Question

Example: I have the numbers form 1 to 10. All possible combinations, where in every combination every variable in included once without any repetition, are… well… 3628800 (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3628800).

In my case, the computer has to check ALL of the combinations, instead of picking random ones. Afterwords, the system will store the needed combinations in an array. But I can’t think of an algorithm and I can’t find one in the internet (probably because I’m not searching the right way).

What algorithm can I use for mixing a number of variables, where all of the combinations have no repeating variables?

Answer 1

What you are looking for is called permutations.

Wikipedia lists a few different ways:

Slow Way to get all permutations

A naive slow way involves creating a function which given an integer i, returns the ith permutation, and then just call the function N! times.

Take a look at the answer to this question here.

In-Order Way

The Lexicographic method is described as:

The following algorithm generates the next permutation lexicographically after a given permutation. It changes the given permutation in-place.

1. Find the largest index k such that a[k] < a[k + 1]. If no such index exists, the permutation is the last permutation.

2. Find the largest index l such that a[k] < a[l]. Since k + 1 is such an index, l is well defined and satisfies k < l.

3. Swap a[k] with a[l].

4. Reverse the sequence from a[k + 1] up to and including the final element a[n].

You should sort your sequence first to get all permutations in order.

Minimal-Swapping

May be faster, but I didn’t see any code examples on my quick look.

Consider the description of the Steinhaus-Johnson-Trotter algorithm.