam-challenge-example.json ) Note:
The environment where you write and run your program is yours to pick, but you need to give us a way to access it in order to evaluate your solution (provide us a READ-ME.txt file). Deliverables To be considered for judging the implemented solution must meet the base requirements. Winners will be chosen from solutions, eligible for judging, based on success of code and demonstration of creativity when meeting the themed requirement. Although this problem is one part computational and one part interface design, the interface design portion carries more weight in choosing winners.
Base Requirement:
o Optimal solution output file (result of your program execution) in JSON file format titled <codejam-challenge.json>. Structure of this file should be same as the structure in <codejam-challenge-example.json>.
Themed Requirement o An interactive output interface.
Example: Web application/page. The output should vary depending on the user. If I am a professor teaching Mathematics, I should see something very different from if I am a student taking Mathematics. Provide a “read-me” file detailing how to access and use this interface.

回复 King_Shultz :你们老师要求你们安排学生课程时间，并没有要求你根据课程表和学生时间相互妥协进行改进式建议从而达到最优解，那么这题从描述解剖不难。然后我们观察数据发现玄机：80个学生要安排至少5门课，也就是400个周学时单位，而一门课一周2次，共10门，一门20人，刚好400个周学时单位。也就是说这是一个苛刻的匹配问题，更像是解密码问题。
而这类题要考虑的限制条件很多，学生选课的实际范围，课程重叠特性，而这些条件没有实际情况去定性是非常难确定复杂度的，也可能是我学艺不精，数学、图论知识欠缺，没有得出一个具体的步骤。所以我认为这类问题为np问题，我没有能力把它转化为p问题。但是如果这是个项目，可以根据时间表和课程表的实际特性去尝试转化为其他问题。
进化算法，蒙特卡洛算法都是傻瓜式算法的改进式算法，对np问题的解决暴力而有效。