Hi
Tarek,
Nice puzzle.
If I convert your visual puzzle in to numeric values then it looks like as follows:
- Code: Select all
030000000000024000000000000000000
-99-99000-12-99000000040008000000
031000000-99-99000-99-99000-99-99
-99-99000000000000-99-99000000000
000000-99000-99-58018000000-10-99
081000-99044-99000-99000-99000-01
000000-99000-99000000000-17+12-99
-99+10000000000000-99-99000000000
000000-37-99-99000-99+23000-99-99
-99-99000+10-99070000000000-79004
000000000000000000000062000000052
Whereas:
1) each three digits represent a cell;
2) 000 in a cell means empty cell;
3) -99 in a cell means a thief in a cell;
4) +/-02 to +/-98 in a cell means to jump forward/backward towards aero head cell;
5) -1 means starting cell position; and
5) 81 means finishing cell position.
If a brute-force backtrack solver be written, then it will create another single dimension array of 81 elements that will represent move wise cell position as follows:
- Code: Select all
65, -1, -1,109, -1, -1, -1, 19, -1,
-1, -1, -1, -1, -1, -1, -1, 74, 50,
-1, -1, -1, -1, -1, 4, -1, -1, -1,
-1, -1, 0, 22, -1, -1, -1, -1, -1,
90, -1, -1, 18, -1, -1, -1, 58, -1,
-1, -1, -1, -1, -1, -1,120, -1, -1,
-1, -1, -1, 49, -1, -1, -1, -1, -1,
-1, -1, -1, -1, -1, -1,104, -1, -1,
-1, -1, -1, -1, -1, -1,108, -1, 55
Whereas:
1) first number represent starting zeroth move cell;
2) last number represent finishing end move cell; and
3) -1 represent to be searched cell position for specific move number.
a pseudocode should be, check from starting move cell position to each 8 positions for next move as follows:
1) Top-Right by subtracting 10 from cell position;
2) Right by adding 2 to cell position;
3) Bottom-Right by adding 12 to cell position;
4) Bottom by adding 11 to cell position;
5) Bottom-Left by adding 10 to cell position;
6) Left by subtracting 1 from cell position;
7) Top-Left by subtracting 12 from cell position; and
8) Top by subtracting 11 from cell position.
Note:
1) after adding above value:
a) if cell position exceed from [INT (cell / 9) + 10] value then subtract 11; and
b) if cell position still exceed 120 value then further subtract 120.
2) after subtracting above value:
a) if cell position decreased from [INT (cell / 9)] value then add 11;
b) if cell position still decreased from 0 value then further add 120.
1to9only wrote:so (79)r10c10 - (80)r8c10 - (81)r6c1 in one likely exit route.
Similarly, some more possible move cell positions are as follows:
Move / Cell: 1 / 87, 2 / 85, 3 / 107, 59 / 71, 60 / 93, 61 / 115.
R. Jamil
but once the concept is visualized you will not worry too much about the edges. This was tested to be human solvable and should have one single solution.
