Python生成器实现八皇后算法详解

本示例展示了如何使用Python的生成器迭代机制来解决经典的八皇后问题。内容包含完整的代码实现与结果分析，供读者参考学习。

问题描述：在一个8x8的国际象棋棋盘上放置8个皇后，要求它们彼此之间不能相互攻击。即任意两个皇后不能处于同一行、同一列或同一条对角线上，必须找到所有满足这一约束条件的布局状态。

# -*- coding: utf-8 -*-
#python 2.7.13
__metaclass__ = type
def confict(state, nextX):
  nextY = len(state)
  for i in range(nextY):
    if abs(state[i] - nextX) in (0, nextY - i):
      return True
  return False
def queens(num=8, state=()):
  for pos in range(num):
    if not confict(state, pos):
      if len(state) == num -1:
        yield (pos,)
      else:
        for result in queens(num, state + (pos,)):
          yield (pos,) + result
print list(queens()) #打印输出

程序运行后输出的具体布局结果如下：

[(0, 4, 7, 5, 2, 6, 1, 3), (0, 5, 7, 2, 6, 3, 1, 4), (0, 6, 3, 5, 7, 1, 4, 2), (0, 6, 4, 7, 1, 3, 5, 2), (1, 3, 5, 7, 2, 0, 6, 4), (1, 4, 6, 0, 2, 7, 5, 3), (1, 4, 6, 3, 0, 7, 5, 2), (1, 5, 0, 6, 3, 7, 2, 4), (1, 5, 7, 2, 0, 3, 6, 4), (1, 6, 2, 5, 7, 4, 0, 3), (1, 6, 4, 7, 0, 3, 5, 2), (1, 7, 5, 0, 2, 4, 6, 3), (2, 0, 6, 4, 7, 1, 3, 5), (2, 4, 1, 7, 0, 6, 3, 5), (2, 4, 1, 7, 5, 3, 6, 0), (2, 4, 6, 0, 3, 1, 7, 5), (2, 4, 7, 3, 0, 6, 1, 5), (2, 5, 1, 4, 7, 0, 6, 3), (2, 5, 1, 6, 0, 3, 7, 4), (2, 5, 1, 6, 4, 0, 7, 3), (2, 5, 3, 0, 7, 4, 6, 1), (2, 5, 3, 1, 7, 4, 6, 0), (2, 5, 7, 0, 3, 6, 4, 1), (2, 5, 7, 0, 4, 6, 1, 3), (2, 5, 7, 1, 3, 0, 6, 4), (2, 6, 1, 7, 4, 0, 3, 5), (2, 6, 1, 7, 5, 3, 0, 4), (2, 7, 3, 6, 0, 5, 1, 4), (3, 0, 4, 7, 1, 6, 2, 5), (3, 0, 4, 7, 5, 2, 6, 1), (3, 1, 4, 7, 5, 0, 2, 6), (3, 1, 6, 2, 5, 7, 0, 4), (3, 1, 6, 2, 5, 7, 4, 0), (3, 1, 6, 4, 0, 7, 5, 2), (3, 1, 7, 4, 6, 0, 2, 5), (3, 1, 7, 5, 0, 2, 4, 6), (3, 5, 0, 4, 1, 7, 2, 6), (3, 5, 7, 1, 6, 0, 2, 4), (3, 5, 7, 2, 0, 6, 4, 1), (3, 6, 0, 7, 4, 1, 5, 2), (3, 6, 2, 7, 1, 4, 0, 5), (3, 6, 4, 1, 5, 0, 2, 7), (3, 6, 4, 2, 0, 5, 7, 1), (3, 7, 0, 2, 5, 1, 6, 4), (3, 7, 0, 4, 6, 1, 5, 2), (3, 7, 4, 2, 0, 6, 1, 5), (4, 0, 3, 5, 7, 1, 6, 2), (4, 0, 7, 3, 1, 6, 2, 5), (4, 0, 7, 5, 2, 6, 1, 3), (4, 1, 3, 5, 7, 2, 0, 6), (4, 1, 3, 6, 2, 7, 5, 0), (4, 1, 5, 0, 6, 3, 7, 2), (4, 1, 7, 0, 3, 6, 2, 5), (4, 2, 0, 5, 7, 1, 3, 6), (4, 2, 0, 6, 1, 7, 5, 3), (4, 2, 7, 3, 6, 0, 5, 1), (4, 6, 0, 2, 7, 5, 3, 1), (4, 6, 0, 3, 1, 7, 5, 2), (4, 6, 1, 3, 7, 0, 2, 5), (4, 6, 1, 5, 2, 0, 3, 7), (4, 6, 1, 5, 2, 0, 7, 3), (4, 6, 3, 0, 2, 7, 5, 1), (4, 7, 3, 0, 2, 5, 1, 6), (4, 7, 3, 0, 6, 1, 5, 2), (5, 0, 4, 1, 7, 2, 6, 3), (5, 1, 6, 0, 2, 4, 7, 3), (5, 1, 6, 0, 3, 7, 4, 2), (5, 2, 0, 6, 4, 7, 1, 3), (5, 2, 0, 7, 3, 1, 6, 4), (5, 2, 0, 7, 4, 1, 3, 6), (5, 2, 4, 6, 0, 3, 1, 7), (5, 2, 4, 7, 0, 3, 1, 6), (5, 2, 6, 1, 3, 7, 0, 4), (5, 2, 6, 1, 7, 4, 0, 3), (5, 2, 6, 3, 0, 7, 1, 4), (5, 3, 0, 4, 7, 1, 6, 2), (5, 3, 1, 7, 4, 6, 0, 2), (5, 3, 6, 0, 2, 4, 1, 7), (5, 3, 6, 0, 7, 1, 4, 2), (5, 7, 1, 3, 0, 6, 4, 2), (6, 0, 2, 7, 5, 3, 1, 4), (6, 1, 3, 0, 7, 4, 2, 5), (6, 1, 5, 2, 0, 3, 7, 4), (6, 2, 0, 5, 7, 4, 1, 3), (6, 2, 7, 1, 4, 0, 5, 3), (6, 3, 1, 4, 7, 0, 2, 5), (6, 3, 1, 7, 5, 0, 2, 4), (6, 4, 2, 0, 5, 7, 1, 3), (7, 1, 3, 0, 6, 4, 2, 5), (7, 1, 4, 2, 0, 6, 3, 5), (7, 2, 0, 5, 1, 4, 6, 3), (7, 3, 0, 2, 5, 1, 6, 4)]

程序最终输出的合法布局总数为：

print len(list(queens()))# 输出：92

如需进一步了解Python编程技巧，可参考本站相关专题：《Python数学运算技巧总结》、《Python数据结构与算法教程》、《Python函数使用技巧总结》、《Python字符串操作技巧汇总》、《Python入门与进阶经典教程》及《Python文件与目录操作技巧汇总》。

希望上述关于Python程序设计的解析能对您有所帮助。