c - Generating all distinct partitions of a number

Question

I am trying to write a C code to generate all possible partitions (into 2 or more parts) with distinct elements of a given number. The sum of all the numbers of a given partition should be equal to the given number. For example, for input n = 6, all possible partitions having 2 or more elements with distinct elements are:

• 1, 5
• 1, 2, 3
• 2, 4

I think a recursive approach should work, but I am unable to take care of the added constraint of distinct elements. A pseudo code or a sample code in C/C++/Java would be greatly appreciated.

Thanks!

Edit: If it makes things easier, I can ignore the restriction of the partitions having atleast 2 elements. This will allow the number itself to be added to the list (eg, 6 itself will be a trivial but valid partition).

Answer 1

What you're trying to do doesn't make a lot of sense to me but here's how I would approach it.

First, I'd create a loop that iterates i from 1 to n - 1. In the first loop, you could add the partition 1, i. Then I'd go recursive using the value in i to get all the sub-partitions that can also be added to 1.

And then continue to 2, and so on.