Created
August 17, 2018 19:36
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8 queens problem in python
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def n_queens(N, rows = None, arrangements = None): | |
if rows is None: | |
rows = N | |
if arrangements is None: | |
arrangements = [] | |
if rows == 0: | |
return arrangements | |
if rows == N: | |
arrangements = [[]] | |
new_arrangements = [] | |
for col in range(N): | |
cell = N - rows, col | |
# if `arrangements` is empty, then this list comprehension is also empty. | |
# that's a problem for starting out the list of possible arrangements. | |
# We therefore do a hack in L12 in order to populate the first row of | |
# the board | |
new_arrangements += [[cell] + arrangement for arrangement in arrangements | |
if no_conflict(cell, arrangement)] | |
return n_queens(N, rows - 1, new_arrangements) | |
def no_conflict(cell, arrangement): | |
for position in arrangement: | |
if position[0] == cell[0] or position[1] == cell[1]: | |
return False | |
if abs(position[0] - cell[0]) == abs(position[1] - cell[1]): | |
return False | |
return True | |
if __name__ == '__main__': | |
print(n_queens(0)) | |
print(n_queens(1)) | |
print(n_queens(2)) | |
print(n_queens(3)) | |
print(n_queens(4)) | |
print(len(n_queens(8))) | |
for i in range(10): | |
assert(all(len(arrangement) == i for arrangement in n_queens(i))) | |
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