Question

I’m having trouble solving this problem:

Create a function that given a character set C, can generate the Nth combination OR return the series of combination given a starting position (Ns) and ending position (Ne) and the maximum length of the combination (Mx).

A concrete example:

Let C = [A,B,C]

We know that different combinations would look like the following assuming Mx = 3 (the combination would be different for different lengths):

1. AAA
2. AAB
3. AAC
4. ABA
5. ABB
6. ABC
N. ... Etc

If we was to pass the following parameters :

C = [A,B,C] Mx = 3 Ns = 3 Ne = 3

we would expect the following result:

AAC

If we was to pass the following parameters :

C = [A,B,C] Mx = 3 Ns = 4 Ne = 6

we would expect the following result:

4. ABA
5. ABB
6. ABC

For the solution, the programming language is not relevant. However C# would be preferred. Also most important would be an explanation of how its solved.

I look forward to the amazing Guru’s of Stack Overflow…

Answer 1

Given an index N (0-based) into the sequence of combinations of n symbols, you can get the i‘th symbol by calculating N / nⁱ % n (using integer division and remainder)

For example:

C = {A, B, C} (giving n = 3)
N = 6
i = 0 => 6 / 3^0 % 3 = 0 (symbol 0 = A)
i = 1 => 6 / 3^1 % 3 = 2 (symbol 2 = C)
i = 2 => 6 / 3^2 % 3 = 0 (symbol 0 = A)
Resulting sequence: ACA

The sequence is treated as a base-n number, and the individual digits are calculated.