Question

I have a matrix like:

0 | 1 | 2 | 3
-------------
7 | 6 | 5 | 4
-------------
8 | 9 | A | B
-------------
F | E | D | C

in code:

var matrix = new char[][]
{ 
    new char[] { '0', '1', '2', '3' },
    new char[] { '7', '6', '5', '4' },
    new char[] { '8', '9', 'A', 'B' },
    new char[] { 'F', 'E', 'D', 'C' }
};

I need to get all possible combination of this matrix with 5 chars each, but every char must be the next immediate neighbor, for instance, 0,5 and 4,8 are invalid but 0,6 and 3,4 are valid.

This matrix will not be static as is in the sample, it is generated with the hex numbers in any position every time.

Thanks!

Answer 1

Just for fun – Delphi code. ‘shl’ is left shift (<<), strings are one-based. Borders are added around the matrix as sentinels to simplify checks.

Some additional comments: I use 6×6 matrix – 4×4 core with digits, and one-cell width outer border. 36 bits of Int64 are used as sentinels. Bit value of 1 denotes border or visited cell. Procedure StartTravel initiates path finding from some starting cell of core. Path finding goes like DFS (deep-first search), but interrupts when path length becomes 5.

const
  Directions: array[0..3] of Integer = (-1, -6, 1, 6);

var
  Digits: string;
  Mask: Int64;
  i, j: Integer;

  procedure Travel(AFrom: Integer; Visited: Int64; Path: string);
  var
    i, Dir: Integer;
    NewMask: Int64;
  begin
    if Length(Path) = 5 then
      PrintOut(Path)
    else
      for i := 0 to 3 do begin
        Dir := Directions[i];
        NewMask := 1 shl (AFrom + Dir);
        if (Visited and NewMask) = 0 then
          Travel(AFrom + Dir, Visited or NewMask, Path + Digits[AFrom + Dir + 1]);
      end;
  end;

  procedure Init;
  var
    i: Integer;
  begin
    Digits := '-------0123--7654--89AB--FEDC-------';
    Mask := 0;
    for i := 1 to Length(Digits) do
      if Digits[i] = '-' then
        Mask := Mask or (1 shl (i - 1));
  end;

  procedure StartTravel(Row, Col: Integer);
  var
    APos: Integer;
  begin
    APos := Row * 6 + Col + 7;
    Travel(APos, Mask or (1 shl APos), Digits[APos + 1]);
  end;

begin
  Init;
  for i := 0 to 3 do
    for j := 0 to 3 do
      StartTravel(i, j);

432 combinations:
01234
01256
01254
0125A
01678
01652
01654
0165A
01698
0169A
0169E
07612
07652
....
CBADE
CB456
CB452
CB45A
CB432