Surely the data model is helpful, not only in keeping data integrity intact by disallowing invalid state. But also to help you think about your data, and discover simplifications and subtle rules to improve your model.
I attacked the old 8-queens problem years ago as part of a contest in Byte Magazine. All the solutions published modelled the board as an 8X8 array with a 1 or zero to indicate the presence of a queen. They all ran slow and suffered from invalid game states confusing the algorithms.
My solution was to observe that only 1 queen could be in each column (all solutions require queens to not be able to capture one another, and they can capture vertically). So I represented the board by an array of 8 values, the height of the queen in the column represented by indexing the array.
Further, since only one queen can be in each row, the values were the numbers 1-8.
My solution then, was to seed the array with the value 1, 2, 3, 4, 5, 6, 7, 8. Then test if array[i]-array[j] == (i-j) or (j-i), which would mean a diagonal capture.
Simply permuting the values, searched a subset of board states that had to contain all possible solutions. And the permutation tree could be truncated as soon as for any (i,j) the test failed.
Anyway, the program was tiny and finished in negligible time. A pity I didn't enter the contest!
I attacked the old 8-queens problem years ago as part of a contest in Byte Magazine. All the solutions published modelled the board as an 8X8 array with a 1 or zero to indicate the presence of a queen. They all ran slow and suffered from invalid game states confusing the algorithms.
My solution was to observe that only 1 queen could be in each column (all solutions require queens to not be able to capture one another, and they can capture vertically). So I represented the board by an array of 8 values, the height of the queen in the column represented by indexing the array.
Further, since only one queen can be in each row, the values were the numbers 1-8.
My solution then, was to seed the array with the value 1, 2, 3, 4, 5, 6, 7, 8. Then test if array[i]-array[j] == (i-j) or (j-i), which would mean a diagonal capture.
Simply permuting the values, searched a subset of board states that had to contain all possible solutions. And the permutation tree could be truncated as soon as for any (i,j) the test failed.
Anyway, the program was tiny and finished in negligible time. A pity I didn't enter the contest!