N-Queen

51. N-Queens

Input: 4
Output: [
 [".Q..",  // Solution 1
  "...Q",
  "Q...",
  "..Q."],

 ["..Q.",  // Solution 2
  "Q...",
  "...Q",
  ".Q.."]
]
Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above.

52. N-Queens II

Input: 4
Output: 2
Explanation: There are two distinct solutions to the 4-queens puzzle as shown below.
[
 [".Q..",  // Solution 1
  "...Q",
  "Q...",
  "..Q."],

 ["..Q.",  // Solution 2
  "Q...",
  "...Q",
  ".Q.."]
]

class Solution:
    def totalNQueens(self, n: int) -> int:
        self.result=[]
        self.pie=set();self.na=set();self.cols=set()
        self._dfs(n,0,[])
        return len(self.result)
    
    def _dfs(self,n,row,c):
        if n<1:return []
        if row>=n:
            self.result.append(c)
            return
        for col in range(n):
            if col in self.cols or col-row in self.pie or col+row in self.na:
                continue
            self.cols.add(col)
            self.pie.add(col-row)
            self.na.add(col+row)
            
            self._dfs(n,row+1,c)
            
            self.cols.remove(col)
            self.pie.remove(col-row)
            self.na.remove(col+row)
        

DFS

class Solution:
    def totalNQueens(self, n: int) -> int:
        if n < 1:return []
        self.count = 0
        self._dfs(n,0,0,0,0)
        return self.count
    
    def _dfs(self,n,row,col,pie,na):
        if row>=n:
            self.count +=1
            return
        bits = (~(pie|col|na)&(1<<n)-1)
        while bits:
            p = bits & (-bits)
            self._dfs(n,row+1,col|p,(pie|p)<<1,(na|p)>>1)
            bits = bits & (bits-1)


row=0,col=0,pie=0,na=0
bits= 15
p= 1
row=1,col=1,pie=2,na=0
bits= 12
p= 4
row=2,col=5,pie=12,na=2
bits= 0
p= 8
row=2,col=9,pie=20,na=4
bits= 2
p= 2
row=3,col=11,pie=44,na=3
bits= 0
p= 2
row=1,col=2,pie=4,na=1
bits= 8
p= 8
row=2,col=10,pie=24,na=4
bits= 1
p= 1
row=3,col=11,pie=50,na=2
bits= 4
p= 4
p= 4
row=1,col=4,pie=8,na=2
bits= 1
p= 1
row=2,col=5,pie=18,na=1
bits= 8
p= 8
row=3,col=13,pie=52,na=4
bits= 2
p= 2
p= 8
row=1,col=8,pie=16,na=4
bits= 3
p= 1
row=2,col=9,pie=34,na=2
bits= 4
p= 4
row=3,col=13,pie=76,na=3
bits= 0
p= 2
row=2,col=10,pie=36,na=3
bits= 0

二进制法