Algorithm to generate spanning set

Question

Given this input: [1,2,3,4]

I\'d like to generate the set of spanning sets:

[1] [2] [3] [4]
[1] [2] [3,4]
[1] [2,3] [4]
[1] [3] [2,4]
[1,2] [3] [4]
[1,3]         


        

Answer 1

What about this? I haven't tested it yet, but I'll try it later…

I think this technique is called Dynamic Programming:

1. Take the first element [1]
   What can you create with it? Only [1]

2. Take the second one [2]
   Now you've got two possibilities: [1,2] and [1] [2]

3. Take the third one [3]
   With the first of number 2 [1,2] one can create [1,2,3] and [1,2] [3]
   With the second of number 2 [1] [2] one can create [1,3] [2] and [1] [2,3] and [1] [2] [3]

I hope it is clear enough what I tried to show. (If not, drop a comment!)