First of all, ensure the fairness of the schedule. Give a plan that every team gets the same rest in the middle of every two games and the rest time is as long as possible.
So it can be extended to 5 teams and n classes. When the training involved this problem, the instructor gave us a plan. How many breaks at most? Round ((n-3)/2)。 For this problem, each team can have a rest at most under the condition of ensuring fairness. For this problem, n=5, the optimal solution of the odd model established by our school can be solved like this.
In the table, 1, 2, 3, 4, 5 ... are the numbers of each team.
Note: n=5, to build a vertical table, n is other odd numbers and so on. Even numbers and odd numbers have different arrangement rules. See the arrow in the table for specific rules.
Optimal arrangement method: pick out PK: 12, 34, 52, 14, 35, 24, 13, 54, 23, 15 according to the S-shaped path in the figure. Solved it.
Attachment: n=7 model diagram, look at the numbers on each blue dotted line, isn't it interesting?
My personal solution: a, b, c, d, e? Team five. Write five groups in pairs in the table below.
Process: (Because there are many arrangements, I will make one at random. You can use my knowledge of tables and permutations to figure out how many permutations there are, so I won't count them here. )
? 1. Choose a group of people from the table as the first round. For example, if you choose a BD, you can cross it out yourself.
? 2. Of course, the second round of BD cannot appear, so the PK of the row where B is located and the column where D is located will not be considered. Of course, AB and DE can't be chosen, because B and D have to rest. Pick one of the rest. I choose AC.
? 3. After the third round, I choose BE. 4. Germany. 5. CD-ROM. 6.AB .7. Chief Executive. 8. AD 200. 9. BC 200. 10.AE.
Final schedule BD? AC？ De? CD？ AB？ CE？ AD？ BC? AE .
? 4. Note: it is arbitrary to find according to the method, and there may be cases where the last remaining group has the same letter as the penultimate group you are looking for, of course not! Don't worry, just put the last group in the right place.
? The advantage of my method evaluation is that it is easy to use, and there is no mistake in finding one painting. Disadvantages n If you do dozens, you can only smile at it. The first solution can be extended to n teams, and rules can be found by compiling more tables. And it is the best scheme, so that each team can rest as long as possible.
If you are interested, you can find that modeling topic to study.