Python回溯算法-解决八皇后问题

In [4]: n = 8

In [5]: x =[]

In [6]: X = [] #所有解

In [8]: def conflict(k): #冲突检测
   ...:     global x
   ...:     for i in range(k):
   ...:         if x[i]==x[k] or abs(i-k) ==abs(x[i]-x[k]):
   ...:             return True
   ...:     return False
   ...:

In [9]: def queens(k):
   ...:     global n,x,X
   ...:     if k>=n:
   ...:         X.append(x[:])#加入一个解
   ...:     else:
   ...:         for i in range(n):
   ...:             x.append(i)
   ...:             if not conflict(k):
   ...:                 queens(k+1)#成功则继续搜索下一列
   ...:             x.pop()#失败回溯，换一列
   ...:
   ...:

In [10]: def show(x):
    ...:     global n
    ...:     for i in range(n):
    ...:         print('. '*(x[i])+'X '+'. '*(n-x[i]-1))

In [11]: print(X[-1])
[7, 3, 0, 2, 5, 1, 6, 4]

In [12]: show(X[-1])
. . . . . . . X
. . . X . . . .
X . . . . . . .
. . X . . . . .
. . . . . X . .
. X . . . . . .
. . . . . . X .
. . . . X . . .