hello-algo/codes/python/chapter_backtracking/n_queens.py

63 lines
1.9 KiB
Python
Raw Normal View History

"""
File: n_queens.py
Created Time: 2023-04-26
Author: Krahets (krahets@163.com)
"""
def backtrack(
row: int,
n: int,
state: list[list[str]],
res: list[list[list[str]]],
cols: list[bool],
diags1: list[bool],
diags2: list[bool],
):
"""回溯算法N 皇后"""
# 当放置完所有行时,记录解
if row == n:
res.append([list(row) for row in state])
return
# 遍历所有列
for col in range(n):
# 计算该格子对应的主对角线和副对角线
diag1 = row - col + n - 1
diag2 = row + col
# 剪枝:不允许该格子所在列、主对角线、副对角线上存在皇后
2023-06-21 02:56:28 +08:00
if not cols[col] and not diags1[diag1] and not diags2[diag2]:
# 尝试:将皇后放置在该格子
state[row][col] = "Q"
cols[col] = diags1[diag1] = diags2[diag2] = True
# 放置下一行
backtrack(row + 1, n, state, res, cols, diags1, diags2)
# 回退:将该格子恢复为空位
state[row][col] = "#"
cols[col] = diags1[diag1] = diags2[diag2] = False
def n_queens(n: int) -> list[list[list[str]]]:
"""求解 N 皇后"""
# 初始化 n*n 大小的棋盘,其中 'Q' 代表皇后,'#' 代表空位
state = [["#" for _ in range(n)] for _ in range(n)]
cols = [False] * n # 记录列是否有皇后
diags1 = [False] * (2 * n - 1) # 记录主对角线上是否有皇后
diags2 = [False] * (2 * n - 1) # 记录副对角线上是否有皇后
res = []
backtrack(0, n, state, res, cols, diags1, diags2)
return res
"""Driver Code"""
if __name__ == "__main__":
n = 4
res = n_queens(n)
print(f"输入棋盘长宽为 {n}")
print(f"皇后放置方案共有 {len(res)}")
for state in res:
print("--------------------")
for row in state:
print(row)