The n-queens puzzle is the problem of placing n queens on an n x n chessboard such that no two queens attack each other.
Given an integer n, return all distinct solutions to the n-queens puzzle. You may return the answer in any order.
Each solution contains a distinct board configuration of the n-queens' placement, where 'Q' and '.' both indicate a queen and an empty space, respectively.
def solveNQueens(self, n: int) -> List[List[str]]:
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 = []
for _, col in sorted(queens):
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