Queen can go straight, cross walk, go sideways.
Backtracking:
Mean backtracking is in a position to lay down after the queen, the findings do not comply with the rules, and then put the Queen to take up the re-release, it can be understood as undo.
In solving queens problem, we need to know is that a relationship between Western chess the main diagonal (hill_diagonals) and minor diagonal (dale_diagonals) of:
Main diagonal: column number + row number = constant
Minor diagonal: row number - column number = constant
class Solution:
def solveNQueens(self, n: int):
def could_place(row, col):
return not (cols[col] + hill_diagonals[row - col] + dale_diagonals[row + col])
def place_queen(row, col):
queens.add((row, col))
cols[col] = 1
hill_diagonals[row - col] = 1
dale_diagonals[row + col] = 1
def remove_queen(row, col):
queens.remove((row, col))
cols[col] = 0
hill_diagonals[row - col] = 0
dale_diagonals[row + col] = 0
def add_solution():
solution = []
temp = sorted(queens)
for _, col in temp:
solution.append('.' * col + 'Q' + '.' * (n - col - 1))
output.append(solution)
def backtrack(row=0):
for col in range(n):
if could_place(row, col):
place_queen(row, col)
if row + 1 == n:
add_solution()
else:
backtrack(row + 1)
remove_queen(row, col)
cols = [0] * n
hill_diagonals = [0] * (2 * n - 1)
dale_diagonals = [0] * (2 * n - 1)
queens = set()
output = []
backtrack()
return output
n = 4
s = Solution().solveNQueens(n)
for i in s:
print(i)
'''output:
['.Q..', '...Q', 'Q...', '..Q.']
['..Q.', 'Q...', '...Q', '.Q..']
'''
