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Eight queens puzzle
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| --[[ | |
| List all solutions that eight queens on the chess board can't attach each other | |
| example output: | |
| x - - - - - - - | |
| - - - - x - - - | |
| - - - - - - - x | |
| - - - - - x - - | |
| - - x - - - - - | |
| - - - - - - x - | |
| - x - - - - - - | |
| - - - x - - - - | |
| ]]-- | |
| -- size of the chess board | |
| N = 8 | |
| function isPlaceOk(a, row, col) | |
| for i = 1, row - 1 do | |
| if a[i] == col or -- check any queen in the same column | |
| row - i == col - a[i] or --[[ | |
| check any queen in the diagonal (top-left -> bottom-right) | |
| we use the slope value: k1 = (y2-y1) / (x2 - x1) where k1 = 1 to test the diagonal | |
| the other direction is k2 = -k1 | |
| ]]-- | |
| row - i == -1 * (col - a[i]) then -- check any queen in the diagonal (top-right -> bottom-left) | |
| return false | |
| end | |
| end | |
| return true | |
| end | |
| function draw(a) | |
| for row = 1, N do | |
| for col = 1, N do | |
| io.write(a[row] == col and 'x' or '-', ' ') | |
| end | |
| io.write('\n') | |
| end | |
| io.write('\n') | |
| end | |
| --[[ | |
| for each row, test each column and its following row (apply the same to the following row) | |
| until it completes all rows. | |
| ]]-- | |
| function addQueen(a, row) | |
| if (row > N) then | |
| draw(a) -- draw the solution when it is complete. | |
| else | |
| for col = 1, N do | |
| if isPlaceOk(a, row, col) then | |
| a[row] = col | |
| addQueen(a, row + 1) | |
| end | |
| end | |
| end | |
| end | |
| addQueen({}, 1) |
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