python实现n皇后问题回溯法
时间: 2023-07-29 18:09:22 浏览: 46
好的,下面是 Python 实现 n 皇后问题的回溯法代码:
```python
def solveNQueens(n):
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
```
这里的 `solveNQueens(n)` 函数返回一个列表,列表中的每个元素都是一种符合要求的 n 皇后问题的解法。每个解法是一个二维列表,其中 `'Q'` 表示皇后的位置。