N-Queens

## 代码

### 回溯法

``````class Solution(object):
def solveNQueens(self, n):
"""
:type n: int
:rtype: List[List[str]]
"""
self.n = n
result = []
columns = [-1 for i in range(n)]  # [-1, -1, -1, -1]
self.solve(columns, 0, result)
return result

# 绘出完整棋盘
def make_string_list(self, columns):
sol = []  # 一个完整的棋盘
row = ['.' for i in range(self.n)]  # ['.', '.', '.', '.']
for c in columns:
new_row = row[:]
new_row[c] = 'Q'
sol.append(''.join(new_row))  # 将row转为new_row, 将Q加入，然后转为字符串
return sol

# 判断是否符合要求
def is_valid(self, columns, row, col):
# print columns, 'hang', row, 'lie', col
for r in range(row):
c = columns[r]
# print c, col
if c == col:  # 在同一列，放弃
return False
if abs(c - col) == row - r:  # 对角线，放弃
return False
return True

def solve(self, columns, row, result):
if row == self.n:  # 所有列处理完毕
# print 'columns:', columns # [1, 3, 0, 2], [2, 0, 3, 1]
result.append(self.make_string_list(columns))
else:
for col in range(self.n):  # 依次遍历列,每个数字就代表每列皇后放在了第几行
if self.is_valid(columns, row, col):
columns[row] = col
self.solve(columns, row + 1, result)``````

N-Queens II

## 代码

``````class Solution(object):
def totalNQueens(self, n):
"""
:type n: int
:rtype: int
"""
self.n = n
self.result = 0
columns = [-1 for i in range(n)]  # [-1, -1, -1, -1]
self.solve(columns, 0, self.result)
return self.result

def is_valid(self, columns, row, col):
# print columns, 'hang', row, 'lie', col
for r in range(row):
c = columns[r]
# print c, col
if c == col:  # 在同一列，放弃
return False
if abs(c - col) == row - r:  # 对角线，放弃
return False
return True

def solve(self, columns, row, result):
if row == self.n:  # 所有列处理完毕
# print 'columns:', columns # [1, 3, 0, 2], [2, 0, 3, 1]
self.result += 1
else:
for col in range(self.n):  # 依次遍历列,每个数字就代表每列皇后放在了第几行
if self.is_valid(columns, row, col):
columns[row] = col
self.solve(columns, row + 1, result)``````

## 总结

https://github.com/zhsj/nqueen/blob/master/N%E7%9A%87%E5%90%8E%E9%97%AE%E9%A2%98.md