八皇后II

用一个数组state记录已经选择的每一行皇后所在的位置，DFS

 count = 0
 N = 8
 state = [0]*N

 def dfs(row):
     global count
     for col in range(N):
         for i in range(row):
             if col == state[i] or abs(i-row) == abs(col-state[i]):
                 break
         else:
             if row == N-1:
                 count += 1
             else:
                 state[row] = col
                 dfs(row+1)

 dfs(0)
 print(count)

在整数shu,pie,na中用每个bit位记录已经被占用的 竖，撇，捺

 count, N, pie, na, shu = 0, 8, 0, 0, 0

 def dfs(row):
     global count, pie, na, shu
     for col in range(N):
         j, i = row+col, N-1-row+col
         #验证此位置是否可行
         if not ((shu >> col) | (pie >> j) | (na >> i)) & 1:
             if row == N-1:
                 count += 1
             else:
                 #记录此位置
                 shu ^= (1 << col); pie ^= (1 << j); na ^= (1 << i)
                 dfs(row+1)
                 #清除此位置信息
                 shu ^= (1 << col); pie ^= (1 << j); na ^= (1 << i)

 if __name__ == '__main__':
     dfs(0)
     print(count)