如何使用树结构对对象进行分组（使用java）

Question

Here's what I'm trying to do:

I'm working on a program and part of what it is supposed to do is to take a large group of people and divide them into a number of groups (given a particular number of participants/groups). However, each person has to travel through each group exactly once (the order doesn't matter) and I want to minimize the number of people who travel together through the different groups.

So far I've been able to create a tree structure, which has a root branching off into a node for each group, which each branch off into nodes for all the other groups (except the parent group), which each branch into nodes for the remaining groups (except the parent, or the parent's parent, etc).

This can be visualized below (given 5 groups -- A,B,C,D,E):

Level 1:    A         B         C           D          E  
Level 2: B C D E   A C D E   A B D E     A B C E    A B C D  
Level 3 (for node E only) :                     BCD ACD ABD ABC  
etc. (with n levels for n groups)

Each level represents one grouping of all the participants and at each level every participant must be in a group.

In my program each person is currently represented as an integer, stored in an ArrayList. The whole ArrayList starts at the root, then is divided (randomly) into even groups at each node (in the example above, 5 groups at the first level, 4 at the second, etc) until the end of the tree (when every participant has gone through each group once). I'm currently implementing this recursively.

What I am having trouble figuring out is how to make sure the number of participants in each group at each level are equivalent (or off by one). This is easy when the number of participants is equal to the total number of nodes at the last level (or some multiple thereof), but get more tricky when that is not the case (and at each node the participants do not divide evenly into the number of children nodes).

I'm not looking for specific code to solve this problem, just ideas of how I could ensure evenly sized groups at each level (especially a solution that would work with a wide range of inputed number of participants and groups).

Thanks in advance and let me know if I'm unclear at all (as I found it rather hard to describe my problem)!

Answer 1

I thought your description was quite good. If I understand correctly, this could apply to a workshop or something where there are a number of group activities at different stations, and everyone needs to do every station (but ideally with a different mix of people).

I think you might be over complicating your architecture with a tree. Why not start by dividing the people by the number of groups to get the appropriate number of people per group (randomly decide who starts in what group), then just have each group maintain state about who has been there, then for each 'move', randomly select from the remaining people? You'd always have the right number per group, and you wouldn't have any overlap, and randomness would ensure that people don't just move from group to group together.

If your people didn't divide evenly by the number of groups, you could always just have one group that maintains a different number, or apply some additional logic to move the odd number of people to a random group on each move