## BJP3 Exercise 12.20: subsets

Language/Type: Java recursion recursive backtracking
Author: Marty Stepp (on 2013/04/01)

Write a method `subsets` that uses recursive backtracking to find every possible sub-list of a given list. A sub-list of a list L contains 0 or more of L's elements. Your method should accept a `List` of strings as its parameter and print every sub-list that could be created from elements of that list, one per line. For example, suppose a variable called `list` stores the following elements:

```[Janet, Robert, Morgan, Char]
```

The call of `subsets(list);` would produce output such as the following:

```[Janet, Robert, Morgan, Char]
[Janet, Robert, Morgan]
[Janet, Robert, Char]
[Janet, Robert]
[Janet, Morgan, Char]
[Janet, Morgan]
[Janet, Char]
[Janet]
[Robert, Morgan, Char]
[Robert, Morgan]
[Robert, Char]
[Robert]
[Morgan, Char]
[Morgan]
[Char]
[]
```

The order in which you show the sub-lists does not matter, and the order of the elements of each sub-list also does not matter. The key thing is that your method should produce the correct overall set of sub-lists as its output. Notice that the empty list is considered one of these sub-lists. You may assume that the list passed to your method is not `null` and that the list contains no duplicates. Do not use any loops in solving this problem.

Hint: This problem is somewhat similar to the permutations problem. Consider each element and try to generate all sub-lists that do include it, as well as all sub-lists that do not include it.

It can be hard to see a pattern from looking at the lines of output. But notice that the first 8 of 16 total lines of output constitute all the sets that include Janet, and the last 8 lines are the sets that do not have her as a member. Within either of those groups of 8 lines, the first 4 of them are all the sets that include Robert, and the last 4 lines are the ones that do not include him. Within a clump of 4, the first 2 are the ones including Morgan, and the last 2 are the ones that do not include Morgan. And so on. Once again, you do not have to match this exact order, but looking at it can help with figuring out the patterns and the recursion.