java - Find all combinations of a given set of numbers

Question

say I have a set of numbers '0', '1', '2', ..., '9'. I want to find all numbers that contain exactly one of each of the numbers in my set.

The problem is: Before I start my program, I do not know how many numbers and which numbers my set will include. (For example, the set could include the numbers '1', '3' and '14'.)

I searched the internet, and stumbled upon the term 'dynamic programming' which apparently is something to use to solve problems like mine, but I did not understand the examples.

Can somebody give me a hint on how to solve this problem (possibly with dynamic programming)?

EDIT: When the set includes numbers like '14' the different numbers of the set would of course have to be separated by some means, e.g. when the set includes the numbers '1', '3', and '14', combinations could be something like 1-3-14 or 3-14-1 (= individual numbers separated by a '-'-character).

EDIT 2: One problem that seems to be somewhat similar is described here: one of the solutions uses dynamic programming.

Answer 1

To me, it looks like you are looking for all permutations of a given set of elements.

If you use C++ there is a standard function next_permutation() that does exactly what you are looking for. You start with the sorted array and then call next_permutation repeatedly.

The example is here: http://www.cplusplus.com/reference/algorithm/next_permutation/