问题
I am attempting to make a Bejeweled cascade simulator with bit boards. So far, I have been able to detect and remove the matches, but now I need to have the jewels fall down. My state is represented by a list of bit boards, one for each type of jewel. I have a mask of all the jewels that are removed.
Is it possible to use some bitwise magic to do this?
Example of two initial bit boards (let's just assume that there are only two types of jewels and that it's a 4x4 board instead of 8x8). The first bit is the bottom left, the fourth bit is top left, and the last bit is top right.
0 0 1 1 1 1 0 0
1 0 0 0 0 1 1 1
1 1 1 1 0 0 0 0
0 0 1 0 1 1 0 1
After removing matches:
0 0 1 1 1 1 0 0
1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 1 0 1 1 0 1
The mask used is:
0 0 0 0
0 1 1 1
1 1 1 1
0 0 0 0
And after gravity it should look like:
0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0
1 0 1 1 0 1 0 0
0 0 1 0 1 1 0 1
This is implemented with integers, and the steps would look like:
[43814, 21721] # Initial state
[35076, 4249], 26210 # State after matches have been removed, mask used to remove matches
[8962, 4149] # State after gravity has been applied
回答1:
To fall the bits you need to move your mask one row up with bitshift. Select bits from row above using the mask and copy that selected bits one row down using bit shift and oring. Simple algorithm would loop mask up to top and doing row by row movement down. But optimization could be extending the mask with bit shifts and oring with self and then moving all above bits down with single operation.
Good source for bit board operatinos is chess wiki: https://chessprogramming.wikispaces.com/General+Setwise+Operations
回答2:
Let's call the left jewel board, A; the right, B; and the physical representation of the board, AB.
After the removals, we have:
0 0 1 1 1 1 0 0 1111
AB = A | B = 1 0 0 0 or 0 0 0 0 = 1000
0 0 0 0 0 0 0 0 0000
0 0 1 0 1 1 0 1 1111
Algorithm:
For each row (r, a temporary variable) above the lowest row with removals:
For each jewel type:
starting with the lowest row where removals occurred (AB_row)
While r is not zero
make a temporary copy of AB_row (AB_row_copy)
new row for jewel_type := (row | AB_row) ^ same_row_for_other_jewel_types
r := r & AB_row_copy
ascend to next row of AB
Example:
Update the first row above the lowest row with removals:
# AB_row is the lowest row with removals from the bitboard that combines all
# jewel types; r_A is a copy from the A bitboard of the first row above AB_row
r_A = 1 0 0 0, AB_row = 0 0 0 0
# make a copy of AB_row
AB_row_copy = 0 0 0 0
# calculate the new row for jewel type A
# new row for jewel_type := (row | AB_row) ^ same_row_for_other_jewel_types
new row for A = (1 0 0 0 | 0 0 0 0) ^ 0 0 0 0 = 1 0 0 0
# update the fallen bits from r_A
# r := r & AB_row_copy
r_A = 1 0 0 0 & 0 0 0 0 = 0 0 0 0
# r_B at this row is zero, nothing to do.
r_B = 0 0 0 0
Update the second row above the lowest row with removals:
# row for A has the same process same as above
r_A = 0 0 1 1, AB_row = 1 0 0 0 // AB_row is the lowest row with removals
AB_row_copy = 1 0 0 0
new row for A = (0 0 1 1 | 1 0 0 0) ^ 0 0 0 0 = 1 0 1 1
r_A = 0 0 1 1 & 1 0 0 0 = 0 0 0 0
# AB_row is the lowest row with removals from the bitboard that combines all
# jewel types; r_B is a copy from the B bitboard of the second row above AB_row
r_B = 1 1 0 0, AB_row = 1 0 1 1
# make a copy of AB_row
AB_row_copy = 1 0 1 1
# calculate the new row for jewel type B
# new row for jewel_type := (row | AB_row) ^ same_row_for_other_jewel_types
new row for B = (1 1 0 0 | 1 0 1 1) ^ 1 0 1 1 = 0 1 0 0
# update the fallen bits from r_B
# r := r & AB_row_copy
r_B = 1 1 0 0 & 1 0 1 1 = 1 0 0 0
# since there are still set bits remaining in r_B after removing the fallen
# bit, we continue with r_B, proceeding to the next row up.
# AB_row now is the next row up from the lowest row with removals, again from
# the bitboard combining all jewel types; r_B is the same variable, now with
# one set bit less (one "fallen" bit)
r_B = 1 0 0 0, AB_row = 0 0 0 0
# make a copy of AB_row
AB_row_copy = 0 0 0 0
# calculate the new row for jewel type B
# new row for jewel_type := (row | AB_row) ^ same_row_for_other_jewel_types
new row for B = (1 0 0 0 | 0 0 0 0) ^ 0 0 0 0 = 1 0 0 0
# update the fallen bits from r_B
r_B = 1 0 0 0 & 0 0 0 0 = 0 0 0 0
#r_B is now zero so the while loop is terminated
来源：https://stackoverflow.com/questions/25524678/bejeweled-bit-board-applying-gravity