Java permutations of offsets

Question

Had a question regarding generating a list of 10-digit phone numbers on a PhonePad, given a set of possible moves and a starting number.

The PhonePad :
1 2 3
4 5 6
7 8 9
* 0 #

Possible moves :
The same number of moves a Queen in chess can make (so north, south, east, west, north-east, north-west, south-east, south-west... n-spaces per each orientation)

Starting number : 5

So far I have implemented the PhonePad as a 2-dimensional char array, implemented the possible moves a Queen can make in a HashMap (using offsets of x and y), and I can make the Queen move one square using one of the possible moves.

My next step is to figure out an algorithm that would give me all 10-digit permutations (phone numbers), using the possible moves in my HasMap. Repetition of a number is allowed. * and # are not allowed in the list of phone numbers returned.

I would imagine starting out with
- 5555555555, 5555555551, 5555555552... and so on up to 0,
- 5555555515, 5555555155, 5555551555.. 5155555555.. and with the numbers 2 upto 0
- 5555555151, 5555551515, 5555515155.. 5151555555.. and with numbers 2 upto 0
... and so on for a two digit combination

Any suggestions on a systematic approach generating 10-digit combinations? Even a pseudocode algorithm is appreciated! Let me know if further clarification is required.

Thanks in advance! :)

Answer 1

In more detail, the simplest approach would be a recursive method, roughly like:

• It accepts a prefix string initially empty, a current digit (initially '5'), and a number of digits to generate (initially 10).
• If the number of digits is 1, it will simply output the prefix concatenated with the current digit.
• If the number of digits is greater than 1, then it will make a list of all possible next digits and call itself recursively with (prefix + (current digit), next digit, (number of digits)-1 ) as the arguments.

Other approaches, and refinements to this one, are possible of course. The "output" action could be writing to a file, adding to a field in the current class or object, or adding to a local variable collection (List or Set) that will be returned as a result. In that last case, the (ndigits>1) logic would have to combine results from multiple recursive calls to get a single return value.